main_math.ind

\begin{theindex}

  \item $(G,\cdot )$-space, \hyperpage{211}
  \item $E$-valued random variable, \hyperpage{347}
  \item $F$-distribution with degrees of freedom $d_1$ and $d_2$, 
		\hyperpage{252}
  \item $F$-invariant, \hyperpage{339}
  \item $F$-linearly independent, \hyperpage{170}
  \item $K$-field morphism, \hyperpage{165}
  \item $N$-th partial sum of $Sf$, \hyperpage{83}
  \item $N$-th partial sum of the series, \hyperpage{76}, 
		\hyperpage{105}
  \item $P$ and $Q$ are both true, \hyperpage{8}
  \item $P$ and $Q$ have the same truth-value, \hyperpage{8}
  \item $Q$ is true whenever $P$ is true, \hyperpage{8}
  \item $T$-periodic, \hyperpage{81}
  \item $T_0$ space, \hyperpage{212}
  \item $T_1$ space, \hyperpage{212}
  \item $T_2$ space, \hyperpage{212}
  \item $T_3$ space, \hyperpage{212}
  \item $T_4$ space, \hyperpage{212}
  \item $T_{2\frac  {1}{2}}$ space, \hyperpage{212}
  \item $\alpha $-limit point, \hyperpage{131}
  \item $\alpha $-limit set, \hyperpage{131}
  \item $\ensuremath  {\mathbb  {C}}$-differentiable, \hyperpage{109}
  \item $\ensuremath  {\mathbb  {R}}$-differentiable, \hyperpage{110}
  \item $\mathcal  {C}^0$-$\varepsilon $-close, \hyperpage{336}
  \item $\mathcal  {C}^1$-$\varepsilon $-close, \hyperpage{336}
  \item $\mathcal  {C}^{k,\theta }$-Hölder continuous, \hyperpage{351}
  \item $\omega $-limit point, \hyperpage{131}
  \item $\omega $-limit set, \hyperpage{131}
  \item $\sigma $-additivity, \hyperpage{173}, \hyperpage{291}
  \item $\sigma $-algebra, \hyperpage{172}, \hyperpage{291}, 
		\hyperpage{346}
  \item $\sigma $-algebra generated, \hyperpage{172}
  \item $\sigma $-algebra generated by $X$, \hyperpage{347}
  \item $\sigma $-algebra generated by $\boldsymbol  {\mathrm  {X}}$, 
		\hyperpage{321}
  \item $\sigma $-algebra generated by $\mathcal  {F}$, \hyperpage{346}
  \item $\sigma $-algebra of all Lebesgue measurable sets in $\ensuremath  {\mathbb  {R}}^n$, 
		\hyperpage{175}
  \item $\sigma $-finite, \hyperpage{346}
  \item $\tau $ methods, \hyperpage{379}
  \item $d$-dimensional standard Brownian motion, \hyperpage{332}
  \item $i$-th pivot, \hyperpage{14}
  \item $k$-linear map, \hyperpage{155}
  \item $k$-th hitting time, \hyperpage{322}
  \item $m$-dimensional projective subvariety, \hyperpage{67}
  \item $m$-th dyadic cube, \hyperpage{291}
  \item $n$-dimensional projective space, \hyperpage{67}
  \item $n$-dimensional volume, \hyperpage{58, 59}
  \item $n$-periodic, \hyperpage{90}
  \item $n$-step distribution, \hyperpage{319}
  \item $n$-step transition matrix, \hyperpage{319}
  \item $n$-step transition probabilities, \hyperpage{319}
  \item $n$-th Fourier coefficient, \hyperpage{83}
  \item $n$-th Lyapunov constant, \hyperpage{226}
  \item $n$-th ball, \hyperpage{210}
  \item $n$-th cyclotomic polynomial, \hyperpage{164}
  \item $n$-th derivative of $f$ at the point $a\in \ensuremath  {\mathbb  {R}}$, 
		\hyperpage{31}
  \item $n$-th primitive root of unity, \hyperpage{170}
  \item $n$-th root of unity, \hyperpage{170}
  \item $n-1$-th sphere, \hyperpage{210}
  \item $p$-group, \hyperpage{41}
  \item $p$-value, \hyperpage{199}
  \item $s$-stage Runge-Kutta methods, \hyperpage{260}
  \item $t$-test, \hyperpage{201}
  \item $x$-simple, \hyperpage{59}
  \item $xy$-simple, \hyperpage{59}
  \item $xz$-simple, \hyperpage{59}
  \item $y$-simple, \hyperpage{59}
  \item $yz$-simple, \hyperpage{59}
  \item (left) $G$-set, \hyperpage{40}
  \item (left) group action, \hyperpage{40}
  \item 2-forms, \hyperpage{62}
  \item 3-forms, \hyperpage{62}

  \indexspace

  \item A priori estimate, \hyperpage{362}
  \item A-stable, \hyperpage{261}
  \item a.e., \hyperpage{293}
  \item Abel's summation formula, \hyperpage{77}, \hyperpage{106}
  \item Abel's test, \hyperpage{77, 78}, \hyperpage{80}, 
		\hyperpage{107}
  \item Abel's theorem, \hyperpage{79}, \hyperpage{108}
  \item Abel-Ruffini theorem, \hyperpage{171}
  \item abelian, \hyperpage{37}, \hyperpage{170}
  \item absolute condition numbers, \hyperpage{89}
  \item absolute error, \hyperpage{89}
  \item Absolute geometry, \hyperpage{64}
  \item absolute value, \hyperpage{25}
  \item absolutely continuous, \hyperpage{178}, \hyperpage{180}, 
		\hyperpage{347}
  \item absolutely convergent, \hyperpage{77}, \hyperpage{106}, 
		\hyperpage{117}, \hyperpage{300}
  \item absolutely stable, \hyperpage{261}
  \item absoulte variation, \hyperpage{382}
  \item Abstract Fredholm alternative, \hyperpage{358}
  \item Acceptance-rejection method, \hyperpage{370}
  \item acceptation region, \hyperpage{199}
  \item ACCP, \hyperpage{46}
  \item accumulation point, \hyperpage{26}, \hyperpage{54}
  \item action, \hyperpage{211}, \hyperpage{278}
  \item Adams method, \hyperpage{262}
  \item Adams-Bashforth method, \hyperpage{262}
  \item Adams-Moulton method, \hyperpage{262}
  \item adapted, \hyperpage{348}, \hyperpage{381}
  \item adherence, \hyperpage{54}
  \item adherent point, \hyperpage{54}, \hyperpage{207}
  \item adjacency matrix, \hyperpage{50}
  \item adjacent, \hyperpage{49}
  \item adjoint, \hyperpage{24}
  \item adjoint operator, \hyperpage{312}
  \item adjugate matrix, \hyperpage{15}
  \item adjusted coefficient of determination, \hyperpage{252}
  \item affine combination, \hyperpage{69}
  \item affine coordinates, \hyperpage{70}
  \item Affine Gra\ss mann formulas, \hyperpage{70}
  \item affine plane, \hyperpage{66}
  \item affine space, \hyperpage{69}
  \item affine subvariety, \hyperpage{70}
  \item affinely equivalent, \hyperpage{378}
  \item affinely independents, \hyperpage{69}
  \item affinity, \hyperpage{70}
  \item AIC, \hyperpage{257}
  \item Aitken's $\Delta ^2$ method, \hyperpage{91}
  \item Akaike information criterion, \hyperpage{257}
  \item Algebra, \hyperpage{172}
  \item algebra, \hyperpage{172}
  \item algebraic, \hyperpage{164, 165}
  \item algebraic closure, \hyperpage{170}
  \item algebraic curve, \hyperpage{135}
  \item algebraic multiplicity, \hyperpage{20}
  \item algebraic value, \hyperpage{153}
  \item algebraically closed, \hyperpage{170}
  \item algebraically closed field, \hyperpage{21}
  \item almost everywhere, \hyperpage{293}
  \item Almost orthogonality lemma, \hyperpage{306}
  \item alpha limit, \hyperpage{340}
  \item alternating, \hyperpage{155}
  \item alternating group, \hyperpage{42}
  \item alternating series, \hyperpage{77}
  \item alternative hypothesis, \hyperpage{199}
  \item Ambrosetti-Rabinowitz theorem, \hyperpage{368}
  \item amplification factor, \hyperpage{270}
  \item amplification polynomial, \hyperpage{273}
  \item Ampère's law, \hyperpage{278}
  \item Ampère-Maxwell circuital law, \hyperpage{278}
  \item an asymptotically normal estimator, \hyperpage{194}
  \item analytic, \hyperpage{79}, \hyperpage{113}
  \item analytic at $a$, \hyperpage{32}
  \item Analytic continuation theorem, \hyperpage{114}
  \item angle, \hyperpage{24}, \hyperpage{63}
  \item angle-preserving, \hyperpage{149}
  \item anisotropic, \hyperpage{74}
  \item annihilator, \hyperpage{19}
  \item antithetic method, \hyperpage{371}
  \item aperiodic, \hyperpage{320}
  \item Aplication, \hyperpage{367}
  \item approximation of identity, \hyperpage{79}, \hyperpage{241}
  \item approximations of the identity, \hyperpage{235}
  \item arc length, \hyperpage{60}
  \item arc length parameter, \hyperpage{60}
  \item arc-length function, \hyperpage{142}
  \item arc-length parameter, \hyperpage{141}
  \item Archimedean, \hyperpage{64}
  \item Archimedean property, \hyperpage{25}
  \item argument, \hyperpage{104}
  \item Argument principle, \hyperpage{118}
  \item Arnold family, \hyperpage{338}
  \item Artin's lemma, \hyperpage{169}
  \item Arzelà-Ascoli theorem, \hyperpage{121}, \hyperpage{125}, 
		\hyperpage{304}
  \item ASA criterion, \hyperpage{64}
  \item ascending chain condition on principal ideals, \hyperpage{46}
  \item associated, \hyperpage{45}
  \item associated multivalued function, \hyperpage{110}
  \item Associative property, \hyperpage{76}
  \item Asymptotic behaviour of the LRT, \hyperpage{200}
  \item asymptotic direction, \hyperpage{150}
  \item asymptotic efficient estimator, \hyperpage{196}
  \item asymptotic error constant, \hyperpage{91}
  \item asymptotic line, \hyperpage{150}
  \item asymptotically stabilizable, \hyperpage{354}
  \item asymptotically stable, \hyperpage{131}, \hyperpage{353}
  \item asymptotically unbiased estimator, \hyperpage{194}
  \item atlas, \hyperpage{216}
  \item attracting, \hyperpage{131}
  \item attracting parabolic sector, \hyperpage{133}
  \item attractive, \hyperpage{353}
  \item attractor fixed point, \hyperpage{91}
  \item auto-adjoint, \hyperpage{24}
  \item autonomous, \hyperpage{122}
  \item average, \hyperpage{289}
  \item average response, \hyperpage{253}
  \item Axiom of Archimedes, \hyperpage{63}
  \item Axiom of choice, \hyperpage{213}
  \item Axiom of completeness, \hyperpage{63}
  \item Axiom of extensionality, \hyperpage{6}
  \item Axiom of Parallels, \hyperpage{64}
  \item axiomatic projective space, \hyperpage{66}
  \item axis of perspectivity, \hyperpage{68}

  \indexspace

  \item backward Euler method, \hyperpage{258}
  \item Backward-time central-space, \hyperpage{268}, \hyperpage{274}
  \item Baire's theorem, \hyperpage{309}
  \item balance equation, \hyperpage{329}
  \item ball, \hyperpage{205}
  \item Banach fixed-point theorem, \hyperpage{125}
  \item Banach space, \hyperpage{300}
  \item Banach-Alaoglu theorem, \hyperpage{349}
  \item Banach-Steinhaus theorem, \hyperpage{309}
  \item bandlimited, \hyperpage{239}
  \item Barrow's law, \hyperpage{298}
  \item barycenter, \hyperpage{69}
  \item Basic bootstrap confidence interval, \hyperpage{202}
  \item basic bootstrap confidence interval, \hyperpage{202}
  \item basic feasible solutions, \hyperpage{51}
  \item basin, \hyperpage{131}
  \item basin of attraction, \hyperpage{353}
  \item basis, \hyperpage{16}, \hyperpage{206}
  \item basis functions, \hyperpage{378}
  \item Bautin's theorem, \hyperpage{226}
  \item Bayes estimate, \hyperpage{203}
  \item Bayes' formula, \hyperpage{174}
  \item Bayesian point estimates, \hyperpage{203}
  \item Bendixson's theorem, \hyperpage{137}
  \item Bendixson-Dulac theorem, \hyperpage{137}
  \item Bernoulli differential equation, \hyperpage{123}
  \item Bernoulli distribution, \hyperpage{177}
  \item Bernoulli numbers, \hyperpage{96}
  \item Bernoulli polynomials, \hyperpage{96}
  \item Bessel's inequality, \hyperpage{87}, \hyperpage{313}
  \item Beta distribution, \hyperpage{179}
  \item beta distribution, \hyperpage{179}
  \item beta function, \hyperpage{179}
  \item BFGS method, \hyperpage{264}
  \item Bias, \hyperpage{193}
  \item bias, \hyperpage{193}
  \item Bias on the estimations, \hyperpage{255}
  \item Bias on the predictions, \hyperpage{255}
  \item biased estimator, \hyperpage{193}
  \item bidual space, \hyperpage{307}
  \item bijective, \hyperpage{7}
  \item bilinear, \hyperpage{22}
  \item bilinear form, \hyperpage{22}
  \item Binomial coefficient formulas, \hyperpage{9}
  \item Binomial distribution, \hyperpage{177}
  \item binomial distribution, \hyperpage{177}
  \item Binomial theorem, \hyperpage{119}
  \item binormal vector, \hyperpage{143}
  \item bipartite, \hyperpage{50}
  \item birth and death process, \hyperpage{329}
  \item Bisection method, \hyperpage{90}
  \item Black-Scholes model, \hyperpage{374}
  \item Black-Scholes process, \hyperpage{390}
  \item block matrix, \hyperpage{15}
  \item blow-down, \hyperpage{225}
  \item Blow-up in cartesian coordinates, \hyperpage{226}
  \item Blow-up in generalized polar coordinates, \hyperpage{225}
  \item Blow-up in polar coordinates, \hyperpage{225}
  \item blowing-up, \hyperpage{225}
  \item BLUE, \hyperpage{251}
  \item Bogdanov-Takens bifurcation, \hyperpage{227}
  \item Bolzano's theorem, \hyperpage{28}, \hyperpage{215}
  \item Bolzano-Weierstra\ss \ theorem, \hyperpage{27}, \hyperpage{54}
  \item Bonferroni's method, \hyperpage{252}
  \item Bonnet's theorem, \hyperpage{152}
  \item Boolean ring, \hyperpage{42}
  \item Bootstrap, \hyperpage{366}
  \item bootstrap distribution, \hyperpage{202}
  \item Bootstrap-t confidence interval, \hyperpage{202}
  \item bootstrap-t confidence interval, \hyperpage{202}
  \item Borel $\sigma $-algebra, \hyperpage{172}, \hyperpage{295}
  \item Borel measurable, \hyperpage{181}, \hyperpage{295}
  \item Borel's theorem, \hyperpage{191}
  \item Borsuk-Ulam theorem, \hyperpage{215}
  \item Boundary, \hyperpage{207}
  \item boundary, \hyperpage{54}, \hyperpage{157}, \hyperpage{207}
  \item boundary point, \hyperpage{54}
  \item bounded, \hyperpage{26, 27}, \hyperpage{105}
  \item bounded by compact sets, \hyperpage{121}
  \item bounded from above, \hyperpage{25, 26}
  \item bounded from below, \hyperpage{25, 26}
  \item bounded set, \hyperpage{54}
  \item bounded variation, \hyperpage{343}
  \item box topology, \hyperpage{209}
  \item Box-Cox transformation, \hyperpage{257}
  \item Box-Muller method, \hyperpage{371}
  \item Bramble-Hilbert lemma, \hyperpage{378}
  \item bridge, \hyperpage{50}
  \item Brouwer's fixed-point theorem, \hyperpage{215}
  \item Brower fixed point, \hyperpage{363}
  \item Brownian motion, \hyperpage{330}, \hyperpage{381}
  \item Broyden's method, \hyperpage{263}
  \item Broyden-Fletcher-Goldfarb-Shanno method, \hyperpage{264}
  \item BTCS, \hyperpage{268}
  \item Budan-Fourier theorem, \hyperpage{92}
  \item bump functions, \hyperpage{240}
  \item Butcher tableau, \hyperpage{260}
  \item Bézout's theorem, \hyperpage{10, 11}

