DeepNLP Equation is a repo/website (http://www.deepnlp.org/equation) to host latex code and text explanation of equations in all science and quantitative fields. We will continue to collect and grow the size of resources and hopefully this repo of resources can be helpful to research and development of large language model, machine learning and AI4Science communities.
Maxwell Equations Integral
Fourier Series：
Fourier Transforms
Lorentz Transformation Latex
Red and Blue Shift
Stress-energy Tensor
General Relativity
Riemannian Tensor
Einstein Field Equations
Electric Oscillations
Harmonic Oscillations
Mechanic Oscillations
Waves In Long Conductors
Amplitude of a driven oscillation
Coupled Conductors and Transformers
Pendulums
Angular frequency for a damped oscillation
Wave Equation
Plane Waves
Spherical Waves
Cylindrical Waves
The general solution of Wave Equation
The Stationary Phase Method Wave Equation
Green functions for the initial-value problem
Waveguides and resonating cavities
Non-linear Wave Equation
Bending of light Snell's law
Bending of light Fermat's principle
Optics Paraxial Geometrical
Mirrors
Optics Principal Planes
Optics Magnification
Optical System Matrix Methods
Reflection and Transmission
Fresnel Equations
Optics Polarization
Prisms and Dispersion
Diffraction
Birefringence and Dichroism
Fabry Perot Interferometer
Angular frequency for a damped oscillation
Displacement of a driven oscillator
Thermodynamics Statistical Basis
Thermodynamics Ideal Mixtures
Thermodynamics Definitions
Thermal Heat Capacity
Thermodynamics Conservation of Energy
Thermodynamics Nernst Law
State functions Maxwell Relations
Reversible Adiabatic Processes
Isobaric Processes
Throttle Processes
The Carnot Cycle
Phase Transitions
Thermodynamic Potential
Displacement of a slightly damped oscillator
Energy change in a damped oscillation
Energy transmitted by a harmonic wave
Harmonic Wave Function
Phase constant of a driven oscillation
Angular Momentum
Average Acceleration
Bulk Modulus
Centripetal Acceleration
Mechanics Compressibility
Mechanics Continuity Equation
Mechanics Displacement
Newton Second Law Force
Shear Modulus
Simple Harmonic Motion Acceleration
Speed of Sound Waves in a Fluid
Mechanics Stress
Velocity
Viscous Flow
Youngs Modulus
Black Body Radiation
The Compton Effect
Quantum Wave Functions
Operators in Quantum Physics
The Uncertainty Principle
The Schrödinger Equation
Parity
The Tunnel Effect
Harmonic Oscillator Quantum
Kullback-Leibler Divergence
KL-Divergence
Support Vector Machine SVM
Bellman Equation
Jensen-Shannon Divergence JS-Divergence
Energy and Principal Quantum Number
Radii of stable orbits in Bohr model
Rydberg Equation
Speed of Light
List of Math Calculus and Linear Algebra Equations
Maxwell Equations Integral
Taylor Series
Maclaurin Series
Determinants of a Matrix
Eigenvalues and Eigenvectors
Fourier Series
Laplace Transform
Fourier Transforms
Regression Least Squares Fitting
General Relativity
Arithmetic and Geometric Progressions
Convergence of Series
Binomial Expansion
Power Series with Real Variables
Plane Wave Expansion
Diffusion Conduction Equation
Wave Equation
Heat Equation
Laplace Equation
Legendre Equation
Bessel Equation
Spherical Harmonics Equation
Complex Numbers
De Moivre's Theorem
Power Series for Complex Variables
Electric Oscillations
Mechanic Oscillations
Waves In Long Conductors
Pendulums
Average Treatment Effect ATE
Conditional Average Treatment Effect CATE
S-Learner
T-Learner
gaussian process
Diffusion Model Forward Process
Diffusion Model Reverse Process
Diffusion Model Variational Lower Bound
Diffusion Model Variational Lower Bound Loss
Generative Adversarial Networks GAN
Variational AutoEncoder VAE
Maximum Mean Discrepancy MMD
TransE
Graph Laplacian
Graph Convolutional Networks GCN
GraphSage
Graph Attention Network GAT
Model-Agnostic Meta-Learning MAML
Domain Adaptation H-Divergence
Bound on Target Domain Error
Domain-Adversarial Neural Networks DANN
Equation of Exchange
Ito Lemma
Geometric Brownian Motion SDEs
Stock Prices as Geometric Brownian Motion
Sharpe Ratio
Risk-Neutral Valuation and Power Contracts
Cox-Ingersoll-Ross CIR
Gamma Distribution
