Introductory Numerical Analysis

Abstract

The aim of this book is to provide a simple and useful introduction for the fresh students into the vast field of numerical analysis. Like any other introductory course on numerical analysis, this book contains the basic theory, which in the present text refers to the following topics: linear equations, nonlinear equations, eigensystems, interpolation, approximation of functions, numerical differentiation and integration, stochastics, ordinary differential equations and partial differential equations.

Because the students need to quickly understand why the numerical methods correctly work, the proofs of theorems were shorted as possible, insisting more on ideas than on a lot of algebra manipulation. The included examples are presented with a minimum of complications, emphasizing the steps of the algorithms.

The numerical methods described in this book are illustrated by computer programs written in C. Our goal was to develop very simple programs which are easily to read and understand by students. Also, the programs should run without modification on any compiler that implements the ANSI C standard.

Because our intention was to easily produce screen input-output (using, scanf and printf), in case of WINDOWS visual programming environments, like Visual C++ (Microsoft) and Borland C++ Builder, the project should be console-application. This will be not a problem for DOS and LINUX compilers.

If this material is used as a teaching aid in a class, I would appreciate if under such circumstances, the instructor of such a class would send me a note at the address below informing me if the material is useful. Also, I would appreciate any suggestions or constructive criticism regarding the content of these lecture notes.