(* Examples of solving equations/finding roots *)
(* Simply paste each one at the Mathemtica prompt *)



(* Newton's method's pitfalls *)
FindRoot[x^2 -1  == 0., {x,  0}]

(* A fix-up *)
FindRoot[x^2 -1  == 0., {x, Random[]}]

(* Two equations *)
FindRoot[{Sin[x] == Cos[y], x+y == 1}, {x, 0.1}, {y, 0.1}]

(* Force secant method. No analytic derivatives needed. *)
FindRoot[Erf[x] == x, {x, {0, 1} }]