Numerical Methods for Engineers and Scientists 3rd Edition

Contents

Preface

Chapter 1 Introduction

1.1 Background

1.2 Representation of Numbers on a Computer

1.3 Errors in Numerical Solutions

1.3.1 Round-Off Errors

1.3.2 Truncation Errors

1.3.3 Total Error

1.4 Computers and Programming

1.5 Problems

Chapter 2 Mathematical Background

2.1 Background

2.2 Concepts from Pre-Calculus and Calculus

2.3 Vectors

2.3.1 Operations with Vectors

2.4 Matrices and Linear Algebra

2.4.1 Operations with Matrices

2.4.2 Special Matrices

2.4.3 Inverse of a Matrix

2.4.4 Properties of Matrices

2.4.5 Determinant of a Matrix

2.4.6 Cramer's Rule and Solution of a System of Simultaneous Linear Equations

2.4.7 Norms

2.5 Ordinary Differential Equations (ODE)

2.6 Functions of Two or More Independent Variables

2.6.1 Definition of the Partial Derivative

2.6.2 Chain Rule

2.6.3 The Jacobian

2.7 Taylor Series Expansion of Functions

2.7.1 Taylor Series for a Function of One Variable

2.7.2 Taylor Series for a Function of Two Variables

2.8 Inner Product and Orthogonality

2.9 Problems

Chapter 3 Solving Nonlinear Equations

3.1 Background

3.2 Estimation of Errors in Numerical Solutions

3.3 Bisection Method

3.4 Regula Falsi Method

3.5 Newton's Method

3.6 Secant Method

3.7 Fixed-Point Iteration Method

3.8 Use of MATLAB Built-In Functions for Solving Nonlinear Equations

3.8.1 The fzero Command

3.8.2 The roots Command

3.9 Equations with Multiple Solutions

3.10 Systems of Nonlinear Equations

3.10.1 Newton's Method for Solving a System of Nonlinear Equations

3.10.2 Fixed-Point Iteration ...