This book is divided into two parts: part one, ordinary differential equations and their approximations and part two, partial differential equations and their approximations. part one consists of chapters 1 to? and deals with ordinary differential equations (ode) and their approximations.?chapter 1 contains a simple presentation of the fundamental ideas in the theory of scalar equations.?chapter? presents the core of the first part of the book and is where most of the important concepts on finite difference approximations are introduced and explained for the most basic method of all, the explicit euler method.?the remaining chapters in part one deal with higher order approximations, implicit methods, multistep methods, and systems of ode. part two consists of chapters 7-11 and addresses partial differential equations in one space dimension and their approximations.