  \indexspace

  \item Calculation of integrals, \hyperpage{117}
  \item canonical form of a linear programming to maximize, 
		\hyperpage{51}
  \item canonical form of a linear programming to minimize, 
		\hyperpage{51}
  \item Cantor set, \hyperpage{209}, \hyperpage{342}
  \item Cantor's theorem, \hyperpage{9}
  \item Cantor-Bernstein theorem, \hyperpage{9}
  \item Carathéodory, \hyperpage{365}
  \item Cardano-Vieta's formulas, \hyperpage{114}
  \item cardinal, \hyperpage{6}
  \item Cartesian equations, \hyperpage{70}
  \item Cartesian form, \hyperpage{104}
  \item Cartesian geometry, \hyperpage{64}
  \item Cartesian product, \hyperpage{7}
  \item Casorati-Weierstra\ss \ theorem, \hyperpage{118}
  \item Cauchy, \hyperpage{105}
  \item Cauchy condition in $p$-th mean, \hyperpage{189}
  \item Cauchy condition in probability, \hyperpage{187}
  \item Cauchy distribution, \hyperpage{179}
  \item Cauchy in $p$-th mean, \hyperpage{189}
  \item Cauchy in probability, \hyperpage{187}
  \item Cauchy momentum equation, \hyperpage{277}
  \item Cauchy principal value, \hyperpage{241}
  \item Cauchy problem, \hyperpage{122}
  \item Cauchy product, \hyperpage{106}
  \item Cauchy sequence, \hyperpage{27}, \hyperpage{54}
  \item Cauchy's functional equation, \hyperpage{256}
  \item Cauchy's inequality, \hyperpage{114}
  \item Cauchy's integral theorem, \hyperpage{116}
  \item Cauchy's mean value theorem, \hyperpage{30}
  \item Cauchy's test, \hyperpage{76}, \hyperpage{78}, \hyperpage{80}, 
		\hyperpage{107}
  \item Cauchy's theorem, \hyperpage{41}
  \item Cauchy-Hadamard theorem, \hyperpage{107}
  \item Cauchy-Riemann equations, \hyperpage{111}
  \item Cauchy-Riemann theorem, \hyperpage{111}
  \item Cauchy-Schwarz inequality, \hyperpage{24}, \hyperpage{53}, 
		\hyperpage{82}, \hyperpage{185}, \hyperpage{310}
  \item Cavalieri's principle, \hyperpage{59}
  \item Cayley's theorem, \hyperpage{39}
  \item Cayley-Hamilton theorem, \hyperpage{21}
  \item CC, \hyperpage{64}
  \item cdf, \hyperpage{176}
  \item cells, \hyperpage{275}
  \item Center, \hyperpage{120}
  \item center, \hyperpage{41}, \hyperpage{131}, \hyperpage{133}
  \item Center of a group, \hyperpage{41}
  \item Center of mass, \hyperpage{59}
  \item center of mass, \hyperpage{59}
  \item Center of masses, \hyperpage{35}
  \item center of masses, \hyperpage{35}
  \item central manifolds, \hyperpage{223}
  \item centre of perspectivity, \hyperpage{68}
  \item Cesàro summable, \hyperpage{85}
  \item chain, \hyperpage{126}
  \item chain of paths, \hyperpage{115}
  \item Chain rule, \hyperpage{29}, \hyperpage{56}, \hyperpage{109}
  \item Change of basis formula, \hyperpage{18}
  \item change of parameter, \hyperpage{141}
  \item Change of variable theorem, \hyperpage{60}
  \item Change of variables, \hyperpage{159}, \hyperpage{300}
  \item change of variables, \hyperpage{300}
  \item change-of-basis matrix, \hyperpage{18}
  \item Chaos, \hyperpage{230}
  \item chaotic, \hyperpage{230}, \hyperpage{337}
  \item chaotic behavior, \hyperpage{91}
  \item Chapman-Kolmogorov equation, \hyperpage{320}, \hyperpage{326}
  \item characteristic, \hyperpage{162}
  \item characteristic curves, \hyperpage{279}
  \item Characteristic equation, \hyperpage{123}, \hyperpage{222}
  \item characteristic equation, \hyperpage{123}
  \item Characteristic function, \hyperpage{191}
  \item characteristic function, \hyperpage{9}, \hyperpage{191}
  \item characteristic polynomial, \hyperpage{20}, \hyperpage{49}
  \item Chasles relation, \hyperpage{384}
  \item Chebyshev method, \hyperpage{90}
  \item Chebyshev polynomials, \hyperpage{96}
  \item Chebyshev's inequality, \hyperpage{186}, \hyperpage{297}
  \item Chetaev's theorem, \hyperpage{354}
  \item chi-squared distribution with $n$ degrees of freedom, 
		\hyperpage{197}
  \item Chinese remainder theorem, \hyperpage{11}
  \item Christoffel symbols, \hyperpage{151}
  \item circle, \hyperpage{120}, \hyperpage{337}
  \item circulation, \hyperpage{61}, \hyperpage{159}
  \item class, \hyperpage{56}
  \item class $\mathcal  {C}^\infty $ at $a$, \hyperpage{31}
  \item class $\mathcal  {C}^n$ at a point $a\in \ensuremath  {\mathbb  {R}}$, 
		\hyperpage{31}
  \item class $\mathcal  {C}^p$, \hyperpage{31}
  \item class $\mathcal  {KL}$, \hyperpage{353}
  \item class $\mathcal  {K}$, \hyperpage{353}
  \item class $\mathcal  {K}^\infty $, \hyperpage{353}
  \item classical solution, \hyperpage{356}
  \item Classification of affine quadrics, \hyperpage{75}
  \item Classification of compact connected surfaces, \hyperpage{219}
  \item Classification of connected 1-manifolds, \hyperpage{217}
  \item Classification of cyclic groups, \hyperpage{38}
  \item Classification of Euclidean motions, \hyperpage{73}
  \item Classification of isometries, \hyperpage{73}
  \item Classification of projective qua\-drics in $\ensuremath  {\mathbb  {C}}$, 
		\hyperpage{74}
  \item Classification of projective qua\-drics in $\ensuremath  {\mathbb  {F}}_q$, 
		\hyperpage{75}
  \item Classification of projective qua\-drics in $\ensuremath  {\mathbb  {R}}$, 
		\hyperpage{75}
  \item Classification of quadratic forms in $\ensuremath  {\mathbb  {C}}$, 
		\hyperpage{74}
  \item Classification of quadratic forms in $\ensuremath  {\mathbb  {F}}_q$, 
		\hyperpage{74}
  \item Classification of quadratic forms in $\ensuremath  {\mathbb  {R}}$, 
		\hyperpage{74}
  \item clopen, \hyperpage{206}
  \item closed, \hyperpage{49}, \hyperpage{54}, \hyperpage{156}, 
		\hyperpage{206}, \hyperpage{208}
  \item closed ball, \hyperpage{54}
  \item Closed forms, \hyperpage{48}
  \item Closed function, \hyperpage{208}
  \item Closed graph theorem, \hyperpage{309}
  \item Closed interval, \hyperpage{25}
  \item Closed Newton-Cotes Formulas, \hyperpage{95}
  \item closed trail, \hyperpage{49}
  \item Closure, \hyperpage{206}
  \item closure, \hyperpage{206}
  \item Cochran's theorem, \hyperpage{252}
  \item Cocountable topology, \hyperpage{206}
  \item Codazzi-Mainardi equations, \hyperpage{152}
  \item codimension, \hyperpage{223}
  \item coefficient of determination, \hyperpage{252}
  \item coefficients, \hyperpage{11}
  \item coercive, \hyperpage{356}, \hyperpage{366}
  \item cofactor, \hyperpage{136}
  \item cofactor matrix, \hyperpage{15}
  \item Cofinite topology, \hyperpage{206}
  \item collineation, \hyperpage{66}
  \item Collocation methods, \hyperpage{379}
  \item collocation points, \hyperpage{379}
  \item column rank, \hyperpage{16}
  \item Combinations with repetition, \hyperpage{10}
  \item Combinations without repetition, \hyperpage{10}
  \item communicate, \hyperpage{320}
  \item commutative, \hyperpage{37}
  \item compact, \hyperpage{54}, \hyperpage{213}
  \item compact operator, \hyperpage{307}
  \item Compact space, \hyperpage{213}
  \item compact subset, \hyperpage{213}
  \item compact support, \hyperpage{79}
  \item compactly embedded, \hyperpage{351}
  \item compactness, \hyperpage{213}
  \item Comparison test, \hyperpage{76}, \hyperpage{80}, 
		\hyperpage{183}
  \item compatibility condition, \hyperpage{273}
  \item compatible, \hyperpage{149}, \hyperpage{158}
  \item compatible with, \hyperpage{97}
  \item complement, \hyperpage{6}
  \item Complementary property, \hyperpage{52}
  \item complementary subspace, \hyperpage{17}
  \item complete, \hyperpage{54}, \hyperpage{300}, \hyperpage{312}
  \item complete graph, \hyperpage{49}
  \item Complete pivoting, \hyperpage{102}
  \item complex conjugate, \hyperpage{24}, \hyperpage{104}
  \item complex cosecant, \hyperpage{109}
  \item complex cosine, \hyperpage{108}
  \item complex cotangent, \hyperpage{109}
  \item complex exponential function, \hyperpage{108}
  \item complex function, \hyperpage{106}
  \item complex hyperbolic cosecant, \hyperpage{109}
  \item complex hyperbolic cosine, \hyperpage{109}
  \item complex hyperbolic cotangent, \hyperpage{109}
  \item complex hyperbolic secant, \hyperpage{109}
  \item complex hyperbolic sine, \hyperpage{109}
  \item complex hyperbolic tangent, \hyperpage{109}
  \item complex natural logarithm, \hyperpage{108}
  \item complex power series, \hyperpage{107}
  \item complex random variable, \hyperpage{191}
  \item complex secant, \hyperpage{109}
  \item complex sine, \hyperpage{108}
  \item complex tangent, \hyperpage{109}
  \item Composite Simpson's rule, \hyperpage{96}
  \item Composite Trapezoidal rule, \hyperpage{95}
  \item composition, \hyperpage{7}
  \item compositum, \hyperpage{165}
  \item Compound probability formula, \hyperpage{174}
  \item computational efficiency, \hyperpage{91}
  \item concave, \hyperpage{30}
  \item Condensation test, \hyperpage{76}
  \item condition number, \hyperpage{99}, \hyperpage{378}
  \item conditional consistency, \hyperpage{269}
  \item conditional expectation, \hyperpage{186}
  \item conditional expectation of $X$ given $\mathcal  {G}$, 
		\hyperpage{347}
  \item conditional expectation of $X$ given $Y$, \hyperpage{348}
  \item conditional law of $X$ given $Y$, \hyperpage{348}
  \item conditional probability, \hyperpage{174}
  \item conditional probability density function, \hyperpage{182}
  \item conditional probability mass function, \hyperpage{182}
  \item conditionally absolutely stable, \hyperpage{261}
  \item conditionally convergent, \hyperpage{269}
  \item cone, \hyperpage{108}
  \item confidence band, \hyperpage{254}
  \item Confidence interval for the average response, \hyperpage{253}
  \item Confidence interval for the predicted value, \hyperpage{254}
  \item confidence intervals, \hyperpage{198}
  \item confidence level, \hyperpage{198}
  \item confidence region, \hyperpage{198}
  \item configuration, \hyperpage{67}
  \item conformal, \hyperpage{119}, \hyperpage{149}
  \item conformal representation, \hyperpage{119}
  \item conforming Galerkin method, \hyperpage{377}
  \item Congruence axioms, \hyperpage{63}
  \item congruence relation, \hyperpage{63}
  \item conic, \hyperpage{73}
  \item conjugacy, \hyperpage{132}
  \item conjugacy equation, \hyperpage{336}
  \item conjugate, \hyperpage{104}, \hyperpage{132}, \hyperpage{202}, 
		\hyperpage{339}
  \item conjugate dynamical systems, \hyperpage{131}
  \item Conjugate gradient method, \hyperpage{264}
  \item conjugate Poisson kernel, \hyperpage{248}
  \item conjugation action, \hyperpage{41}
  \item connected, \hyperpage{50}, \hyperpage{54}, \hyperpage{214}
  \item connected components, \hyperpage{50}, \hyperpage{215}
  \item Connected space, \hyperpage{214}
  \item connected subset, \hyperpage{214}
  \item Connected sum, \hyperpage{217}
  \item connected sum, \hyperpage{217}
  \item Connected sum of surfaces, \hyperpage{217}
  \item Conservation of energy, \hyperpage{282}
  \item conservative, \hyperpage{61}, \hyperpage{328}
  \item consistency condition, \hyperpage{333}
  \item consistent, \hyperpage{259}, \hyperpage{262}, \hyperpage{269}
  \item consistent estimator in $L^2$, \hyperpage{194}
  \item constant coefficients, \hyperpage{122}, \hyperpage{126}
  \item constant term, \hyperpage{11}, \hyperpage{13}
  \item constructible field, \hyperpage{64}
  \item Construction of a non-Paschian geometry, \hyperpage{65}
  \item Construction of a non-SAS geometry, \hyperpage{66}
  \item contact, \hyperpage{144}
  \item contact of order $\geq n$ at $a$, \hyperpage{31}
  \item Continuation method, \hyperpage{362}
  \item Continuity axioms, \hyperpage{63}
  \item Continuity correction, \hyperpage{192}
  \item continuity correction, \hyperpage{192}
  \item Continuity from above, \hyperpage{173}
  \item Continuity from below, \hyperpage{173}
  \item continuous, \hyperpage{28}, \hyperpage{55}, \hyperpage{106}, 
		\hyperpage{130}, \hyperpage{356}
  \item continuous at $x_0$, \hyperpage{28}
  \item Continuous equation, \hyperpage{277}
  \item continuous equation, \hyperpage{277}
  \item continuous Euler scheme, \hyperpage{373}
  \item Continuous function, \hyperpage{208}
  \item continuous local martingale, \hyperpage{383}
  \item Continuous memorylessness property, \hyperpage{178}
  \item Continuous uniform distribution, \hyperpage{178}
  \item continuous uniform distribution, \hyperpage{178}
  \item continuous-time Markov chain, \hyperpage{326}
  \item contractible, \hyperpage{139}
  \item contraction, \hyperpage{55}, \hyperpage{90}
  \item contrast matrix, \hyperpage{201}
  \item control variate, \hyperpage{371}
  \item controllability matrix, \hyperpage{354}
  \item controllable, \hyperpage{354}
  \item converge in mean, \hyperpage{298}
  \item converge in norm $L^p$, \hyperpage{87}
  \item convergent, \hyperpage{26}, \hyperpage{54}, \hyperpage{76}, 
		\hyperpage{79}, \hyperpage{98}, \hyperpage{105, 106}, 
		\hyperpage{117}, \hyperpage{259}
  \item convergent series, \hyperpage{300}
  \item converges, \hyperpage{105}
  \item converges absolutely, \hyperpage{80}
  \item converges almost surely, \hyperpage{188}
  \item converges in distribution, \hyperpage{190}
  \item converges in probability, \hyperpage{187}
  \item converges in the $p$-th mean, \hyperpage{189}
  \item converges pointwise, \hyperpage{77, 78}, \hyperpage{106, 107}
  \item converges strongly, \hyperpage{349}
  \item converges uniformly, \hyperpage{77, 78}, \hyperpage{106, 107}
  \item converges weakly, \hyperpage{349}
  \item converges weakly-*, \hyperpage{349}
  \item convex, \hyperpage{30}, \hyperpage{115}
  \item convex functional, \hyperpage{308}
  \item convex hull, \hyperpage{363}
  \item convolution, \hyperpage{79}, \hyperpage{240}, \hyperpage{244}
  \item Cook's distance, \hyperpage{255}
  \item coordinate chart, \hyperpage{147}, \hyperpage{216}
  \item coordinates, \hyperpage{16}
  \item Coordination theorem, \hyperpage{17}, \hyperpage{68}
  \item coprime, \hyperpage{10, 11}
  \item corrected sample variance, \hyperpage{193}
  \item correlation coefficient, \hyperpage{185}
  \item Correspondence theorem, \hyperpage{40}, \hyperpage{44}
  \item countable, \hyperpage{25}, \hyperpage{213}
  \item Countable subadditivity, \hyperpage{173}
  \item Courant-Friedrichs-Lewy condition, \hyperpage{269}
  \item Covariance, \hyperpage{185}
  \item covariance, \hyperpage{185}, \hyperpage{249}
  \item covariance function, \hyperpage{330}
  \item covariance matrix, \hyperpage{181}, \hyperpage{196}, 
		\hyperpage{249}
  \item covariant derivative, \hyperpage{152}
  \item Cover, \hyperpage{213}
  \item cover, \hyperpage{213}
  \item Cramér-Rao bound, \hyperpage{196}
  \item Crank-Nicolson, \hyperpage{272}
  \item Crank-Nicolson scheme, \hyperpage{272}, \hyperpage{274}
  \item credible interval, \hyperpage{203}
  \item credible region, \hyperpage{203}
  \item critical point, \hyperpage{57}, \hyperpage{131}
  \item critical region, \hyperpage{199}
  \item cross product, \hyperpage{142}
  \item Cross ratio, \hyperpage{69}
  \item cross ratio, \hyperpage{69}, \hyperpage{120}
  \item cubic convergence, \hyperpage{91}
  \item Cubic Hermite spline, \hyperpage{94}
  \item Cubic periodic spline, \hyperpage{94}
  \item cubic polynomial, \hyperpage{162}
  \item cubic splines, \hyperpage{94}
  \item Cumulative distribution function, \hyperpage{176}
  \item cumulative distribution function, \hyperpage{176}
  \item curl, \hyperpage{61}
  \item Curl theorem, \hyperpage{159}
  \item curvature, \hyperpage{61}, \hyperpage{143}
  \item cusp, \hyperpage{224}
  \item cycle, \hyperpage{8}, \hyperpage{49}, \hyperpage{115}
  \item cyclic, \hyperpage{170}
  \item cyclic group, \hyperpage{37}
  \item cyclotomic, \hyperpage{170}
  \item càd, \hyperpage{326}
  \item càdlàg, \hyperpage{176}
  \item Céa's lemma, \hyperpage{377}