Fisher Skewness
Binomial Distribution
Poisson Distribution
Normal Gaussian Distribution
Exponential Distribution
Area of a Circle
Area of a Parallelogram
Area of a Rectangle
Area of a Regular Polygon
Area of a Rhombus
Area of a Square
Area of a Sector
Area of a Trapezoid
Area of a Triangle
Area of a Ellipse
Surface area of a cube
Area of a Equilateral Triangle
Surface area of a Cuboid
Surface area of a cylinder
Surface area of a Sphere
Cartesian to Cylindrical Coordinates
Cartesian to Spherical Coordinates
Cartesian to Polar Coordinates
Cylindrical to Spherical Coordinates
Distance Between Two Points 2D
Distance Between Two Points 3D
Eccentricity of a Hyperbola
Eccentricity of an Ellipse
Circle
Hyperbolic Paraboloid
Hyperbola
Parabola
Plane
Sphere
Ellipse
Elliptic Cone
Ellipsoid
Elliptic Cylinder
Spiral of Archimedes
Elliptic Paraboloid
Uniform Distribution
Beta Distribution
Bernoulli Distribution
Geometric Distribution
Beta Binomial Distribution
Poisson Binomial Distribution
Chi-Squared Distribution
Gumbel Distribution
Student t-Distribution
Laplace Distribution
List of Machine Learning Equation
Language Modelling
LORA Low Rank Adaptation
PPO Proximal Policy Optimization
DPO Direct Policy Optimization
Perplexity of LM
Transformer
GAN Generative Adversarial Networks
VAE Variational Autoencoder
CRF Conditional Random Field
HMM Hidden Markov Model
Diffusion Model Forward Process
Diffusion Model Forward Process Reparameterization
Diffusion Model Reverse Process
Diffusion Model Variational Lower Bound
Diffusion Model Variational Lower Bound Loss
GCN graph convolutional network
GAT graph attention network
GraphSage
KL Divergence
Huber Loss
Support Vector Machine
MAE Mean Absolute Error
MSE Mean Squared Error
MAML Model Agnostic Meta Learning
Bregman Divergences
MMOE Multi Gate Mixture of Experts
Progressive Layered Extraction
AUUC Area Under Uplift Curve
S Learner
T Learner
Propensity Score
QINI Coefficient
List of Economics and Financial Engineering Equation
Simple Interest
Compound Interest
Effective Rate
Future Value of Ordinary Annuities
Present Value of Ordinary Annuities
Annuities Due
Allocative Efficiency Condition
Average Fixed Cost
Average Product
Average Total Cost
Average Revenue
Average Variable Cost
Cross-Price Elasticity of Demand
Elasticity of Supply
Marginal Revenue Product
Factor of Production Hiring Rule
Marginal Cost
Marginal Product of Labor
Marginal Factor Cost MFC
Marginal Revenue
Marginal Revenue Product of Labor MRPL
Optimal Combination of Resources Condition
Price Elasticity of Demand
Optimal Consumption Rule
Price for a Competitive Firm
Production Efficiency Condition
Profit
Slope of the Total Product Curve
Profit-Maximizing Output Level
Socially Optimal Level of Output
Total Costs
Distributive Efficiency Condition
Gini Coefficient
Investment
Autonomous Spending Multiplier
Balanced Budget Multiplier
Banks Reserve Ratio
Consumption Function
Consumer Price Index CPI
Equality of Leakages and Injections
Equation of Exchange
Gross Domestic Product Deflator
Merchandise Trade Balance
Nominal Interest Rate
Real GDP
Real Interest Rate
Tax Multiplier
Unemployment Rate
Forwards
Put-Call Parity
Calls and Puts with Different Strikes
Calls and Puts Arbitrage
Call and Put Price Bounds
Varying Times to Expiration
Early Exercise for American Options
Standard Brownian Motion
Geometric Brownian Motion
Ito Lemma
Geometric Brownian Motion SDEs
Stock Prices as Geometric Brownian Motion
Sharpe Ratio
Risk-Neutral Valuation and Power Contracts
Asian Options
Monte-Carlo Simulations
Black-Derman-Toy BDT
Bonds and Interest Rates
Cox-Ingersoll-Ross CIR
Compound Interest
Total Costs
Gini Coefficient
Gross Domestic Product Deflator
Forwards
Put-Call Parity
Calls and Puts with Different Strikes
Calls and Puts Arbitrage
Call and Put Price Bounds
Varying Times to Expiration
Early Exercise for American Options
Standard Brownian Motion
Geometric Brownian Motion
Ito Lemma
Geometric Brownian Motion SDEs
Stock Prices as Geometric Brownian Motion
Sharpe Ratio
Risk-Neutral Valuation and Power Contracts
Asian Options
Monte-Carlo Simulations
Black-Derman-Toy BDT
Bonds and Interest Rates
Cox-Ingersoll-Ross CIR