Numerical Methods for Engineers and Scientists Using MATLAB®, 2nd Edition

1

Background and Introduction

This chapter is divided into two parts. In Part 1, a review of some essential mathematical concepts as related to differential equations and matrix analysis is presented. In Part 2, fundamentals of numerical methods, such as sources of computational errors, as well as iterations and rates of convergence are introduced. The materials presented here will be fully integrated throughout the book.

Part 1: Background

1.1 Differential Equations

Differential equations are divided into two main groups: ordinary differential equations (ODEs) and partial differential equations (PDEs). An equation involving an unknown function and one or more of its derivatives is called a differential equation. When there is only ...