  \indexspace

  \item D'Alembert formula, \hyperpage{140}, \hyperpage{281}
  \item D'Alembert theorem, \hyperpage{12}
  \item Dahlquist's theorem, \hyperpage{262}
  \item damping parameter, \hyperpage{263}
  \item Darboux theorem, \hyperpage{138}
  \item Darboux's theorem, \hyperpage{30}
  \item De Moivre's formula, \hyperpage{108}
  \item De Moivre-Laplace theorem, \hyperpage{192}
  \item De Morgan's laws, \hyperpage{6}
  \item decreasing, \hyperpage{28}
  \item Dedekind's lemma, \hyperpage{170}
  \item Dedekind's test, \hyperpage{107}
  \item Degenerated distribution, \hyperpage{177}
  \item degenerated distribution, \hyperpage{177}
  \item degree, \hyperpage{11}, \hyperpage{45}, \hyperpage{135}, 
		\hyperpage{155}, \hyperpage{164}
  \item degree of a vertex, \hyperpage{49}
  \item degree of precision, \hyperpage{95}
  \item degree sequence, \hyperpage{49}
  \item Dehomogenization, \hyperpage{74}
  \item dehomogenization, \hyperpage{70}
  \item Delta method, \hyperpage{196}
  \item Denjoy theorem, \hyperpage{344}
  \item Denjoy-Koksma inequality, \hyperpage{344}
  \item dense, \hyperpage{207}
  \item density, \hyperpage{278}, \hyperpage{347}
  \item density function, \hyperpage{178}
  \item Dependence on $\boldsymbol  {\mathrm  {\lambda }}$, 
		\hyperpage{129}
  \item Dependence on $\boldsymbol  {\mathrm  {x}}_0$, \hyperpage{129}
  \item Dependence on $t_0$, \hyperpage{129}
  \item depressed equation, \hyperpage{162}
  \item derivative of $f$ at $x_0$, \hyperpage{29}
  \item derivative of $f$ at $z_0$, \hyperpage{109}
  \item Desargues configuration, \hyperpage{68}
  \item Desargues' theorem, \hyperpage{68}
  \item Descartes' rule of signs, \hyperpage{24}, \hyperpage{92}
  \item descent direction, \hyperpage{264}
  \item Descent method, \hyperpage{264}
  \item descent method, \hyperpage{264}
  \item design matrix, \hyperpage{250}
  \item Determinant, \hyperpage{14}
  \item determinant, \hyperpage{142}
  \item determination, \hyperpage{110}
  \item determination of the argument of $f$, \hyperpage{104}
  \item determination of the logarithm, \hyperpage{110}
  \item determined and consistent, \hyperpage{14}
  \item developable, \hyperpage{151}
  \item dextrorotation, \hyperpage{145}
  \item DFT, \hyperpage{239}
  \item diagonal, \hyperpage{20}
  \item diagonalizable, \hyperpage{20}
  \item Diagonalization theorem, \hyperpage{20}
  \item diameter, \hyperpage{378}
  \item dicyclic group, \hyperpage{42}
  \item diffeomorphism, \hyperpage{57}
  \item Differentiability criterion, \hyperpage{56}
  \item differentiable, \hyperpage{29}, \hyperpage{55}, \hyperpage{147}, 
		\hyperpage{152}, \hyperpage{154}, \hyperpage{156, 157}
  \item differentiable at $x_0\in (a,b)$, \hyperpage{29}
  \item differentiable manifold, \hyperpage{216}
  \item differential, \hyperpage{55}, \hyperpage{70}, \hyperpage{110}, 
		\hyperpage{148}, \hyperpage{155}, \hyperpage{157}
  \item differential $\ell $-form, \hyperpage{156}
  \item differential $k$-form, \hyperpage{155}
  \item differential 1-form, \hyperpage{62}
  \item differential operator over distributions, \hyperpage{245}
  \item differential system, \hyperpage{122}
  \item differentiation operator, \hyperpage{285}
  \item diffusion, \hyperpage{389}
  \item diffusion coefficient, \hyperpage{278}
  \item Diffusion equation, \hyperpage{278}
  \item diffusion flux, \hyperpage{278}
  \item diffusions, \hyperpage{390}
  \item diffusivity, \hyperpage{278}
  \item digital topology, \hyperpage{206}
  \item dihedral group, \hyperpage{42}
  \item dilatation, \hyperpage{119}
  \item dimension, \hyperpage{16}, \hyperpage{66}, \hyperpage{69}, 
		\hyperpage{193}
  \item Dini's theorem, \hyperpage{85}, \hyperpage{234}
  \item Dirac's $\delta $ distribution, \hyperpage{241}, 
		\hyperpage{285}
  \item direct, \hyperpage{16}
  \item direct product, \hyperpage{245}
  \item Direct sum, \hyperpage{16}
  \item directional derivative, \hyperpage{55}
  \item director subspace, \hyperpage{70}
  \item Dirichlet, \hyperpage{274}
  \item Dirichlet boundary condition, \hyperpage{356}
  \item Dirichlet boundary conditions, \hyperpage{377}
  \item Dirichlet kernel, \hyperpage{84}, \hyperpage{233}
  \item Dirichlet problem, \hyperpage{140}, \hyperpage{288}
  \item Dirichlet problem in the disc, \hyperpage{288}
  \item Dirichlet's principle, \hyperpage{288}
  \item Dirichlet's test, \hyperpage{77, 78}, \hyperpage{80}, 
		\hyperpage{107}
  \item disconnected, \hyperpage{214}
  \item Discontinuity of the first kind, \hyperpage{28}
  \item Discontinuity of the second kind, \hyperpage{28}
  \item discrete, \hyperpage{130}, \hyperpage{176}, \hyperpage{180}
  \item discrete $\sigma $-algebra, \hyperpage{172}
  \item discrete Fourier transform, \hyperpage{239}
  \item discrete laplacian, \hyperpage{274}
  \item discrete map of order $m$, \hyperpage{222}
  \item Discrete maximum principle, \hyperpage{274}
  \item Discrete memorylessness property, \hyperpage{177}
  \item discrete metric, \hyperpage{205}
  \item Discrete minimum principle, \hyperpage{274}
  \item Discrete topology, \hyperpage{206}
  \item Discrete uniform distribution, \hyperpage{177}
  \item discrete uniform distribution, \hyperpage{177}
  \item discretization method, \hyperpage{375}
  \item discriminant, \hyperpage{169}
  \item displacement current, \hyperpage{278}
  \item distance, \hyperpage{53}, \hyperpage{82}, \hyperpage{205}, 
		\hyperpage{300}
  \item distance between two affine subvarieties, \hyperpage{72}
  \item distance between two points, \hyperpage{72}
  \item Distribution, \hyperpage{240}, \hyperpage{285}
  \item distribution, \hyperpage{176}, \hyperpage{180}, \hyperpage{240}, 
		\hyperpage{285}
  \item distribution functions, \hyperpage{176}
  \item distribution of order $N\in \ensuremath  {\mathbb  {N}}\cup \{0\}$, 
		\hyperpage{241}
  \item distributional derivative, \hyperpage{242}, \hyperpage{285}
  \item divergence, \hyperpage{61}
  \item divergence form, \hyperpage{356}
  \item Divergence theorem, \hyperpage{160}
  \item Divergence theorem on $\ensuremath  {\mathbb  {R}}^2$, 
		\hyperpage{62}
  \item Divergence theorem on $\ensuremath  {\mathbb  {R}}^3$, 
		\hyperpage{62}, \hyperpage{160}
  \item divergent, \hyperpage{26}, \hyperpage{76}, \hyperpage{105, 106}
  \item divided difference, \hyperpage{93}
  \item Doléans-Dade exponential, \hyperpage{388}
  \item domain, \hyperpage{115}, \hyperpage{148}
  \item dominant eigenvalue, \hyperpage{100}
  \item dominant eigenvector, \hyperpage{100}
  \item Dominated convergence theorem, \hyperpage{184}, \hyperpage{189}, 
		\hyperpage{297}, \hyperpage{346}
  \item Doob's maximal inequality, \hyperpage{382}
  \item Doob's optional sampling theorem, \hyperpage{382}
  \item Doob's optional sampling theorem for local martingales, 
		\hyperpage{383}
  \item dot product, \hyperpage{53}
  \item double, \hyperpage{90}
  \item Double dual space, \hyperpage{19}
  \item double dual space, \hyperpage{19}
  \item drift, \hyperpage{389}
  \item drift term, \hyperpage{387}
  \item Du Bois-Reymond's test, \hyperpage{107}
  \item Du-Fort-Frankel scheme, \hyperpage{274}
  \item dual basis, \hyperpage{19}
  \item Dual map, \hyperpage{19}
  \item dual map, \hyperpage{19}, \hyperpage{308}
  \item dual program, \hyperpage{51}
  \item dual space, \hyperpage{19}, \hyperpage{307}
  \item Duality principle, \hyperpage{66}
  \item Duhamel principle, \hyperpage{287}
  \item dummy variable, \hyperpage{253}
  \item dyadic partition of order $n$, \hyperpage{183}
  \item dynamical system, \hyperpage{130}

  \indexspace

  \item edges, \hyperpage{160}
  \item efficient estimator, \hyperpage{196}
  \item eigenspace, \hyperpage{20}
  \item eigenvalue, \hyperpage{309}
  \item eigenvector, \hyperpage{20}
  \item eigenvectors, \hyperpage{309}
  \item Eikonal equation, \hyperpage{278}
  \item Eisenstein's criterion, \hyperpage{45}, \hyperpage{47}
  \item either $P$ or $Q$ are true, \hyperpage{8}
  \item elastodynamics, \hyperpage{277}
  \item elementary region, \hyperpage{59}
  \item elementary symmetric polynomials, \hyperpage{163}
  \item elliptic, \hyperpage{74}, \hyperpage{273}
  \item elliptic equation, \hyperpage{277}
  \item elliptic point, \hyperpage{150}
  \item elliptic sector, \hyperpage{133}
  \item embedded, \hyperpage{351}
  \item embedded methods, \hyperpage{260}
  \item empirical distribution, \hyperpage{202}
  \item empty set, \hyperpage{6}
  \item energy functional, \hyperpage{288}
  \item entire function, \hyperpage{109}
  \item Entropy, \hyperpage{256}
  \item entropy, \hyperpage{256}
  \item Entropy condition, \hyperpage{280}
  \item envelope, \hyperpage{144}
  \item equal, \hyperpage{6}
  \item equal almost surely, \hyperpage{176}
  \item equal in distribution, \hyperpage{176}
  \item equally-spaced, \hyperpage{93}
  \item equation of the hyperplane, \hyperpage{67}
  \item equicontinuous, \hyperpage{121}
  \item equicontinuous at a point, \hyperpage{125}, \hyperpage{304}
  \item equilibrium point, \hyperpage{221}
  \item equiprobable space, \hyperpage{177}
  \item equivalence, \hyperpage{131}
  \item equivalence class, \hyperpage{8}, \hyperpage{17}
  \item equivalence relation, \hyperpage{8}
  \item equivalent, \hyperpage{13}, \hyperpage{17}, \hyperpage{23}, 
		\hyperpage{73}, \hyperpage{130}, \hyperpage{132}, 
		\hyperpage{306}, \hyperpage{372}
  \item equivalent dynamical systems, \hyperpage{131}
  \item Ergotic theorem, \hyperpage{324, 325}
  \item error of type I, \hyperpage{199}
  \item error of type II, \hyperpage{199}
  \item error sum of squares, \hyperpage{252}
  \item Essential singularity, \hyperpage{117}
  \item essential singularity, \hyperpage{117}
  \item estimated average response, \hyperpage{253}
  \item estimation of the prediction, \hyperpage{253}
  \item estimator, \hyperpage{193}
  \item Euclid's axioms, \hyperpage{63}
  \item Euclid's theorem, \hyperpage{10}
  \item Euclidean, \hyperpage{64}
  \item Euclidean affine space, \hyperpage{72}
  \item Euclidean metric, \hyperpage{205}
  \item Euclidean motion, \hyperpage{73}
  \item Euclidean plane, \hyperpage{64}
  \item Euclidean space, \hyperpage{53}
  \item Euclidean vector space, \hyperpage{24}
  \item Euclidian division, \hyperpage{11}
  \item Euler characteristic, \hyperpage{218}
  \item Euler method, \hyperpage{258}, \hyperpage{373}
  \item Euler theorem, \hyperpage{50}
  \item Euler's formula, \hyperpage{108}, \hyperpage{150}
  \item Euler's theorem, \hyperpage{11}
  \item Euler's totient function, \hyperpage{11}
  \item Euler-Maclaurin formula, \hyperpage{96}
  \item Eulerian, \hyperpage{50}
  \item Eulerian circuit, \hyperpage{50}
  \item Eulerian trail, \hyperpage{50}
  \item evaluation, \hyperpage{12}, \hyperpage{162}
  \item even extension, \hyperpage{84}
  \item even periodic extension, \hyperpage{283}
  \item event, \hyperpage{173}
  \item events, \hyperpage{347}
  \item evolute, \hyperpage{144}
  \item exact, \hyperpage{156}
  \item Examples of Euclidean motions, \hyperpage{73}
  \item Excluded point topology, \hyperpage{206}
  \item Existence and uniqueness of solutions of SDEs, \hyperpage{389}
  \item Existence of a lift, \hyperpage{337}
  \item Existence of orthogonal polynomials, \hyperpage{96}
  \item Existence of the rotation number, \hyperpage{338}
  \item Existence of the splitting field, \hyperpage{167}
  \item exists and it is finite, \hyperpage{298}
  \item expansion map, \hyperpage{335}
  \item Expansive fixed point theorem, \hyperpage{229}
  \item Expectation, \hyperpage{183}, \hyperpage{347}
  \item expectation, \hyperpage{178}, \hyperpage{182--184}, 
		\hyperpage{249}
  \item expectation of $X$, \hyperpage{347}
  \item explicit, \hyperpage{258}
  \item explicit Euler method, \hyperpage{258}
  \item explicit form, \hyperpage{122}
  \item Explicit scheme in finite differences, \hyperpage{286}
  \item exponent, \hyperpage{89}
  \item exponential, \hyperpage{257}
  \item Exponential distribution, \hyperpage{178}
  \item exponential distribution, \hyperpage{178}
  \item exponential factor, \hyperpage{138}
  \item exponential function with base $a$, \hyperpage{29}
  \item exponential generating function, \hyperpage{48}
  \item exponential series, \hyperpage{48}
  \item exponentially stable, \hyperpage{353}
  \item extended complex plane, \hyperpage{105}
  \item extended real numbers, \hyperpage{105}
  \item extension, \hyperpage{126}, \hyperpage{308}, \hyperpage{351}
  \item extension operator, \hyperpage{351}
  \item exterior, \hyperpage{54}
  \item exterior angle, \hyperpage{160}
  \item Exterior angle theorem, \hyperpage{64}
  \item exterior differential, \hyperpage{156, 157}
  \item exterior point, \hyperpage{54}
  \item exterior product, \hyperpage{155}
  \item exterior vectors, \hyperpage{157}
  \item externally studentized residuals, \hyperpage{254}

  \indexspace

  \item failure, \hyperpage{177}
  \item false, \hyperpage{177}
  \item Fano configuration, \hyperpage{67}
  \item fast Fourier transform, \hyperpage{240}
  \item Fatou's lemma, \hyperpage{184}, \hyperpage{297}, 
		\hyperpage{346}
  \item feasible region, \hyperpage{51}
  \item feasible solution, \hyperpage{51}
  \item Fejér kernel, \hyperpage{85}, \hyperpage{234}
  \item Fejér mean, \hyperpage{234}
  \item Fejér means, \hyperpage{86}
  \item Fejér's theorem, \hyperpage{86}
  \item FEM, \hyperpage{275}
  \item Fermat's little theorem, \hyperpage{11}
  \item Fermat's principle, \hyperpage{278}
  \item Feynman-Kac's formula, \hyperpage{391}
  \item FFT, \hyperpage{240}
  \item Fick's law, \hyperpage{278}
  \item Fick's law of diffusion, \hyperpage{278}
  \item Field, \hyperpage{42}
  \item field, \hyperpage{42}
  \item field extension, \hyperpage{164}
  \item field morphism, \hyperpage{162}
  \item field of complex numbers, \hyperpage{104}
  \item field of fractions, \hyperpage{46}, \hyperpage{163}
  \item field of rational functions, \hyperpage{163}
  \item filtered probability space, \hyperpage{348}
  \item filtration, \hyperpage{321}, \hyperpage{348}
  \item filtration space, \hyperpage{321}
  \item finer, \hyperpage{205}
  \item finer than, \hyperpage{32}, \hyperpage{58}
  \item finite, \hyperpage{25}, \hyperpage{49}, \hyperpage{164}, 
		\hyperpage{213}, \hyperpage{294}
  \item finite $k$-th moment, \hyperpage{185}
  \item finite difference estimator, \hyperpage{374}
  \item finite difference method, \hyperpage{265}
  \item finite difference scheme, \hyperpage{268}
  \item finite element, \hyperpage{377}
  \item finite element method, \hyperpage{275}
  \item finite expectation, \hyperpage{182--184}
  \item Finite field, \hyperpage{166}
  \item finite field, \hyperpage{166}
  \item finite moment of order $k$, \hyperpage{185}
  \item Finite subadditivity, \hyperpage{173}
  \item finite variation, \hyperpage{382}
  \item Finite-dimensional distributions, \hyperpage{333}
  \item finite-dimensional distributions, \hyperpage{333}
  \item finite-rank operator, \hyperpage{307}
  \item finitely generated, \hyperpage{165}
  \item first and second characteristic polynomials, \hyperpage{261}
  \item First Borel-Cantelli lemma, \hyperpage{188}
  \item first fundamental form, \hyperpage{148}
  \item first integral, \hyperpage{134}, \hyperpage{154}
  \item First isomorphism theorem, \hyperpage{18}, \hyperpage{39}, 
		\hyperpage{44}
  \item first order reflection, \hyperpage{352}
  \item First Sylow theorem, \hyperpage{41}
  \item Fisher information, \hyperpage{195}
  \item Fisher's theorem, \hyperpage{197}
  \item Fisher-Neyman factorization theorem, \hyperpage{194}
  \item fixed field, \hyperpage{168}
  \item fixed point, \hyperpage{71}, \hyperpage{221}
  \item Fixed-point theorem, \hyperpage{90}
  \item flat, \hyperpage{203}
  \item Floating-point representation, \hyperpage{89}
  \item floating-point representation, \hyperpage{89}
  \item floating-point representation by rounding, \hyperpage{89}
  \item floating-point representation by truncation, \hyperpage{89}
  \item flow, \hyperpage{128}, \hyperpage{132}
  \item Flow box theorem, \hyperpage{132}
  \item flow of the linear ODE, \hyperpage{126}
  \item flux, \hyperpage{62}, \hyperpage{159}
  \item formal adjoint, \hyperpage{358}
  \item Formal derivative, \hyperpage{167}
  \item formal derivative, \hyperpage{167}
  \item Forward and backward difference formula of order 1, 
		\hyperpage{94}
  \item forward Euler method, \hyperpage{258}
  \item Forward-time backward-space, \hyperpage{268}
  \item Forward-time central-space, \hyperpage{268}, \hyperpage{274}
  \item Forward-time forward-space, \hyperpage{268}
  \item Fourier coefficients, \hyperpage{313}
  \item Fourier series, \hyperpage{83}, \hyperpage{313}
  \item Fourier transform, \hyperpage{231}, \hyperpage{237}, 
		\hyperpage{244}, \hyperpage{313}
  \item Fourier transform operator, \hyperpage{232}
  \item Fourier's law, \hyperpage{278}
  \item Fredholm alternative, \hyperpage{314}
  \item Fredholm operator with kernel $K$, \hyperpage{307}
  \item free variables, \hyperpage{14}
  \item Frenet-Serret formulas, \hyperpage{143}
  \item Frenet-Serret frame, \hyperpage{143}
  \item Fresnel integrals, \hyperpage{113}
  \item Frobenius endomorphism, \hyperpage{166}
  \item Fréchet, \hyperpage{212}
  \item Fréchet derivative, \hyperpage{365}
  \item Fréchet differentiable, \hyperpage{365}
  \item FTBS, \hyperpage{268}
  \item FTCS, \hyperpage{268}
  \item FTFS, \hyperpage{268}
  \item Fubini, \hyperpage{346}
  \item Fubini's theorem, \hyperpage{59}, \hyperpage{175}, 
		\hyperpage{299}
  \item Fubini's theorem for elementary regions, \hyperpage{59}
  \item full QR decomposition, \hyperpage{267}
  \item function, \hyperpage{7}
  \item functionally independent, \hyperpage{134}
  \item Fundamental lemma of calculus of variations, \hyperpage{240}, 
		\hyperpage{279}
  \item fundamental matrix solution, \hyperpage{127}
  \item fundamental polygon of the surface, \hyperpage{218}
  \item fundamental solution, \hyperpage{245, 246}, \hyperpage{285}
  \item Fundamental theorem of affine geometry, \hyperpage{72}
  \item Fundamental theorem of algebra, \hyperpage{45}, \hyperpage{114}, 
		\hyperpage{170}
  \item Fundamental theorem of arithmetic, \hyperpage{10}
  \item Fundamental theorem of calculus, \hyperpage{33}, 
		\hyperpage{298}
  \item Fundamental theorem of curves, \hyperpage{146}
  \item Fundamental theorem of Galois theory, \hyperpage{169}
  \item Fundamental theorem of projective geometry, \hyperpage{68}
  \item Fundamental theorem of symmetric polynomials, \hyperpage{164}

