Simpler README example, also ref to Roots.jl. Fixes JuliaNLSolvers#264.

README.md

@@ -22,12 +22,14 @@ further below for a formal definition and the related commands.
 
 There is also an identical API for solving fixed points (i.e., taking as input a function `F(x)`, and solving `F(x) = x`).
 
-# Simple example
+Note, if a single equation and not a system is to be solved, consider using [Roots.jl](https://github.com/JuliaMath/Roots.jl).
+
+# A super simple example
 
 We consider the following bivariate function of two variables:
 
 ```jl
-(x, y) -> ((x+3)*(y^3-7)+18, sin(y*exp(x)-1))
+(x, y) -> [(x+3)*(y^3-7)+18, sin(y*exp(x)-1)]
 ```
 
 In order to find a zero of this function and display it, you would write the
@@ -36,6 +38,27 @@ following program:
 ```jl
 using NLsolve
 
+function f(x)
+    [(x[1]+3)*(x[2]^3-7)+18,
+    sin(x[2]*exp(x[1])-1)]
+end
+
+sol = nlsolve(f, [ 0.1, 1.2])
+sol.zero
+```
+The first argument to `nlsolve` is the function to be solved which
+takes a 2-vector as input and returns a 2-vector as output.
+The second argument is the starting point for algorithm.
+The `sol.zero` retrieves the solution, if converged.
+
+# A simple example
+
+Continuing on the same system of equations, but now using an in-place
+function and a user-specified Jacobian for improved performance:
+
+```jl
+using NLsolve
+
 function f!(F, x)
     F[1] = (x[1]+3)*(x[2]^3-7)+18
     F[2] = sin(x[2]*exp(x[1])-1)
@@ -66,7 +89,7 @@ particular, the field `zero` of that structure contains the solution if
 convergence has occurred. If `r` is an object of type `SolverResults`, then
 `converged(r)` indicates if convergence has occurred.
 
-# Specifying the function and its Jacobian
+# Ways to specify the function and its Jacobian
 
 There are various ways of specifying the residuals function and possibly its
 Jacobian.