  \indexspace

  \item Gagliardo, Nirengerg and Sobolev's inequality, \hyperpage{351}
  \item Galerkin approximation, \hyperpage{275}
  \item Galerkin methods, \hyperpage{379}
  \item Galois, \hyperpage{168}
  \item Galois extension, \hyperpage{168}
  \item Galois group, \hyperpage{166}
  \item Gambler's ruin problem, \hyperpage{318}
  \item Gamma distribution, \hyperpage{179}
  \item gamma distribution, \hyperpage{179}
  \item Gamma function, \hyperpage{81}
  \item Gau\ss ' law, \hyperpage{278}
  \item Gau\ss ' law for magnetism, \hyperpage{278}
  \item Gau\ss ' lemma, \hyperpage{47}
  \item Gau\ss ' theorem, \hyperpage{10, 11}, \hyperpage{14}
  \item Gau\ss ' Theorema Egregium, \hyperpage{152}
  \item Gau\ss -Markov, \hyperpage{251}
  \item Gau\ss -Seidel method, \hyperpage{100}
  \item Gau\ss \ curvature, \hyperpage{149}
  \item Gau\ss \ equations, \hyperpage{152}
  \item Gau\ss \ map, \hyperpage{149}
  \item Gau\ss ian integers, \hyperpage{47}
  \item Gaussian elimination, \hyperpage{101}
  \item Gaussian process, \hyperpage{330}
  \item Gaussian vector, \hyperpage{330}
  \item General Cauchy's integral formula, \hyperpage{115}
  \item General Cauchy's integral formula for derivatives, 
		\hyperpage{116}
  \item General Eisenstein's criterion, \hyperpage{45}
  \item General Frenet-Serret formulas, \hyperpage{143}
  \item General linear model, \hyperpage{250}
  \item general solution of the ODE, \hyperpage{122}
  \item general term of the series, \hyperpage{76}, \hyperpage{105}
  \item Generalized argument principle, \hyperpage{118}
  \item Generalized Bendixson-Dulac theorem, \hyperpage{137}
  \item Generalized compound probability formula, \hyperpage{174}
  \item generalized eigenspace, \hyperpage{128}
  \item generalized eigenvector, \hyperpage{128}
  \item generalized heat kernel, \hyperpage{286}
  \item Generalized Hölder's inequality, \hyperpage{237}
  \item generalized Itô integral, \hyperpage{386}
  \item generalized solution, \hyperpage{245}
  \item generating set, \hyperpage{16}
  \item Generator, \hyperpage{390}
  \item generator, \hyperpage{390}
  \item generator tree, \hyperpage{50}
  \item generatrix, \hyperpage{147}
  \item genus $g$ orientable surface, \hyperpage{217}
  \item genus $h$ non-orientable surface, \hyperpage{217}
  \item geodesic, \hyperpage{153}
  \item geodesic curvature, \hyperpage{153}
  \item Geometric Brownian motion, \hyperpage{390}
  \item Geometric distribution, \hyperpage{177}
  \item geometric distribution, \hyperpage{177}
  \item geometric multiplicity, \hyperpage{20}
  \item Gershgorin circle theorem, \hyperpage{92}
  \item Giranov's theorem, \hyperpage{389}
  \item Glide orthogonal reflections, \hyperpage{73}
  \item glide reflection, \hyperpage{72}
  \item glide vector, \hyperpage{73}
  \item Global Gau\ss -Bonnet theorem, \hyperpage{160}
  \item global interpolant, \hyperpage{378}
  \item Global interpolation error, \hyperpage{379}
  \item global maximum, \hyperpage{57}
  \item global minimum, \hyperpage{57}
  \item global stable manifold, \hyperpage{222}
  \item global truncation error, \hyperpage{258}
  \item global unstable manifold, \hyperpage{222}
  \item globally smooth, \hyperpage{379}
  \item globally stable, \hyperpage{353}
  \item Goodness of fit, \hyperpage{200}
  \item Goursat's theorem, \hyperpage{112}
  \item Gra\ss mann formula, \hyperpage{16}, \hyperpage{67}
  \item gradient, \hyperpage{56}
  \item Gradient descent, \hyperpage{264}
  \item gradient vector field, \hyperpage{61}
  \item Gram-Schmidt process, \hyperpage{23}, \hyperpage{313}
  \item graph, \hyperpage{49}, \hyperpage{55}, \hyperpage{227}
  \item Graph of a function, \hyperpage{55}
  \item Great Picard's theorem, \hyperpage{118}
  \item greatest common divisor, \hyperpage{10}, \hyperpage{46}
  \item greatest element, \hyperpage{126}
  \item Green identities, \hyperpage{279}
  \item Green's formula, \hyperpage{159}
  \item Green's theorem, \hyperpage{62}
  \item grid, \hyperpage{268}
  \item Gronwall's lemma, \hyperpage{389}
  \item Group, \hyperpage{37}
  \item group, \hyperpage{37}
  \item Group morphism, \hyperpage{38}
  \item group morphism, \hyperpage{38}
  \item Grönwall's lemma, \hyperpage{129}
  \item Gâteaux derivative, \hyperpage{365}
  \item Gâteaux differentiable, \hyperpage{365}

  \indexspace

  \item Hahn-Banach theorem, \hyperpage{308}
  \item half-line, \hyperpage{63}
  \item half-plane, \hyperpage{63}
  \item Hamilton-Jacobi equation, \hyperpage{279}
  \item Hamiltonian, \hyperpage{134}
  \item Hamiltonian system, \hyperpage{134}
  \item Hamiltonian vector field, \hyperpage{337}
  \item Handshaking lemma, \hyperpage{49}
  \item Hardy-Littlewood maximal function, \hyperpage{298}
  \item harmonic, \hyperpage{115}
  \item harmonic ratio, \hyperpage{69}
  \item Hartman-Grobman theorem, \hyperpage{134}, \hyperpage{222}
  \item has $t$ correct decimal digits, \hyperpage{89}
  \item has $u$ significant digits, \hyperpage{89}
  \item Hausdorff, \hyperpage{212}
  \item Heat equation, \hyperpage{140}, \hyperpage{278}
  \item heat equation, \hyperpage{140}
  \item heat flux, \hyperpage{278}
  \item heat kernel, \hyperpage{285}
  \item Heaviside step function, \hyperpage{242}, \hyperpage{285}
  \item Heine's theorem, \hyperpage{55}
  \item Heine-Borel theorem, \hyperpage{214}
  \item Hermite interpolation problem, \hyperpage{94}
  \item Hermite reduction method, \hyperpage{35}
  \item Hessian matrix, \hyperpage{56}
  \item heteroclinic orbit, \hyperpage{133}
  \item Heun method, \hyperpage{259}
  \item high-leverage point, \hyperpage{255}
  \item high-leverage points, \hyperpage{255}
  \item highest posterior density, \hyperpage{204}
  \item Hilbert basis, \hyperpage{312}
  \item Hilbert field, \hyperpage{64}
  \item Hilbert plane, \hyperpage{64}
  \item Hilbert space, \hyperpage{310}
  \item Hilbert transform, \hyperpage{247}
  \item Hilbert's basis theorem, \hyperpage{43}
  \item Hilbert's Nullstellensatz, \hyperpage{45}
  \item Hilbert-Schmidt operator with kernel $K$, \hyperpage{307}
  \item Hilbert-Schmidt spectral representation theorem, 
		\hyperpage{313}
  \item hitting time, \hyperpage{382}
  \item holding times, \hyperpage{327}
  \item holes, \hyperpage{216}
  \item holomorphic, \hyperpage{109}
  \item holomorphic differential equation, \hyperpage{221}
  \item homeomorphic, \hyperpage{208}
  \item homeomorphism, \hyperpage{208}
  \item Homoclinic bifurcation, \hyperpage{226}
  \item homoclinic bifurcation, \hyperpage{226}
  \item homoclinic orbit, \hyperpage{133}
  \item homogeneous, \hyperpage{49}, \hyperpage{122}, \hyperpage{126}, 
		\hyperpage{356}
  \item homogeneous adjoint problem, \hyperpage{358}
  \item homogeneous coordinates, \hyperpage{67}
  \item Homogeneous distribution, \hyperpage{245}
  \item homogeneous of degree $k$, \hyperpage{221}
  \item homogeneous of degree $r\in \ensuremath  {\mathbb  {R}}$, 
		\hyperpage{245}
  \item homogeneous SDE, \hyperpage{390}
  \item Homogenization, \hyperpage{74}
  \item homogenization, \hyperpage{70}
  \item homography, \hyperpage{67}
  \item homologous to zero, \hyperpage{115}
  \item Homotheties, \hyperpage{72}
  \item homothety, \hyperpage{19}, \hyperpage{72}
  \item homotopic, \hyperpage{139}
  \item homotopy, \hyperpage{139}
  \item Hopf bifurcation theorem, \hyperpage{226}
  \item Hopf's lemma, \hyperpage{362}
  \item Hopf-bifurcation, \hyperpage{226}
  \item Hurwitz's theorem, \hyperpage{119}
  \item hyperbolic, \hyperpage{268}, \hyperpage{273}
  \item hyperbolic critical point, \hyperpage{134}
  \item hyperbolic equations, \hyperpage{277}
  \item Hyperbolic geometry, \hyperpage{65}
  \item hyperbolic matrix, \hyperpage{134}
  \item hyperbolic periodic orbit, \hyperpage{136}
  \item hyperbolic plane, \hyperpage{74}
  \item hyperbolic point, \hyperpage{150}
  \item hyperbolic sector, \hyperpage{133}
  \item hyperbolicity, \hyperpage{336}
  \item Hypergeometric distribution, \hyperpage{177}
  \item hypergeometric distribution, \hyperpage{177}
  \item hyperplane, \hyperpage{67}, \hyperpage{70}
  \item hypothesis, \hyperpage{199}
  \item Hypothesis test, \hyperpage{199}
  \item hypothesis test, \hyperpage{199}
  \item Hölder condition, \hyperpage{247}
  \item Hölder conjugates, \hyperpage{302}
  \item Hölder continuity, \hyperpage{351}
  \item Hölder's inequality, \hyperpage{302}

  \indexspace

  \item i.i.d., \hyperpage{181}
  \item Ideal, \hyperpage{43}
  \item ideal, \hyperpage{43}
  \item idempotent, \hyperpage{14}
  \item identifiable, \hyperpage{193}
  \item ill-conditioned, \hyperpage{90}
  \item image, \hyperpage{7}, \hyperpage{17}, \hyperpage{38}, 
		\hyperpage{115}
  \item imaginary part, \hyperpage{104}
  \item Immersion, \hyperpage{146}
  \item immersion, \hyperpage{146}
  \item implicit, \hyperpage{258}
  \item implicit Euler method, \hyperpage{258}
  \item implicit form, \hyperpage{122}
  \item Implicit function theorem, \hyperpage{57}
  \item Implicit scheme in finite differences, \hyperpage{286}
  \item importance sampling estimator, \hyperpage{372}
  \item improper, \hyperpage{37}, \hyperpage{203}
  \item improper integral, \hyperpage{79}
  \item in perspective with respect to a line, \hyperpage{68}
  \item in perspective with respect to a point, \hyperpage{68}
  \item Incidence axioms, \hyperpage{63}
  \item incidence relation, \hyperpage{63}
  \item incident, \hyperpage{49}
  \item incompressible flow, \hyperpage{277}
  \item inconsistent, \hyperpage{14}
  \item increasing, \hyperpage{28}, \hyperpage{181}
  \item increment, \hyperpage{181}
  \item incremental function, \hyperpage{258}
  \item independent, \hyperpage{134}, \hyperpage{181}, \hyperpage{316}
  \item independent and identically distributed, \hyperpage{181}
  \item independent events, \hyperpage{174}
  \item independent increments, \hyperpage{326}
  \item Independent samples with known variances, \hyperpage{198}
  \item Independent samples with unknown equal variances, 
		\hyperpage{198}
  \item Independent samples with unknown variances, \hyperpage{198}
  \item independent variable, \hyperpage{122}
  \item indeterminate, \hyperpage{11}, \hyperpage{14}
  \item index, \hyperpage{14}, \hyperpage{39}, \hyperpage{74}, 
		\hyperpage{113}, \hyperpage{115}, \hyperpage{138, 139}, 
		\hyperpage{160}
  \item indicator function, \hyperpage{9}
  \item indistinguishable, \hyperpage{331}
  \item induced subgraph, \hyperpage{49}
  \item Induction axiom, \hyperpage{6}
  \item Inexact Newton method, \hyperpage{264}
  \item infimum, \hyperpage{25}
  \item infinite, \hyperpage{25}, \hyperpage{164}
  \item infinite order, \hyperpage{241}
  \item infinite product topology, \hyperpage{209}
  \item infinitesimal generator, \hyperpage{328}
  \item infinitesimal transition scheme, \hyperpage{328}
  \item inflection point, \hyperpage{31}
  \item Information, \hyperpage{256}
  \item information of an event, \hyperpage{256}
  \item initial conditions, \hyperpage{122}
  \item initial distribution, \hyperpage{318}
  \item initial point, \hyperpage{215}
  \item Initial value problem, \hyperpage{122}
  \item initial value problem, \hyperpage{122}
  \item initial values, \hyperpage{48}
  \item injective, \hyperpage{7}
  \item inner product, \hyperpage{24}, \hyperpage{82}, \hyperpage{310}
  \item Inner regularity, \hyperpage{359}
  \item insphere diameter, \hyperpage{378}
  \item integrable, \hyperpage{32}, \hyperpage{182, 183}
  \item integrable function, \hyperpage{59}
  \item integrable function over $E$, \hyperpage{297}
  \item integral, \hyperpage{111}, \hyperpage{158, 159}
  \item integral curve, \hyperpage{154}
  \item integral domain, \hyperpage{44}
  \item Integral in cylindrical coordinates, \hyperpage{60}
  \item Integral in polar coordinates, \hyperpage{60}
  \item Integral in spherical coordinates, \hyperpage{60}
  \item integral of $f$ over $\ensuremath  {\mathbb  {R}}^n$, 
		\hyperpage{296}
  \item integral of $f$ over $E$, \hyperpage{297}
  \item integral of $f$ over a measurable set $E\subseteq \ensuremath  {\mathbb  {R}}^n$, 
		\hyperpage{296}
  \item integral of $f$ over the region $R$, \hyperpage{148}
  \item integral of $f$ with respect to $\mu $, \hyperpage{346}
  \item integral of $s$ over $\ensuremath  {\mathbb  {R}}^n$, 
		\hyperpage{295}
  \item integral of $s$ over a measurable set $E$, \hyperpage{295}
  \item Integral test, \hyperpage{77}, \hyperpage{80}
  \item Integrating factor, \hyperpage{124}
  \item integrating factor, \hyperpage{124}, \hyperpage{138}
  \item Integration by parts, \hyperpage{33}, \hyperpage{298}
  \item Integration by substitution, \hyperpage{33}
  \item inter-arrival times, \hyperpage{327}
  \item Interior, \hyperpage{206}
  \item interior, \hyperpage{54}, \hyperpage{206}
  \item interior ball condition, \hyperpage{362}
  \item interior point, \hyperpage{54}, \hyperpage{157}, 
		\hyperpage{207}
  \item interior product, \hyperpage{156}
  \item Intermediate value theorem, \hyperpage{28}, \hyperpage{55}, 
		\hyperpage{94}, \hyperpage{215}
  \item internally studentized residuals, \hyperpage{254}
  \item interpolant, \hyperpage{379, 380}
  \item Interpolation inequality, \hyperpage{302}
  \item interpolation problem, \hyperpage{93}
  \item intersection, \hyperpage{6}
  \item interval, \hyperpage{291}
  \item Interval for $\mu $ with $\sigma $ known, \hyperpage{198}
  \item Intervals for $\mu $ and $\sigma ^2$, \hyperpage{198}
  \item invariance level, \hyperpage{71}
  \item Invariance of the MLE, \hyperpage{195}
  \item Invariance under time shift, \hyperpage{390}
  \item invariant, \hyperpage{131}, \hyperpage{339, 340}
  \item invariant algebraic curve, \hyperpage{135}
  \item invariant subspace, \hyperpage{21}
  \item invariant under an affinity, \hyperpage{71}
  \item inverse discrete Fourier transform, \hyperpage{239}
  \item inverse Fourier transform, \hyperpage{231}, \hyperpage{237}, 
		\hyperpage{244}
  \item inverse function, \hyperpage{7}
  \item Inverse function rule, \hyperpage{30}
  \item Inverse function theorem, \hyperpage{57}
  \item Inverse function theorem for surfaces, \hyperpage{148}
  \item Inverse power method, \hyperpage{101}
  \item inverse power method, \hyperpage{101}
  \item inverse semidiscrete Fourier transform, \hyperpage{270}
  \item inversion, \hyperpage{119}
  \item Inversion theorem, \hyperpage{233}
  \item invertible, \hyperpage{7}, \hyperpage{14}
  \item Inviscid flow, \hyperpage{277}
  \item involute, \hyperpage{144}
  \item irreducible, \hyperpage{12}, \hyperpage{44}, \hyperpage{100}, 
		\hyperpage{329}
  \item irreducible chain, \hyperpage{320}
  \item irreducible class, \hyperpage{320}
  \item irreducible polynomial, \hyperpage{164}
  \item is finer than, \hyperpage{306}
  \item isolated point, \hyperpage{54}
  \item isolated singular point, \hyperpage{160}
  \item isolated singularity, \hyperpage{116}, \hyperpage{160}
  \item isometric, \hyperpage{23}
  \item isometry, \hyperpage{23}, \hyperpage{74}, \hyperpage{148}, 
		\hyperpage{384}
  \item isomorphic, \hyperpage{17}, \hyperpage{38}, \hyperpage{50}, 
		\hyperpage{306}
  \item isomorphism, \hyperpage{38}
  \item isomorphism between projective spaces, \hyperpage{67}
  \item Isoperimetric inequality, \hyperpage{88}
  \item isotropic, \hyperpage{22}
  \item iteration matrix, \hyperpage{99}
  \item itinerary, \hyperpage{230}
  \item Itinerary lemma, \hyperpage{229}
  \item Itô integral, \hyperpage{386}
  \item Itô isometry, \hyperpage{386}
  \item Itô process, \hyperpage{387}
  \item Itô term, \hyperpage{388}
  \item Itô's formula, \hyperpage{388}
  \item ivp, \hyperpage{122}

  \indexspace

  \item Jacobi identity, \hyperpage{142}
  \item Jacobi method, \hyperpage{100}
  \item Jacobian determinant, \hyperpage{55}
  \item Jacobian matrix, \hyperpage{55}
  \item Jeffrey's prior, \hyperpage{203}
  \item Jensen's inequality, \hyperpage{236}, \hyperpage{347}
  \item joint pdf, \hyperpage{180}
  \item joint pmf, \hyperpage{180}
  \item joint probability density function, \hyperpage{180}
  \item Joint probability mass function, \hyperpage{180}
  \item joint probability mass function, \hyperpage{180}
  \item jointly Gaussian, \hyperpage{381}
  \item Jordan arc, \hyperpage{61}
  \item Jordan block, \hyperpage{21}
  \item Jordan closed curve, \hyperpage{61}
  \item Jordan curve theorem, \hyperpage{218}
  \item Jordan form, \hyperpage{21}
  \item Jordan matrix, \hyperpage{21}
  \item Jump discontinuity, \hyperpage{28}
  \item jump process, \hyperpage{328}

  \indexspace

  \item Kalmann's theorem, \hyperpage{354}
  \item Kelley's theorem, \hyperpage{213}
  \item kernel, \hyperpage{17}, \hyperpage{38}
  \item kernel function, \hyperpage{79}
  \item Klein bottle, \hyperpage{211}
  \item Kolmogorov, \hyperpage{212}
  \item Kolmogorov axioms, \hyperpage{173}
  \item Kolmogorov extension theorem, \hyperpage{333}
  \item Kolmogorov system, \hyperpage{221}
  \item Kolmogorov's backward equation, \hyperpage{328}
  \item Kolmogorov's continuity theorem, \hyperpage{331}
  \item Kolmogorov's equation, \hyperpage{390}
  \item Kolmogorov's forward equation, \hyperpage{328}
  \item Kolmogorov's strong law of large numbers, \hyperpage{191}
  \item Kronecker delta, \hyperpage{19}
  \item Kronecker's lemma, \hyperpage{164}
  \item Kronecker's theorem, \hyperpage{167}
  \item Kullback-Leibler divergence, \hyperpage{256}
  \item Kuratowski's problem, \hyperpage{207}

  \indexspace

  \item L'H\^opital's rule, \hyperpage{30}
  \item lack of fit test, \hyperpage{254}
  \item Lagrange basis polynomials, \hyperpage{93}
  \item Lagrange multiplier, \hyperpage{367}
  \item Lagrange multipliers, \hyperpage{366, 367}
  \item Lagrange multipliers in several variables, \hyperpage{367}
  \item Lagrange multipliers theorem, \hyperpage{58}
  \item Lagrange's interpolation problem, \hyperpage{93}
  \item Lagrange's theorem, \hyperpage{39}
  \item Laguerre polynomials, \hyperpage{96}
  \item Lamé coefficients, \hyperpage{277}
  \item Langevin equation, \hyperpage{389}
  \item Laplace equation, \hyperpage{140}, \hyperpage{288}
  \item Laplacian, \hyperpage{61}
  \item Lasaalle's invariance principle, \hyperpage{354}
  \item lattice of subgroups, \hyperpage{169}
  \item Laurent series, \hyperpage{117}
  \item Laurent series theorem, \hyperpage{117}
  \item law of $X$, \hyperpage{347}
  \item Law of the iterated logarithm, \hyperpage{333}
  \item Law of total expectation, \hyperpage{186, 187}, \hyperpage{315}
  \item Law of total probability, \hyperpage{174}, \hyperpage{315}
  \item Lax theorem, \hyperpage{261}
  \item Lax-Friedrichs scheme, \hyperpage{268}
  \item Lax-Milgram theorem, \hyperpage{357}
  \item Lax-Richtmyer equivalence theorem, \hyperpage{273}
  \item Lax-Wendroff, \hyperpage{271}
  \item Lax-Wendroff scheme, \hyperpage{271}
  \item leading coefficient, \hyperpage{11}
  \item Leapfrog scheme, \hyperpage{268}, \hyperpage{274}
  \item least common multiple, \hyperpage{10}
  \item least element, \hyperpage{9}
  \item Least-squares method, \hyperpage{250}
  \item least-squares method, \hyperpage{250}
  \item leave, \hyperpage{50}
  \item Lebesgue differentiation theorem, \hyperpage{299}
  \item Lebesgue integrable, \hyperpage{175}
  \item Lebesgue integral, \hyperpage{175}
  \item Lebesgue measurable, \hyperpage{293, 294}
  \item Lebesgue measure, \hyperpage{175}, \hyperpage{293}
  \item left cosets, \hyperpage{39}
  \item Left side, \hyperpage{120}
  \item left singular vectors, \hyperpage{265}
  \item Left-open interval, \hyperpage{25}
  \item left-sided limit of $f$ at $x_0$, \hyperpage{27}
  \item Legendre polynomials, \hyperpage{97}
  \item Leibnitz rule, \hyperpage{243}
  \item Leibnitz's test, \hyperpage{77}
  \item length, \hyperpage{58}, \hyperpage{141}
  \item length of the polygonal, \hyperpage{34}, \hyperpage{60}, 
		\hyperpage{141}
  \item level set, \hyperpage{55}
  \item leverage, \hyperpage{253}
  \item levorotation, \hyperpage{145}
  \item Levy's characterization of Brownian motion, \hyperpage{384}
  \item lexicographic degree, \hyperpage{163}
  \item lexicographic order, \hyperpage{163}
  \item lift, \hyperpage{337}
  \item Likelihood, \hyperpage{195}
  \item likelihood function, \hyperpage{195}
  \item likelihood ratio test, \hyperpage{200}
  \item Likelihood-ratio test, \hyperpage{200}
  \item Limit, \hyperpage{26}
  \item limit, \hyperpage{105}, \hyperpage{188}
  \item Limit comparison test, \hyperpage{76}
  \item limit cycle, \hyperpage{136}
  \item limit distribution, \hyperpage{329}
  \item limit inferior, \hyperpage{27}, \hyperpage{188}
  \item limit of $f$ at infinity, \hyperpage{28}
  \item limit of the function $f$ at the point $x_0$, \hyperpage{27}
  \item limit set, \hyperpage{54}
  \item limit superior, \hyperpage{27}, \hyperpage{188}
  \item line, \hyperpage{67}, \hyperpage{70}
  \item line integral, \hyperpage{61}, \hyperpage{112}
  \item line intergal, \hyperpage{159}
  \item line of curvature, \hyperpage{150}
  \item line search method, \hyperpage{264}
  \item linear, \hyperpage{122}
  \item linear $k$-step method, \hyperpage{261}
  \item linear combination, \hyperpage{16}
  \item linear convergence, \hyperpage{91}
  \item linear discrete map, \hyperpage{222}
  \item linear equation, \hyperpage{13}
  \item Linear loss function, \hyperpage{203}
  \item linear map, \hyperpage{17}
  \item Linear multistep method, \hyperpage{261}
  \item linear programming to maximize, \hyperpage{51}
  \item linear programming to minimize, \hyperpage{51}
  \item linear recurrence relation of order $k$, \hyperpage{48}
  \item linear saddles, \hyperpage{227}
  \item linear second-order PDE, \hyperpage{356}
  \item linear span, \hyperpage{16}
  \item Linearity, \hyperpage{76}
  \item linearization, \hyperpage{221}
  \item linearly dependent, \hyperpage{16}, \hyperpage{82}
  \item linearly independent, \hyperpage{16}, \hyperpage{82}
  \item lines, \hyperpage{63}
  \item Liouville's formula, \hyperpage{127}, \hyperpage{153}
  \item Liouville's theorem, \hyperpage{114}
  \item Lipschitz continuous, \hyperpage{55}
  \item Lipschitz continuous with respect to the second variable, 
		\hyperpage{124}
  \item Lipschitz's theorem, \hyperpage{85}
  \item Little Picard's theorem, \hyperpage{118}
  \item Liénard system, \hyperpage{228}
  \item Liénard's theorem, \hyperpage{228}
  \item load vector, \hyperpage{276}
  \item Local behaviour of a holomorphic function, \hyperpage{116}
  \item local bifurcation, \hyperpage{223}
  \item local canonical form, \hyperpage{145}
  \item Local Cauchy's integral formula, \hyperpage{113}
  \item Local Cauchy's integral formula for derivatives, 
		\hyperpage{113}
  \item Local Cauchy's integral theorem, \hyperpage{112}
  \item local conjugacy, \hyperpage{132}
  \item local diffeomorphism, \hyperpage{141}
  \item local equivalence, \hyperpage{132}
  \item local extremum, \hyperpage{30}, \hyperpage{57}
  \item Local Gau\ss -Bonnet theorem, \hyperpage{160}
  \item local interpolant, \hyperpage{378}
  \item Local interpolation error, \hyperpage{379}
  \item local isometry, \hyperpage{148}
  \item local maximum, \hyperpage{30}, \hyperpage{57}
  \item local minimum, \hyperpage{30}, \hyperpage{57}
  \item Local structure of immersions, \hyperpage{146}
  \item Local structure of submersions, \hyperpage{146}
  \item local transversal section, \hyperpage{132}
  \item local truncation error, \hyperpage{262}
  \item local truncation errors, \hyperpage{258}
  \item localizing sequence, \hyperpage{383}
  \item locally, \hyperpage{214}
  \item locally bounded, \hyperpage{121}, \hyperpage{304}
  \item locally compact, \hyperpage{214}
  \item locally connected, \hyperpage{215}
  \item locally integrable, \hyperpage{79}
  \item locally Lipschitz continuous with respect to the second variable, 
		\hyperpage{124}
  \item locally path-connected, \hyperpage{216}
  \item locally topologically conjugate, \hyperpage{132}
  \item locally topologically equivalent, \hyperpage{132}
  \item LOF test, \hyperpage{254}
  \item log-likelihood function, \hyperpage{195}
  \item log-odds, \hyperpage{257}
  \item logarithm with base $a$, \hyperpage{29}
  \item Logarithmic test, \hyperpage{76}
  \item logistic map, \hyperpage{228}
  \item logit, \hyperpage{257}
  \item Longstaff-Schwartz method, \hyperpage{376}
  \item loop, \hyperpage{49}, \hyperpage{215}
  \item Lorenz system, \hyperpage{228}
  \item loss function, \hyperpage{203}
  \item lower bound, \hyperpage{25}
  \item lower integral, \hyperpage{32}, \hyperpage{58}
  \item lower limit topology, \hyperpage{206}
  \item lower sum, \hyperpage{32}, \hyperpage{58}
  \item lower triangular, \hyperpage{97}
  \item LRT, \hyperpage{200}
  \item LRT test statistic, \hyperpage{200}
  \item LU decomposition, \hyperpage{102}
  \item LU descompostion, \hyperpage{102}
  \item Lyapunov central limit theorem, \hyperpage{192}
  \item Lyapunov exponent, \hyperpage{337}
  \item Lyapunov function, \hyperpage{137}, \hyperpage{354}
  \item Lyapunov stable, \hyperpage{137}
  \item Lyapunov's method, \hyperpage{226}
  \item Lyapunov's theorem, \hyperpage{137}, \hyperpage{223}
  \item Lévy-Lindeberg central limit theorem, \hyperpage{192}

  \indexspace

  \item machine epsilon $\epsilon $, \hyperpage{89}
  \item Malgrange-Ehrenpreis theorem, \hyperpage{247}
  \item Mallow's $C_p$ statistic, \hyperpage{256}
  \item mantissa, \hyperpage{89}
  \item Marcinkiewicz interpolation theorem, \hyperpage{306}
  \item marginal pdf, \hyperpage{180}
  \item marginal pmf, \hyperpage{180}
  \item Marginal probability density functions, \hyperpage{180}
  \item marginal probability density functions, \hyperpage{180}
  \item Marginal probability mass functions, \hyperpage{180}
  \item marginal probability mass functions, \hyperpage{180}
  \item Markov chain, \hyperpage{318}
  \item Markov property, \hyperpage{318}
  \item Markov property for Brownian motion, \hyperpage{381}
  \item Markov's inequality, \hyperpage{185}
  \item Martingale, \hyperpage{381}
  \item martingale, \hyperpage{348}, \hyperpage{381}
  \item martingale term, \hyperpage{387}
  \item material derivative operator, \hyperpage{277}
  \item Matrix, \hyperpage{13}
  \item matrix, \hyperpage{13}, \hyperpage{18}
  \item matrix exponential, \hyperpage{127}
  \item matrix norm, \hyperpage{97}
  \item matrix of the bilinear form, \hyperpage{22}
  \item matrix solution, \hyperpage{127}
  \item maximal, \hyperpage{44}, \hyperpage{126}
  \item maximal element, \hyperpage{9}, \hyperpage{126}
  \item maximum likelihood estimator, \hyperpage{195}
  \item Maximum likelihood method, \hyperpage{195}
  \item Maximum metric, \hyperpage{205}
  \item Maximum modulus principle, \hyperpage{114}
  \item Maximum principle, \hyperpage{287}
  \item Maximum principle on unbounded domains, \hyperpage{287}
  \item Maxwell-Faraday equation, \hyperpage{278}
  \item mean, \hyperpage{178}
  \item mean curvature, \hyperpage{149}
  \item mean function, \hyperpage{330}
  \item mean square error, \hyperpage{251}
  \item mean squared error, \hyperpage{194}
  \item Mean value property, \hyperpage{115}
  \item Mean value theorem, \hyperpage{30}, \hyperpage{56}
  \item Mean value theorem for integrals, \hyperpage{95}, 
		\hyperpage{298}
  \item Mean value theorem for vector-valued functions, \hyperpage{56}
  \item mean vector, \hyperpage{181}, \hyperpage{196}
  \item measurable, \hyperpage{175}, \hyperpage{293, 294}, 
		\hyperpage{346}
  \item measurable space, \hyperpage{346}
  \item Measure, \hyperpage{291}, \hyperpage{346}
  \item measure, \hyperpage{174}, \hyperpage{291}, \hyperpage{346}
  \item measure of $A$, \hyperpage{341}
  \item measure of $U$, \hyperpage{341}
  \item measure on $\mathcal  {C}(\ensuremath  {\mathbb  {T}}^1)$, 
		\hyperpage{339}
  \item measure space, \hyperpage{175}, \hyperpage{346}
  \item Melnikov's method, \hyperpage{227}
  \item memoryless, \hyperpage{177, 178}
  \item meromorphic, \hyperpage{118}
  \item Mersenne Twister algorithm, \hyperpage{370}
  \item Mesh, \hyperpage{275}
  \item mesh, \hyperpage{275}, \hyperpage{382}
  \item mesh-points, \hyperpage{258}
  \item Method of characteristics, \hyperpage{279}
  \item Method of moments, \hyperpage{194}
  \item metric, \hyperpage{205}
  \item metric space, \hyperpage{53}, \hyperpage{205}, \hyperpage{300}
  \item metrizable, \hyperpage{187}, \hyperpage{212}
  \item Meusnier's theorem, \hyperpage{150}
  \item minimal, \hyperpage{221}, \hyperpage{341}
  \item minimal element, \hyperpage{9}
  \item minimal polynomial, \hyperpage{20}
  \item minimal surface, \hyperpage{149}
  \item minimizer, \hyperpage{311}
  \item Minimum modulus principle, \hyperpage{114}
  \item Minimum principle, \hyperpage{287}
  \item Minimum principle on unbounded domains, \hyperpage{288}
  \item minimum-variance unbiased estimator, \hyperpage{194}
  \item Minkowski inequality, \hyperpage{82}, \hyperpage{303}, 
		\hyperpage{310}
  \item Minkowski's integral inequality, \hyperpage{235}
  \item minor, \hyperpage{16}
  \item mirror of the reflection, \hyperpage{71}
  \item mixed random variable, \hyperpage{179}
  \item mixing, \hyperpage{336}
  \item MLE, \hyperpage{195}
  \item MLE method, \hyperpage{251}
  \item Model with interaction, \hyperpage{253}
  \item model with interaction, \hyperpage{253}
  \item Model without interaction, \hyperpage{253}
  \item modulus, \hyperpage{104}
  \item modulus of continuity, \hyperpage{55}
  \item Moment, \hyperpage{185}
  \item Moment of inertia, \hyperpage{59}
  \item moment of inertia, \hyperpage{59}
  \item Moment-generating function, \hyperpage{186}
  \item moment-generating function, \hyperpage{186}
  \item monic, \hyperpage{11}
  \item Monotone convergence theorem, \hyperpage{184}, \hyperpage{296}, 
		\hyperpage{346}
  \item monotonic, \hyperpage{26}, \hyperpage{28}
  \item monotonically decreasing, \hyperpage{26}
  \item monotonically increasing, \hyperpage{26}
  \item Montecarlo estimator, \hyperpage{370}
  \item Montel's theorem, \hyperpage{121}
  \item more efficient than, \hyperpage{194}
  \item Morera's theorem, \hyperpage{114}
  \item morphism of field extensions, \hyperpage{165}
  \item Morrey's embedding, \hyperpage{351}
  \item Mountain pass theorem, \hyperpage{368}
  \item MSE, \hyperpage{194}
  \item multi-index notation, \hyperpage{57}
  \item multicollinearity, \hyperpage{255}
  \item multilinear forms, \hyperpage{155}
  \item multilinear map, \hyperpage{155}
  \item Multinomial distrbution, \hyperpage{180}
  \item multinomial distribution, \hyperpage{180}
  \item multiple, \hyperpage{10}
  \item multiple control variate estimator, \hyperpage{372}
  \item multiple edges, \hyperpage{49}
  \item Multiple shooting method, \hyperpage{264}
  \item multiple shooting method, \hyperpage{264}
  \item multiplicative group, \hyperpage{43}
  \item multiplicity, \hyperpage{114}
  \item multistep, \hyperpage{268}
  \item multivalued function, \hyperpage{104}
  \item multivariate cdf, \hyperpage{181}
  \item multivariate cumulative distribution function, \hyperpage{181}
  \item Multivariate normal distribution, \hyperpage{181}
  \item multivariate normal distribution, \hyperpage{180}, 
		\hyperpage{196}
  \item multivariate standard deviation, \hyperpage{196}
  \item Multivariate standard normal distribution, \hyperpage{180}
  \item Multivariate uniform distribution, \hyperpage{180}
  \item multivariate uniform distribution, \hyperpage{180}
  \item MVUE, \hyperpage{194}
  \item Möbius band, \hyperpage{211}
  \item Möbius transformation, \hyperpage{119}
  \item Möbius transformations, \hyperpage{119}

  \indexspace

  \item naive approach, \hyperpage{375}
  \item Nart-Vila theorem, \hyperpage{171}
  \item Natural cubic spline, \hyperpage{94}
  \item natural filtration, \hyperpage{381}
  \item Navier-Cauchy equation, \hyperpage{277}
  \item negation, \hyperpage{8}
  \item negative, \hyperpage{141}
  \item negative basis, \hyperpage{142}
  \item Negative binomial distribution, \hyperpage{178}
  \item negative binomial distribution, \hyperpage{178}
  \item negative definite, \hyperpage{353}
  \item negative orbit, \hyperpage{340}
  \item negative part, \hyperpage{77}
  \item negative semi-orbit, \hyperpage{130}
  \item negative-definite, \hyperpage{23}
  \item negative-semidefinite, \hyperpage{23}
  \item negatively invariant, \hyperpage{131}, \hyperpage{340}
  \item negatively recurrent points, \hyperpage{340}
  \item negatively rotated, \hyperpage{227}
  \item negatively stable, \hyperpage{131}
  \item negatively-oriented, \hyperpage{142}
  \item Nehari manifold method, \hyperpage{367}
  \item neighbourhood, \hyperpage{25}, \hyperpage{54}, \hyperpage{207}
  \item Neumann, \hyperpage{274}
  \item Neumann boundary condition, \hyperpage{356}
  \item Neumann boundary conditions, \hyperpage{377}
  \item Neumann series, \hyperpage{307}
  \item Neville's algorithm, \hyperpage{93}
  \item Newton method, \hyperpage{262}, \hyperpage{264}
  \item Newton's divided differences\\method, \hyperpage{93}
  \item Newton-Raphson method, \hyperpage{90}
  \item Newton-Raphson modified method, \hyperpage{90}
  \item Neyman-Pearson lemma, \hyperpage{200}
  \item Neyman-Pearson test, \hyperpage{200}
  \item Neymann-Pearson test, \hyperpage{200}
  \item nilpotent, \hyperpage{14}, \hyperpage{224}
  \item Nilpotent singular points classification theorem, 
		\hyperpage{224}
  \item no-intercept, \hyperpage{252}
  \item nodal basis, \hyperpage{275}
  \item nodes, \hyperpage{275}
  \item Noetherian, \hyperpage{43}
  \item Non-Archimedean geometry, \hyperpage{66}
  \item non-autonomous, \hyperpage{122}
  \item non-degenerate, \hyperpage{74}
  \item non-degenerated, \hyperpage{227}
  \item non-Desarguesian planes, \hyperpage{68}
  \item non-divergence form, \hyperpage{356}
  \item Non-parametric bootstrap, \hyperpage{202}
  \item Non-Paschian geometry, \hyperpage{65}
  \item Non-SAS geometry, \hyperpage{66}
  \item non-singular, \hyperpage{131}
  \item non-wandering, \hyperpage{340}
  \item noncommutative ring, \hyperpage{42}
  \item nonsingular, \hyperpage{22}
  \item norm, \hyperpage{24}, \hyperpage{53}, \hyperpage{94}, 
		\hyperpage{300}, \hyperpage{305}
  \item norm associated with the inner product, \hyperpage{24}
  \item normal, \hyperpage{38}, \hyperpage{121}, \hyperpage{167}, 
		\hyperpage{191}, \hyperpage{212}
  \item normal closure, \hyperpage{167}
  \item Normal confidence interval, \hyperpage{202}
  \item normal confidence interval, \hyperpage{202}
  \item normal curvature, \hyperpage{150}
  \item Normal distribution, \hyperpage{178}
  \item normal distribution, \hyperpage{178}
  \item normal form, \hyperpage{223}
  \item Normal plane, \hyperpage{143}
  \item Normal Q-Q plots, \hyperpage{204}
  \item normal unit field, \hyperpage{149}
  \item normalized, \hyperpage{89}, \hyperpage{218}
  \item Normalized power method, \hyperpage{101}
  \item normalized power method, \hyperpage{101}
  \item normalizer, \hyperpage{41}
  \item normed algebra, \hyperpage{307}
  \item normed vector space, \hyperpage{53}, \hyperpage{300}
  \item not integrable, \hyperpage{182}
  \item not orientation-preserving, \hyperpage{217}
  \item Novikov's condition, \hyperpage{388}
  \item null hypothesis, \hyperpage{199}
  \item null recurrent, \hyperpage{324}
  \item null set, \hyperpage{174}, \hyperpage{293}
  \item number of steps, \hyperpage{268}
  \item numeric series, \hyperpage{76}
  \item numeric series of complex numbers, \hyperpage{105}
  \item numerical boundary condition, \hyperpage{272}
  \item numerically stable, \hyperpage{90}
  \item numerically unstable, \hyperpage{90}
  \item Nyquist-Shannon sampling theorem, \hyperpage{239}

  \indexspace

  \item objective function, \hyperpage{51}
  \item observed information, \hyperpage{195}
  \item odd extension, \hyperpage{84}
  \item odd periodic extension, \hyperpage{283}
  \item odds, \hyperpage{257}
  \item ode, \hyperpage{122}
  \item Olinde Rodrigues' theorem, \hyperpage{150}
  \item omega limit, \hyperpage{340}
  \item one-parameter family of rotated vector fields, \hyperpage{227}
  \item One-point compactification, \hyperpage{214}
  \item one-point compactification, \hyperpage{214}
  \item one-sided left tail test, \hyperpage{199}
  \item one-sided right tail test, \hyperpage{199}
  \item one-step, \hyperpage{268}
  \item one-step method, \hyperpage{258}
  \item open, \hyperpage{54}, \hyperpage{205}, \hyperpage{208}
  \item open ball, \hyperpage{54}
  \item open cover, \hyperpage{213}
  \item Open function, \hyperpage{208}
  \item Open interval, \hyperpage{25}
  \item Open mapping theorem, \hyperpage{116}, \hyperpage{309}
  \item open sets, \hyperpage{205}
  \item operator, \hyperpage{124}, \hyperpage{305}
  \item opposite orientations, \hyperpage{142}, \hyperpage{217}
  \item orbit, \hyperpage{8}, \hyperpage{40}, \hyperpage{130}, 
		\hyperpage{340}
  \item Orbit linear structure, \hyperpage{8}
  \item Orbit structure, \hyperpage{8}
  \item Orbit-stabilizer theorem, \hyperpage{40}
  \item Orbits formula, \hyperpage{40}
  \item order, \hyperpage{8}, \hyperpage{37}, \hyperpage{49}, 
		\hyperpage{116}, \hyperpage{259}
  \item Order axioms, \hyperpage{63}
  \item order of accuracy, \hyperpage{259}, \hyperpage{262}
  \item order of consistency, \hyperpage{259}, \hyperpage{262}
  \item Order of convergence, \hyperpage{91}
  \item order of convergence, \hyperpage{91}, \hyperpage{259}
  \item order of convergence at least $p$, \hyperpage{91}
  \item order relation, \hyperpage{63}
  \item order statistic, \hyperpage{196}
  \item order statistics, \hyperpage{196}
  \item ordered field, \hyperpage{25}, \hyperpage{64}
  \item ordinary differential equation, \hyperpage{122}
  \item ordinary generating function, \hyperpage{48}
  \item orientable, \hyperpage{149}, \hyperpage{158}, \hyperpage{217}
  \item orientation, \hyperpage{120}, \hyperpage{142}, \hyperpage{149}, 
		\hyperpage{217}
  \item orientation induced by $M$, \hyperpage{158}
  \item Orientation principle, \hyperpage{120}
  \item orientation-preserving, \hyperpage{142}, \hyperpage{217}
  \item oriented vector space, \hyperpage{142}, \hyperpage{217}
  \item origin, \hyperpage{70}
  \item orthogonal, \hyperpage{22--24}, \hyperpage{72}, \hyperpage{82}, 
		\hyperpage{148}, \hyperpage{310}
  \item orthogonal basis, \hyperpage{96}
  \item orthogonal complement, \hyperpage{22}, \hyperpage{310}
  \item orthogonal coordinates, \hyperpage{148}
  \item orthogonal geometry, \hyperpage{23}
  \item orthogonal group, \hyperpage{145}
  \item Orthogonal polynomials, \hyperpage{96}
  \item orthogonal projection, \hyperpage{23}
  \item orthogonal projection on $F$, \hyperpage{311}
  \item orthogonal reflections, \hyperpage{73}
  \item orthogonal system, \hyperpage{312}
  \item orthogonal with respect to the weight $\omega (x)$, 
		\hyperpage{96}
  \item Orthogonality of martingales, \hyperpage{382}
  \item orthonormal, \hyperpage{22}, \hyperpage{82}
  \item orthonormal system, \hyperpage{82}, \hyperpage{312}
  \item orthonormalization, \hyperpage{313}
  \item osculating circle, \hyperpage{144}
  \item Osculating plane, \hyperpage{143}
  \item osculating sphere, \hyperpage{144}
  \item Outer measure, \hyperpage{292}
  \item outer measure, \hyperpage{292}
  \item outliars, \hyperpage{255}
  \item Over-relaxation methods, \hyperpage{100}

  \indexspace

  \item Palais-Smale condition at level $c$, \hyperpage{368}
  \item Palais-Smale sequence, \hyperpage{368}
  \item Paley-Wiener-Zygmund theorem, \hyperpage{331}
  \item Pappus configuration, \hyperpage{68}
  \item PAQ reduction theorem, \hyperpage{14}
  \item parabolic, \hyperpage{273}
  \item parabolic boundary, \hyperpage{287}
  \item parabolic cylinder, \hyperpage{287}
  \item parabolic point, \hyperpage{150}
  \item parallel, \hyperpage{70}, \hyperpage{152}
  \item parallel transport, \hyperpage{152}
  \item Parallelogram law, \hyperpage{53}, \hyperpage{310}
  \item parameter set, \hyperpage{316}
  \item parameter space, \hyperpage{193}
  \item parametric, \hyperpage{193}
  \item Parametric bootstrap, \hyperpage{202}
  \item parametric bootstrap distribution, \hyperpage{202}
  \item parametric equations, \hyperpage{70}
  \item parametrization, \hyperpage{141}, \hyperpage{147}
  \item parametrized surface, \hyperpage{61}
  \item Parseval identity, \hyperpage{313}
  \item Parseval's identity, \hyperpage{87}
  \item partial derivative, \hyperpage{55}
  \item partial derivative of order $k$, \hyperpage{56}
  \item partial differential equation, \hyperpage{139}
  \item Partial fraction decomposition theorem, \hyperpage{117}
  \item partial inverse Fourier transform, \hyperpage{233}
  \item partial isometry, \hyperpage{384}
  \item partial order relation, \hyperpage{9}
  \item Partial pivoting, \hyperpage{102}
  \item partially ordered set, \hyperpage{9}
  \item Particular point topology, \hyperpage{206}
  \item partition, \hyperpage{32}, \hyperpage{58}, \hyperpage{174}
  \item partition of unity, \hyperpage{158}
  \item Pasch's axiom, \hyperpage{63}
  \item Passage from the affine plane to the projective plane, 
		\hyperpage{66}
  \item Passage from the projective plane to the affine plane, 
		\hyperpage{66}
  \item path, \hyperpage{49}, \hyperpage{215}
  \item path from $x$ to $y$, \hyperpage{215}
  \item path-connected, \hyperpage{215, 216}
  \item path-connected components, \hyperpage{216}
  \item PDE, \hyperpage{139}
  \item pdf, \hyperpage{178}
  \item Peano axioms, \hyperpage{6}
  \item Peano theorem, \hyperpage{125}
  \item Pearson correlation coefficient, \hyperpage{185}
  \item penalized norm, \hyperpage{353}
  \item Percentile confidence interval, \hyperpage{202}
  \item percentile confidence interval, \hyperpage{202}
  \item perfect, \hyperpage{166}
  \item Perfect fields, \hyperpage{166}
  \item period, \hyperpage{320}
  \item Period three theorem, \hyperpage{229}
  \item Period-doubling bifurcation, \hyperpage{229}
  \item period-doubling bifurcation, \hyperpage{229}
  \item period-doubling cascade, \hyperpage{229}
  \item period-halving bifurcation, \hyperpage{229}
  \item periodic, \hyperpage{131}
  \item periodic orbit of period $T$, \hyperpage{221}
  \item periodic point, \hyperpage{228}
  \item periodic with period $T$, \hyperpage{81}
  \item permutation matrix, \hyperpage{102}
  \item Perron-Frobenius theorem, \hyperpage{101}
  \item perspectivity, \hyperpage{69}
  \item pgf, \hyperpage{316}
  \item phase portrait, \hyperpage{130}
  \item phase space, \hyperpage{130}
  \item Picard iteration process, \hyperpage{125}
  \item Picard theorem, \hyperpage{125}
  \item PID, \hyperpage{44}
  \item piecewise linear manifold, \hyperpage{216}
  \item Pigeonhole principle, \hyperpage{10}
  \item Pitchfork bifurcation, \hyperpage{223}
  \item pitchfork bifurcation, \hyperpage{223}
  \item pivot, \hyperpage{198}
  \item Plancherel theorem, \hyperpage{236}, \hyperpage{238}, 
		\hyperpage{240}
  \item plane curve, \hyperpage{141}
  \item plane point, \hyperpage{150}
  \item Playfair's axiom, \hyperpage{63}
  \item Plücker coordinates, \hyperpage{69}
  \item pmf, \hyperpage{176}
  \item Poincaré compactification, \hyperpage{138}
  \item Poincaré disk, \hyperpage{138}
  \item Poincaré index formula, \hyperpage{139}
  \item Poincaré inequality, \hyperpage{289}
  \item Poincaré map, \hyperpage{136}
  \item Poincaré's inequality, \hyperpage{350}
  \item Poincaré's method, \hyperpage{226}
  \item Poincaré-Bendixson theorem, \hyperpage{136}
  \item Poincaré-Hopf theorem, \hyperpage{139}, \hyperpage{161}
  \item Poincaré-Hopf theorem on $S^2$, \hyperpage{139}
  \item Poincaré-Wirtinger's inequality, \hyperpage{350}
  \item points, \hyperpage{63}, \hyperpage{205}
  \item points of the quadric, \hyperpage{73}
  \item pointwise bounded, \hyperpage{125}, \hyperpage{304}
  \item pointwise equicontinuous, \hyperpage{125}, \hyperpage{304}
  \item Poisson distribution, \hyperpage{177}
  \item Poisson equation, \hyperpage{277}
  \item Poisson kernel, \hyperpage{231}, \hyperpage{234}
  \item Poisson process, \hyperpage{326}
  \item Poisson summation formula, \hyperpage{238}, \hyperpage{240}
  \item Polar form, \hyperpage{108}
  \item polar form, \hyperpage{108}
  \item Polar method, \hyperpage{371}
  \item Polarization identity, \hyperpage{310}
  \item Pole, \hyperpage{116}
  \item pole, \hyperpage{116}
  \item Polya's theorem on $\ensuremath  {\mathbb  {Z}}$, 
		\hyperpage{324}
  \item Polya's theorem on $\ensuremath  {\mathbb  {Z}}^2$, 
		\hyperpage{324}
  \item Polya's theorem on $\ensuremath  {\mathbb  {Z}}^3$, 
		\hyperpage{324}
  \item polyhedron, \hyperpage{51}
  \item polynomial, \hyperpage{11}
  \item polynomial ring, \hyperpage{162}
  \item polynomial system, \hyperpage{135}
  \item polynomial vector field, \hyperpage{135}
  \item polytope, \hyperpage{51}
  \item poset, \hyperpage{9}
  \item positive, \hyperpage{141}, \hyperpage{158}
  \item positive basis, \hyperpage{142}
  \item positive definite, \hyperpage{353}
  \item positive orbit, \hyperpage{340}
  \item positive part, \hyperpage{77}
  \item positive recurrent, \hyperpage{324}
  \item positive semi-orbit, \hyperpage{130}
  \item positive-definite, \hyperpage{23}
  \item positive-semidefinite, \hyperpage{23}
  \item positively invariant, \hyperpage{131}, \hyperpage{340}
  \item positively oriented, \hyperpage{142}
  \item positively recurrent points, \hyperpage{340}
  \item positively rotated, \hyperpage{227}
  \item positively stable, \hyperpage{131}
  \item posterior, \hyperpage{202}
  \item posterior distribution, \hyperpage{202}
  \item posterior mean, \hyperpage{203}
  \item posterior median, \hyperpage{203}
  \item posterior mode, \hyperpage{203}
  \item potential, \hyperpage{61}, \hyperpage{277}
  \item power, \hyperpage{199}
  \item power function, \hyperpage{199}
  \item Power method, \hyperpage{101}
  \item power method, \hyperpage{101}
  \item power series, \hyperpage{78}
  \item power set, \hyperpage{6}
  \item pre-Hilbert space, \hyperpage{310}
  \item precompact, \hyperpage{359}
  \item predicate, \hyperpage{6}
  \item prediction, \hyperpage{253}
  \item prediction band, \hyperpage{254}
  \item preditions, \hyperpage{250}
  \item preimage, \hyperpage{7}
  \item preserves orientation, \hyperpage{337}
  \item price of an American option, \hyperpage{375}
  \item primal, \hyperpage{51}
  \item prime, \hyperpage{10}, \hyperpage{12}, \hyperpage{44}
  \item Prime number theorem, \hyperpage{10}
  \item prime period, \hyperpage{228}
  \item primitive element, \hyperpage{164}
  \item Primitive element theorem, \hyperpage{168}
  \item primitive function, \hyperpage{33}
  \item primitive polynomial, \hyperpage{47}
  \item principal argument, \hyperpage{104}
  \item principal curvatures, \hyperpage{149}
  \item principal directons, \hyperpage{149}
  \item Principal ideal, \hyperpage{43}
  \item principal ideal, \hyperpage{43}
  \item principal ideal domain, \hyperpage{44}
  \item principal value, \hyperpage{108}
  \item Principle of least action, \hyperpage{279}
  \item prior, \hyperpage{202}
  \item prior distribution, \hyperpage{202}
  \item probability, \hyperpage{173}
  \item probability density function, \hyperpage{178}
  \item probability kernel, \hyperpage{348}
  \item Probability mass function, \hyperpage{176}
  \item probability mass function, \hyperpage{176}
  \item probability measure, \hyperpage{339}
  \item probability space, \hyperpage{173}, \hyperpage{347}
  \item probability-generating function, \hyperpage{316}
  \item product, \hyperpage{11}, \hyperpage{13}, \hyperpage{106}
  \item Product measure, \hyperpage{346}
  \item product measure, \hyperpage{346}
  \item product topology, \hyperpage{209}
  \item products of group subsets, \hyperpage{40}
  \item progressive, \hyperpage{385}
  \item projection, \hyperpage{71}
  \item Projection theorem, \hyperpage{311}
  \item Projections, \hyperpage{71}
  \item Projective axiom, \hyperpage{66}
  \item projective frame, \hyperpage{67}
  \item projective plane, \hyperpage{66}
  \item projective subvariety, \hyperpage{66}
  \item projectivity, \hyperpage{69}
  \item Propagation of absolute errors, \hyperpage{89}
  \item Propagation of relative errors, \hyperpage{89}
  \item proper, \hyperpage{37}
  \item proper subspace of $T$, \hyperpage{309}
  \item Properties of addition and scalar multiplication of matrices, 
		\hyperpage{13}
  \item Properties of homotheties, \hyperpage{72}
  \item Properties of matrix norms, \hyperpage{98}
  \item Properties of matrix product, \hyperpage{13}
  \item Properties of projections, \hyperpage{71}
  \item Properties of reflections, \hyperpage{71}
  \item Properties of translations, \hyperpage{71}
  \item Proximity theorem, \hyperpage{229}
  \item pull-back, \hyperpage{156}
  \item pure birth process, \hyperpage{329}
  \item pure death process, \hyperpage{329}
  \item purely inseparable, \hyperpage{168}
  \item purely transcendental, \hyperpage{165}
  \item push-forward measure, \hyperpage{339}
  \item Pythagorean, \hyperpage{64}
  \item Pythagorean plane, \hyperpage{64}
  \item Pythagorean theorem, \hyperpage{72}, \hyperpage{310}

  \indexspace

  \item Q-Q plots, \hyperpage{204}
  \item QR decomposition, \hyperpage{267}
  \item QR descompostion, \hyperpage{267}
  \item quadratic convergence, \hyperpage{91}
  \item quadratic form, \hyperpage{74}
  \item Quadratic loss function, \hyperpage{203}
  \item quadratic polynomial, \hyperpage{162}
  \item quadratic space, \hyperpage{74}
  \item Quadratic variation, \hyperpage{382}
  \item quadratic variation, \hyperpage{387}
  \item quadrature formula, \hyperpage{95}
  \item quadrature formula with weight $\omega (x)$, \hyperpage{97}
  \item quadric, \hyperpage{73}
  \item Quantile, \hyperpage{196}
  \item Quantile-Quantile plot, \hyperpage{204}
  \item quartic polynomial, \hyperpage{162}
  \item quasi-Newton method, \hyperpage{263}
  \item quasilinear PDE, \hyperpage{140}
  \item quaternion group, \hyperpage{42}
  \item Quotient group, \hyperpage{39}
  \item quotient group, \hyperpage{39}
  \item quotient map, \hyperpage{210}
  \item quotient space, \hyperpage{17}, \hyperpage{210}, 
		\hyperpage{301}
  \item quotient space of collapsing a set to a point, \hyperpage{211}
  \item quotient topology, \hyperpage{210}

  \indexspace

  \item Raabe's test, \hyperpage{76}
  \item radical, \hyperpage{22}, \hyperpage{170}
  \item radical tower, \hyperpage{170}
  \item radius of convergence, \hyperpage{108}
  \item radius of convergence of the power series, \hyperpage{79}
  \item radius of curvature, \hyperpage{144}
  \item radix-2 decimation-in-time (DIT) FFT, \hyperpage{240}
  \item Radix-2 DIT Cooley-Tukey FFT algorithm, \hyperpage{240}
  \item Radon-Nikodym, \hyperpage{347}
  \item Radó theorem, \hyperpage{218}
  \item random sample, \hyperpage{193}
  \item Random variable, \hyperpage{347}
  \item random variable, \hyperpage{175}
  \item random vector, \hyperpage{179}
  \item Random walk, \hyperpage{319}
  \item random walk, \hyperpage{319}
  \item Rank, \hyperpage{14}
  \item rank, \hyperpage{14}, \hyperpage{16}, \hyperpage{23}, 
		\hyperpage{74}
  \item Rankine-Hugoniot equation, \hyperpage{280}
  \item rate, \hyperpage{179}
  \item rate of convergence, \hyperpage{99}
  \item Ratio test, \hyperpage{26}, \hyperpage{76}
  \item ray, \hyperpage{63}
  \item Rayleigh quotient, \hyperpage{101}
  \item RC, \hyperpage{64}
  \item reachable, \hyperpage{320}
  \item real function, \hyperpage{294}
  \item real part, \hyperpage{104}
  \item real random variable, \hyperpage{175}
  \item realizable, \hyperpage{67}
  \item realization, \hyperpage{193}
  \item rearrangement of the sequence, \hyperpage{77}
  \item rearrangement of the series, \hyperpage{77}
  \item rectangle, \hyperpage{58}
  \item rectifiable, \hyperpage{34}, \hyperpage{60}, \hyperpage{141}
  \item Rectifying plane, \hyperpage{143}
  \item recurrence relation of order $k$, \hyperpage{48}
  \item recurrent, \hyperpage{48}, \hyperpage{322}, \hyperpage{324}
  \item Reduced row echelon form, \hyperpage{14}
  \item reduced row echelon form, \hyperpage{14}
  \item reducible, \hyperpage{100}
  \item Reducible linear ODE of second order, \hyperpage{123}
  \item reflection, \hyperpage{71}, \hyperpage{120}
  \item Reflections, \hyperpage{71}
  \item reflexive, \hyperpage{307, 308}
  \item refractive index, \hyperpage{278}
  \item region, \hyperpage{115}, \hyperpage{148}, \hyperpage{204}
  \item regression axis, \hyperpage{151}
  \item regression coefficients, \hyperpage{250}
  \item regression sum of squares, \hyperpage{252}
  \item regressor coefficients, \hyperpage{250}
  \item Regula falsi method, \hyperpage{90}
  \item regular, \hyperpage{49}, \hyperpage{58}, \hyperpage{131}, 
		\hyperpage{141}, \hyperpage{195, 196}, \hyperpage{212}, 
		\hyperpage{328}, \hyperpage{379}
  \item regular distributions, \hyperpage{241}
  \item regular domain, \hyperpage{148}
  \item regular region, \hyperpage{160}
  \item regular surface, \hyperpage{147}
  \item Regularity up to the boundary, \hyperpage{359}
  \item Reillich-Kondrachov's compactness theorem, \hyperpage{352}
  \item Related samples with unknown variances, \hyperpage{199}
  \item relative condition numbers, \hyperpage{90}
  \item relative error, \hyperpage{89}
  \item relatively compact, \hyperpage{121}, \hyperpage{304}
  \item relatively prime, \hyperpage{10, 11}
  \item relaxation factor, \hyperpage{100}
  \item Removable discontinuity, \hyperpage{28}
  \item Removable singularity, \hyperpage{116}
  \item removable singularity, \hyperpage{116}
  \item reordering, \hyperpage{106}
  \item reparametrization, \hyperpage{60}, \hyperpage{141}
  \item repelling, \hyperpage{131}
  \item repelling parabolic sector, \hyperpage{133}
  \item repulsor fixed point, \hyperpage{91}
  \item residuals, \hyperpage{250}
  \item residue, \hyperpage{116}
  \item Residues theorem, \hyperpage{117}
  \item resolvent set, \hyperpage{359}
  \item response, \hyperpage{253}
  \item restrictions, \hyperpage{51}
  \item Reuter criterion, \hyperpage{330}
  \item Riccati differential equation, \hyperpage{123}
  \item Richardson extrapolation, \hyperpage{95}, \hyperpage{260}
  \item Riemann conformal representation theorem, \hyperpage{121}
  \item Riemann sum, \hyperpage{34}, \hyperpage{58}
  \item Riemann's theorem, \hyperpage{77}
  \item Riemann's theorem on removable singularities, \hyperpage{116}
  \item Riemann-integrable, \hyperpage{58}
  \item Riemann-integrable function, \hyperpage{59}
  \item Riemann-Lebesgue lemma, \hyperpage{85}, \hyperpage{232}, 
		\hyperpage{238}
  \item Riesz representation theorem, \hyperpage{312}
  \item Riesz theorem, \hyperpage{248}
  \item Riesz transform, \hyperpage{248}
  \item Riesz's theorem, \hyperpage{306}
  \item Riesz-Fischer theorem, \hyperpage{313}
  \item right cosets, \hyperpage{39}
  \item Right side, \hyperpage{120}
  \item right singular vectors, \hyperpage{265}
  \item Right-open interval, \hyperpage{25}
  \item right-sided limit of $f$ at $x_0$, \hyperpage{27}
  \item Ring, \hyperpage{42}
  \item ring, \hyperpage{42}
  \item Ring morphism, \hyperpage{43}
  \item ring morphism, \hyperpage{43}
  \item risk-free interest rate, \hyperpage{375}
  \item RK methods, \hyperpage{260}
  \item Robin, \hyperpage{274}
  \item Robin boundary conditions, \hyperpage{377}
  \item Rogers's lemma, \hyperpage{376}
  \item Rolle's theorem, \hyperpage{30}
  \item Romberg Extrapolation, \hyperpage{373}
  \item Romberg method, \hyperpage{96}
  \item root, \hyperpage{12}
  \item root condition, \hyperpage{262}
  \item root of the reflection, \hyperpage{71}
  \item Root test, \hyperpage{26}, \hyperpage{76}
  \item rotation, \hyperpage{119}
  \item rotation number, \hyperpage{338, 339}
  \item Rouché's theorem, \hyperpage{119}
  \item Rouché-Frobenius theorem, \hyperpage{14}
  \item Routh-Hurwitz stability criterion, \hyperpage{227}
  \item Row echelon form, \hyperpage{14}
  \item row echelon form, \hyperpage{14}
  \item row rank, \hyperpage{16}
  \item Ruffini's rule, \hyperpage{12}
  \item ruled surface, \hyperpage{151}
  \item Runge's phenomenon, \hyperpage{94}
  \item Runge-Kutta-Fehlberg method, \hyperpage{260}

  \indexspace

  \item SAA criterion, \hyperpage{64}
  \item Saccheri-Legendre theorem, \hyperpage{64}
  \item saddle point, \hyperpage{57}, \hyperpage{133}
  \item saddle separatrices, \hyperpage{133}
  \item saddle-node, \hyperpage{224}
  \item Saddle-node bifurcation, \hyperpage{223}
  \item saddle-node bifurcation, \hyperpage{223}
  \item same orientation, \hyperpage{142}, \hyperpage{217}
  \item sample correlation coefficient, \hyperpage{249}
  \item sample covariance, \hyperpage{249}
  \item sample mean, \hyperpage{192, 193}
  \item sample quantiles, \hyperpage{204}
  \item Sample space, \hyperpage{173}
  \item sample space, \hyperpage{173}, \hyperpage{193}
  \item sample variance, \hyperpage{193}, \hyperpage{249}
  \item Sample variance and covariance, \hyperpage{249}
  \item SAS criterion, \hyperpage{63, 64}
  \item scalars, \hyperpage{15}
  \item scale, \hyperpage{179}
  \item Schaefer fixed point, \hyperpage{363}
  \item Schauder estimates, \hyperpage{361}
  \item Schauder fixed point, \hyperpage{363}
  \item Schrödinger equation, \hyperpage{279}
  \item Schwartz space, \hyperpage{243}
  \item Schwarz lemma, \hyperpage{120}
  \item Schwarz theorem, \hyperpage{243}
  \item Schwarz's theorem, \hyperpage{57}
  \item Schwarz-Pick lemma, \hyperpage{121}
  \item SCLF, \hyperpage{355}
  \item SCLF continuously at the origin, \hyperpage{355}
  \item score function, \hyperpage{195}
  \item Score test, \hyperpage{202}
  \item score test, \hyperpage{202}
  \item SDE, \hyperpage{389}
  \item Secant method, \hyperpage{90}
  \item secant-like method, \hyperpage{263}
  \item Second Borel-Cantelli lemma, \hyperpage{189}
  \item second derivative of $f$ at $a$, \hyperpage{31}
  \item second fundamental form, \hyperpage{150}
  \item Second isomorphism theorem, \hyperpage{18}, \hyperpage{40}, 
		\hyperpage{44}
  \item Second Sylow theorem, \hyperpage{41}
  \item section, \hyperpage{299}
  \item sectorial decomposition, \hyperpage{133}
  \item seed, \hyperpage{370}
  \item segment, \hyperpage{72}
  \item Segmented regression, \hyperpage{253}
  \item self-adjoint, \hyperpage{312}
  \item self-conjugate, \hyperpage{303}
  \item self-similar, \hyperpage{284}
  \item semi-conjugate, \hyperpage{339}
  \item Semi-hyperbolic singular points classification theorem, 
		\hyperpage{223}
  \item semi-stable, \hyperpage{136}
  \item semiaffinity, \hyperpage{70}
  \item Semidiscrete Fourier transform, \hyperpage{270}
  \item semidiscrete Fourier transform, \hyperpage{270}
  \item Semidiscrete Parseval identity, \hyperpage{270}
  \item semidynamical system, \hyperpage{130}
  \item semilinear, \hyperpage{310}
  \item semilinear isomorphism, \hyperpage{67}
  \item Seminorm, \hyperpage{308}
  \item seminorm, \hyperpage{94}, \hyperpage{308}
  \item sensitive dependence on initial conditions, \hyperpage{230}, 
		\hyperpage{337}
  \item Separability theorem, \hyperpage{168}
  \item separable, \hyperpage{168}, \hyperpage{301}
  \item Separable extension, \hyperpage{168}
  \item separate the points, \hyperpage{303}
  \item separated, \hyperpage{207}
  \item separated by closed neighbourhoods, \hyperpage{207}
  \item separating set, \hyperpage{303}
  \item Separation of variables, \hyperpage{123}, \hyperpage{283}
  \item separation of variables, \hyperpage{283}
  \item sequence, \hyperpage{54}
  \item sequence of complex functions, \hyperpage{106}
  \item sequence of complex numbers, \hyperpage{105}
  \item sequence of real functions, \hyperpage{77}
  \item sequence of real numbers, \hyperpage{26}
  \item series of functions, \hyperpage{78}, \hyperpage{107}
  \item set, \hyperpage{6}
  \item set difference, \hyperpage{6}
  \item set of interior vectors, \hyperpage{157}
  \item set of left cosets, \hyperpage{39}
  \item set of periodic points, \hyperpage{228}
  \item set of periods, \hyperpage{228}
  \item set of polynomials, \hyperpage{42}
  \item set of right cosets, \hyperpage{39}
  \item set of zero-content, \hyperpage{174}
  \item shape, \hyperpage{179}
  \item Sharkovskii's order, \hyperpage{229}
  \item Sharkovskii's theorem, \hyperpage{229}
  \item Shift map, \hyperpage{229}
  \item shift map, \hyperpage{229}, \hyperpage{335}
  \item Shooting method, \hyperpage{264}
  \item shooting method, \hyperpage{264}
  \item Sierpiński topology, \hyperpage{206}
  \item sign, \hyperpage{8}, \hyperpage{89}
  \item signature, \hyperpage{23}
  \item signed curvature, \hyperpage{145}
  \item significance level, \hyperpage{198, 199}
  \item significant, \hyperpage{89}
  \item similar, \hyperpage{20}, \hyperpage{71}
  \item similitude ratio of the homothety, \hyperpage{72}
  \item simple, \hyperpage{49}, \hyperpage{90}, \hyperpage{116}, 
		\hyperpage{164}, \hyperpage{170}, \hyperpage{199}
  \item simple curve, \hyperpage{218}
  \item simple function, \hyperpage{295}
  \item Simple model, \hyperpage{250}
  \item simple random sample, \hyperpage{193}
  \item simple random variable, \hyperpage{182}
  \item simple random walk, \hyperpage{319}
  \item Simple ratio, \hyperpage{72}
  \item simple ratio, \hyperpage{72}
  \item simple region, \hyperpage{160}
  \item Simplex method: Phase I, \hyperpage{51}
  \item Simplex method: Phase II, \hyperpage{51}
  \item simply connected, \hyperpage{116}, \hyperpage{216}
  \item simply normal, \hyperpage{191}
  \item Simpson's rule, \hyperpage{95}
  \item singular point, \hyperpage{131}, \hyperpage{160}
  \item Singular value, \hyperpage{265}
  \item Singular value decomposition, \hyperpage{265}
  \item singular value decomposition, \hyperpage{265}
  \item singular values, \hyperpage{265}
  \item sink, \hyperpage{133}
  \item size, \hyperpage{49}, \hyperpage{199}
  \item Skorokhod's representation theorem, \hyperpage{190}
  \item Slutsky's theorem, \hyperpage{190}
  \item small change, \hyperpage{279}
  \item Sobolev space, \hyperpage{289}
  \item Sobolev spaces, \hyperpage{350}
  \item solution, \hyperpage{90}, \hyperpage{139}
  \item solution of a system of equations, \hyperpage{13}
  \item solution of the ODE, \hyperpage{122}
  \item solution of the SDE, \hyperpage{389}
  \item solvable, \hyperpage{41}, \hyperpage{170}
  \item solvable by radicals, \hyperpage{170}
  \item SOR, \hyperpage{100}
  \item source, \hyperpage{133}
  \item space of rapidly decreasing functions, \hyperpage{243}
  \item special orthogonal group, \hyperpage{145}
  \item specific heat capacity, \hyperpage{278}
  \item spectral methods, \hyperpage{379}
  \item spectral radius, \hyperpage{98}
  \item Spectral theorem, \hyperpage{24}, \hyperpage{313}
  \item spectral values, \hyperpage{309}
  \item spectrum, \hyperpage{97}, \hyperpage{309}, \hyperpage{359}
  \item sphere, \hyperpage{54}
  \item Spline, \hyperpage{94}
  \item spline, \hyperpage{94}
  \item splits into linear factors, \hyperpage{167}
  \item Splitting field, \hyperpage{167}
  \item splitting field, \hyperpage{167}
  \item Squeeze theorem, \hyperpage{26}
  \item SSS criterion, \hyperpage{64}
  \item stability function, \hyperpage{261}
  \item stability number, \hyperpage{134}
  \item stability region, \hyperpage{261}, \hyperpage{268}
  \item stabilizer, \hyperpage{40}
  \item stable, \hyperpage{136}, \hyperpage{261}, \hyperpage{269}, 
		\hyperpage{273}, \hyperpage{328}, \hyperpage{353}
  \item stable degenerated node, \hyperpage{133}
  \item stable focus, \hyperpage{133}
  \item stable manifold, \hyperpage{222}
  \item stable node, \hyperpage{133}
  \item stable star, \hyperpage{133}
  \item standard, \hyperpage{330}
  \item standard $n$-simplex, \hyperpage{218}
  \item Standard deviation, \hyperpage{185}
  \item standard deviation, \hyperpage{178}, \hyperpage{185}
  \item standard error, \hyperpage{185}
  \item standard form, \hyperpage{51}
  \item Standard normal distribution, \hyperpage{178}
  \item standard normal distribution, \hyperpage{178}
  \item standardized form, \hyperpage{179}
  \item star domain, \hyperpage{115}
  \item state space, \hyperpage{316}, \hyperpage{318}
  \item states, \hyperpage{318}
  \item stationary distribution, \hyperpage{325}, \hyperpage{329}
  \item stationary increments, \hyperpage{326}
  \item Statistic, \hyperpage{193}
  \item statistic, \hyperpage{193}
  \item statistical model, \hyperpage{193}
  \item Steepest descent, \hyperpage{264}
  \item Steffensen's method, \hyperpage{92}
  \item Steinitz exchange lemma, \hyperpage{16}
  \item Steinitz's theorem, \hyperpage{164}
  \item step size, \hyperpage{258}, \hyperpage{264}
  \item Stereographic projection, \hyperpage{105}
  \item stereographic projection, \hyperpage{105}
  \item stiff equations, \hyperpage{261}
  \item stiffness matrix, \hyperpage{276}
  \item Stirling's formula, \hyperpage{81}
  \item stochastic differential, \hyperpage{387}
  \item stochastic differential equation, \hyperpage{389}
  \item Stochastic dominated convergence theorem, \hyperpage{386}
  \item Stochastic integration by parts, \hyperpage{388}
  \item Stochastic matrix, \hyperpage{318}
  \item stochastic matrix, \hyperpage{318}
  \item Stochastic process, \hyperpage{316}
  \item stochastic process, \hyperpage{316}
  \item stochastically equivalent, \hyperpage{331}
  \item Stokes theorem, \hyperpage{159}
  \item Stokes' theorem, \hyperpage{62}
  \item Stolz-Cesàro theorem, \hyperpage{27}
  \item Stone-Weierstra\ss \ theorem, \hyperpage{304}
  \item stopped process, \hyperpage{348}, \hyperpage{382}
  \item stopping time, \hyperpage{321}, \hyperpage{348}
  \item strict Lyapunov function, \hyperpage{137}
  \item strictly concave, \hyperpage{30}
  \item strictly control Lyapunov function, \hyperpage{355}
  \item strictly convex, \hyperpage{30}
  \item strictly decreasing, \hyperpage{26}, \hyperpage{28}
  \item strictly diagonally dominant by columns, \hyperpage{99}
  \item strictly diagonally dominant by rows, \hyperpage{99}
  \item strictly increasing, \hyperpage{26}, \hyperpage{28}
  \item Strong duality theorem, \hyperpage{52}
  \item Strong error of the Euler scheme, \hyperpage{373}
  \item Strong law of large numbers, \hyperpage{191}
  \item Strong law of large numbers for Brownian motion, 
		\hyperpage{381}
  \item Strong Markov property, \hyperpage{321, 322}
  \item Strong maximum principle, \hyperpage{362}
  \item Strong minimum principle, \hyperpage{362}
  \item strong solution, \hyperpage{356}
  \item strongly consistent estimator, \hyperpage{194}
  \item strongly lower-semicontinuous, \hyperpage{349}
  \item Structal stability, \hyperpage{336}
  \item Strum's sequence, \hyperpage{92}
  \item Student's $t$-distribution with $n$ degrees of freedom, 
		\hyperpage{197}
  \item Sturm's sequence, \hyperpage{92}
  \item Sturm's theorem, \hyperpage{92}
  \item Sturm-Picone comparison theorem, \hyperpage{283}
  \item sub-martingale, \hyperpage{381}
  \item sub-multiplicativity, \hyperpage{97}
  \item subadditive, \hyperpage{338}
  \item subalgebra, \hyperpage{303}
  \item subbasis, \hyperpage{206}
  \item subcover, \hyperpage{213}
  \item subdivision, \hyperpage{378}
  \item subfield generated, \hyperpage{163}
  \item Subgroup, \hyperpage{37}
  \item subgroup, \hyperpage{37}
  \item subgroup generated, \hyperpage{37}
  \item sublinear, \hyperpage{305}
  \item submanifold, \hyperpage{146}
  \item submanifold with boundary, \hyperpage{157}
  \item submartingale, \hyperpage{348}
  \item Submersion, \hyperpage{146}
  \item submersion, \hyperpage{146}
  \item subordinated matrix norm, \hyperpage{97}
  \item Subring, \hyperpage{42}
  \item subring, \hyperpage{42}
  \item subring generated, \hyperpage{163}
  \item Subsequence, \hyperpage{26}
  \item subsequence, \hyperpage{26}
  \item subset, \hyperpage{6}
  \item subspace topology, \hyperpage{208}
  \item Substitution principle, \hyperpage{315}
  \item success, \hyperpage{177}
  \item Successive over-relaxation \\method, \hyperpage{100}
  \item Successive over-relaxation method, \hyperpage{100}
  \item sufficient, \hyperpage{194}
  \item sum, \hyperpage{11}, \hyperpage{13}, \hyperpage{16}, 
		\hyperpage{70}
  \item sum of the series, \hyperpage{76}, \hyperpage{106}
  \item sum of the series in a pointwise sense, \hyperpage{78}, 
		\hyperpage{107}
  \item sum of the series in an uniform sense, \hyperpage{78}, 
		\hyperpage{107}
  \item super-martingale, \hyperpage{381}
  \item superadditive, \hyperpage{338}
  \item supermartingale, \hyperpage{348}
  \item Superposition operator, \hyperpage{365}
  \item superposition operator, \hyperpage{365}
  \item superquadradicity condition, \hyperpage{368}
  \item support, \hyperpage{8}, \hyperpage{79}, \hyperpage{146}, 
		\hyperpage{176}, \hyperpage{180}, \hyperpage{242}
  \item support of $\mu $, \hyperpage{341}
  \item support plane, \hyperpage{349}
  \item support points, \hyperpage{93}
  \item supremum, \hyperpage{25}
  \item Supremum axiom, \hyperpage{25}
  \item supremum norm, \hyperpage{303}
  \item surface, \hyperpage{58}, \hyperpage{147}, \hyperpage{217}
  \item surface integral, \hyperpage{61, 62}
  \item surface intergal, \hyperpage{159}
  \item Surface of revolution, \hyperpage{34}
  \item surface of revolution, \hyperpage{147}
  \item surjective, \hyperpage{7}, \hyperpage{121}
  \item SVD, \hyperpage{265}
  \item Sylow $p$-subgroup, \hyperpage{41}
  \item Sylvester's criterion, \hyperpage{58}
  \item Sylvester's law of inertia, \hyperpage{23}
  \item symmetric, \hyperpage{22}, \hyperpage{62}, \hyperpage{356}
  \item Symmetric difference formula of order 1, \hyperpage{95}
  \item Symmetric difference formula of order 2, \hyperpage{95}
  \item symmetric group, \hyperpage{8}, \hyperpage{38}
  \item symmetric polynomial, \hyperpage{163}
  \item Symmetric polynomials, \hyperpage{163}
  \item symmetric with respect to the $x$-axis, \hyperpage{221}
  \item symmetric with respect to the $y$-axis, \hyperpage{221}
  \item Symmetry principle, \hyperpage{120}
  \item system of linear differential equations, \hyperpage{126}
  \item system of linear equations, \hyperpage{13}
  \item system of ordinary differential equations, \hyperpage{122}

  \indexspace

  \item tangent, \hyperpage{154}, \hyperpage{156}
  \item tangent function, \hyperpage{148}
  \item tangent line, \hyperpage{141}, \hyperpage{144}
  \item tangent line to the graph at the point $(x_0,f(x_0))$, 
		\hyperpage{29}
  \item tangent plane, \hyperpage{147}
  \item tangent process, \hyperpage{374}
  \item tangent space, \hyperpage{147}, \hyperpage{156, 157}
  \item tangent vector, \hyperpage{141}, \hyperpage{147}, 
		\hyperpage{156}
  \item tangent vector field, \hyperpage{139}
  \item Taxicab metric, \hyperpage{205}
  \item Taylor method, \hyperpage{259}
  \item Taylor method of order $r$, \hyperpage{259}
  \item Taylor polynomial of order $n$ of $f$ centered at $a$, 
		\hyperpage{31}
  \item Taylor's theorem, \hyperpage{57}
  \item tempered distribution, \hyperpage{244}
  \item tends to the boundary, \hyperpage{126}
  \item terminal point, \hyperpage{215}
  \item test, \hyperpage{200}
  \item test functions, \hyperpage{240}
  \item Test of homogenity, \hyperpage{201}
  \item Test of independence, \hyperpage{201}
  \item test problem, \hyperpage{261}
  \item test statistic, \hyperpage{199}
  \item the Best Linear Unbiased Estimator, \hyperpage{251}
  \item The center manifold theorem, \hyperpage{223}
  \item The stable manifold theorem, \hyperpage{222}
  \item theorem, \hyperpage{67}
  \item theoretical quantiles, \hyperpage{204}
  \item thermal conductivity, \hyperpage{278}
  \item thermal diffusivity, \hyperpage{278}
  \item thin QR decomposition, \hyperpage{267}
  \item Third isomorphism theorem, \hyperpage{18}, \hyperpage{40}, 
		\hyperpage{44}
  \item Third Sylow theorem, \hyperpage{41}
  \item Tietze extension theorem, \hyperpage{212}
  \item time-homogeneous Markov chain, \hyperpage{318}
  \item TNB frame, \hyperpage{143}
  \item tolerance, \hyperpage{255}
  \item Tonelli's theorem, \hyperpage{175}, \hyperpage{299}
  \item topological embedding, \hyperpage{214}
  \item topological homeomorphism, \hyperpage{306}
  \item Topological manifold, \hyperpage{216}
  \item topological manifold, \hyperpage{216}
  \item topological property, \hyperpage{213}
  \item Topological space, \hyperpage{205}
  \item topological space, \hyperpage{205}
  \item topological subspace, \hyperpage{208}
  \item topologically conjugate, \hyperpage{132}
  \item topologically equivalent, \hyperpage{131}
  \item topologically transitive, \hyperpage{230}
  \item topology, \hyperpage{205}
  \item topology generated, \hyperpage{206}
  \item Topology induced from the metric, \hyperpage{205}
  \item torsion, \hyperpage{143}
  \item Torus, \hyperpage{210}
  \item torus, \hyperpage{210}
  \item total mean of squares, \hyperpage{252}
  \item total order relation, \hyperpage{9}
  \item total subset, \hyperpage{301}
  \item total sum of squares, \hyperpage{252}
  \item totally disconnected, \hyperpage{215}
  \item totally isotropic, \hyperpage{74}
  \item Tower formula, \hyperpage{165}
  \item tower of fields, \hyperpage{165}
  \item Tower property, \hyperpage{348}
  \item trace, \hyperpage{141}, \hyperpage{289}
  \item trace operator, \hyperpage{352}
  \item Trace theorem, \hyperpage{289}
  \item Traffic flow equation, \hyperpage{280}
  \item trail, \hyperpage{49}
  \item trajectories, \hyperpage{326}
  \item transcendental, \hyperpage{164}
  \item Transcritical bifurcation, \hyperpage{223}
  \item transcritical bifurcation, \hyperpage{223}
  \item transient, \hyperpage{322}, \hyperpage{324}
  \item transition functions, \hyperpage{216}
  \item transition matrix, \hyperpage{318}
  \item transition probabilities, \hyperpage{318}, \hyperpage{326}
  \item transitive, \hyperpage{169}
  \item translation, \hyperpage{71}, \hyperpage{119}
  \item Translations, \hyperpage{71}
  \item transpose, \hyperpage{14}
  \item Transposition, \hyperpage{14}
  \item transposition, \hyperpage{8}
  \item transversal section, \hyperpage{132}
  \item Trapezoidal method, \hyperpage{259}
  \item Trapezoidal rule, \hyperpage{95}
  \item traversable, \hyperpage{50}
  \item tree, \hyperpage{50}
  \item trial functions, \hyperpage{379}
  \item triangle, \hyperpage{160}
  \item Triangular inequality, \hyperpage{25}, \hyperpage{72}
  \item triangular inequality, \hyperpage{53}, \hyperpage{205}, 
		\hyperpage{300}
  \item triangular system, \hyperpage{97}
  \item triangularization, \hyperpage{218}
  \item triangulation, \hyperpage{378}
  \item triple, \hyperpage{90}
  \item trivial $\sigma $-algebra, \hyperpage{172}
  \item Trivial topology, \hyperpage{206}
  \item true, \hyperpage{177}
  \item truncated, \hyperpage{266}
  \item truncated Hilbert transform, \hyperpage{247}
  \item truncated singular value decomposition, \hyperpage{266}
  \item Tsitsiklis-Van Roy method, \hyperpage{375}
  \item TSVD, \hyperpage{266}
  \item two times differentiable, \hyperpage{31}
  \item two times differentiable at $a$, \hyperpage{31}
  \item two-sided test, \hyperpage{200}
  \item Tychonoff's theorem, \hyperpage{213}

  \indexspace

  \item UFD, \hyperpage{45}
  \item umbilic point, \hyperpage{149}
  \item UMP, \hyperpage{200}
  \item unbiased estimator, \hyperpage{193}
  \item Uncertainty principle, \hyperpage{238}
  \item Uncertainty principle in $\ensuremath  {\mathbb  {R}}^n$, 
		\hyperpage{238}
  \item unconditionally absolutely stable, \hyperpage{261}
  \item unconditionally convergent, \hyperpage{268}
  \item uncorrelated, \hyperpage{185}
  \item uncountable, \hyperpage{25}
  \item Unicity of the splitting field, \hyperpage{167}
  \item uniform norm, \hyperpage{301}, \hyperpage{303}
  \item uniformly bounded, \hyperpage{125}, \hyperpage{304}
  \item uniformly continuous, \hyperpage{33}, \hyperpage{55}
  \item uniformly convergent, \hyperpage{117}
  \item uniformly elliptic, \hyperpage{356}
  \item uniformly equicontinuous, \hyperpage{125}, \hyperpage{304}
  \item uniformly integrable, \hyperpage{348}
  \item uniformly most powerful, \hyperpage{200}
  \item union, \hyperpage{6}
  \item unique factorization domain, \hyperpage{45}
  \item uniquely ergodic, \hyperpage{342}
  \item Uniqueness of Dirichlet problem, \hyperpage{288}
  \item Uniqueness of the heat equation, \hyperpage{287}
  \item Uniqueness of the heat equation on the unbounded domains, 
		\hyperpage{288}
  \item unit, \hyperpage{43}
  \item unit normal exterior vector field, \hyperpage{158}
  \item unit normal vector, \hyperpage{143}
  \item unit-speed parametrization, \hyperpage{141}
  \item Universal property of polynomials, \hyperpage{45}
  \item Universal property of polynomials in several variables, 
		\hyperpage{45}, \hyperpage{162}
  \item Universal property of the field of fractions, \hyperpage{163}
  \item unknowns, \hyperpage{13}
  \item unoriented vector space, \hyperpage{142}, \hyperpage{217}
  \item unstable, \hyperpage{136}
  \item unstable degenerated node, \hyperpage{133}
  \item unstable focus, \hyperpage{133}
  \item unstable manifold, \hyperpage{222}
  \item unstable node, \hyperpage{133}
  \item unstable star, \hyperpage{133}
  \item upper bound, \hyperpage{25}, \hyperpage{126}
  \item upper integral, \hyperpage{32}, \hyperpage{58}
  \item upper sum, \hyperpage{32}, \hyperpage{58}
  \item upper triangular, \hyperpage{97}
  \item upwind condition, \hyperpage{269}
  \item Urysohn's lemma, \hyperpage{212}
  \item Urysohn's metrization theorem, \hyperpage{212}

  \indexspace

  \item Van der Pol oscillator, \hyperpage{228}
  \item vanishes nowhere, \hyperpage{303}
  \item variable, \hyperpage{11}
  \item variables, \hyperpage{13}
  \item Variacions with repetition, \hyperpage{10}
  \item Variance, \hyperpage{185}
  \item variance, \hyperpage{178}, \hyperpage{185}
  \item variance inflation factor, \hyperpage{255}
  \item Variation of constants, \hyperpage{123}
  \item variational equations, \hyperpage{129}
  \item variational formulation, \hyperpage{275}, \hyperpage{356}
  \item Variations without repetition, \hyperpage{10}
  \item vector field, \hyperpage{60}, \hyperpage{152}, \hyperpage{154}, 
		\hyperpage{156}
  \item vector space, \hyperpage{15}
  \item vector space of polynomials with real coefficients and degree less than or equal to $n$, 
		\hyperpage{93}
  \item vector subspace, \hyperpage{16}
  \item vectors, \hyperpage{15}
  \item version, \hyperpage{331}
  \item vertices, \hyperpage{160}
  \item VIF, \hyperpage{255}
  \item Viscid flow, \hyperpage{277}
  \item Volterra operator with kernel $K$, \hyperpage{307}
  \item volume, \hyperpage{175}, \hyperpage{291}
  \item volume element, \hyperpage{156}, \hyperpage{158}
  \item Volume of revolution, \hyperpage{34}

  \indexspace

  \item Wald test, \hyperpage{201}
  \item Wald theorem, \hyperpage{315}
  \item walk, \hyperpage{49}
  \item wandering domain, \hyperpage{340}
  \item wandering point, \hyperpage{340}
  \item Waring's method, \hyperpage{164}
  \item Wave equation, \hyperpage{140}, \hyperpage{277}
  \item wave equation, \hyperpage{140}
  \item wave function, \hyperpage{279}
  \item Weak duality theorem, \hyperpage{51}
  \item Weak error of the Euler scheme, \hyperpage{373}
  \item weak formulation, \hyperpage{275}, \hyperpage{356}
  \item Weak law of large numbers, \hyperpage{190}
  \item Weak maximum principle, \hyperpage{360, 361}
  \item Weak minimum principle, \hyperpage{360}, \hyperpage{362}
  \item weak solution, \hyperpage{356}
  \item weak-* lower-semicontinuity, \hyperpage{349}
  \item weakly consistent estimator, \hyperpage{194}
  \item weakly lower-semicontinuity, \hyperpage{349}
  \item Weierstra\ss ' theorem, \hyperpage{55}, \hyperpage{114}, 
		\hyperpage{214}
  \item Weierstra\ss \ approximation theorem, \hyperpage{79}
  \item Weierstra\ss \ kernel, \hyperpage{234}
  \item Weierstra\ss \ M-test, \hyperpage{78}, \hyperpage{107}
  \item Weierstra\ss \ theorem, \hyperpage{28}
  \item Weingarten endomorphsim, \hyperpage{149}
  \item well-conditioned, \hyperpage{90}
  \item well-order relation, \hyperpage{9}
  \item well-ordered set, \hyperpage{9}
  \item well-posed, \hyperpage{258}
  \item well-posed in the Hadamard sense, \hyperpage{258}
  \item Wiener integral, \hyperpage{384}
  \item Wiener isometry, \hyperpage{384}
  \item Wiener process, \hyperpage{330}
  \item winding number, \hyperpage{113}
  \item Wintner lemma, \hyperpage{126}
  \item Wirtinger operators, \hyperpage{111}
  \item Wirtinger's inequality, \hyperpage{87, 88}
  \item With constraints, \hyperpage{364}
  \item Without constraints, \hyperpage{364}, \hyperpage{366}
  \item Witt's theorem, \hyperpage{74}

  \indexspace

  \item Young's convolution inequality, \hyperpage{237}
  \item Young's inequality for products, \hyperpage{302}

  \indexspace

  \item zero, \hyperpage{90}
  \item zero divisor, \hyperpage{44}
  \item zero of multiplicity $m\in \ensuremath  {\mathbb  {N}}$, 
		\hyperpage{90}
  \item Zero-one loss function, \hyperpage{203}
  \item zero-stable, \hyperpage{262}
  \item Zorn's lemma, \hyperpage{126}

\end{theindex}