Modern Engineering Mathematics

Glyn James is currently Emeritus Professor in Mathematics at Coventry University, having previously been Dean of the School of Mathematical and Information Sciences. As in previous editions he has drawn upon the knowledge and experience of his co-authors to provide an excellent revision of the book.

Table of Contents

Chapter 1: Numbers, Algebra and Geometry

1.1    Introduction

1.2    Number and arithmetic

1.3    Algebra

1.4    Geometry

1.5    Numbers and accuracy

1.6    Engineering applications

1.7    Review exercises

 

Chapter 2: Functions

2.1    Introduction

2.2    Basic definitions

2.3    Linear and quadratic functions

2.4    Polynomial functions

2.5    Rational functions

2.6    Circular functions

2.7    Exponential, logarithmic and hyperbolic functions

2.8    Irrational functions

2.9    Numerical evaluation of functions

2.10    Engineering application: a design problem

2.11    Review exercises

 

Chapter 3: Complex Numbers

3.1    Introduction

3.2    Properties

3.3    Powers of complex numbers

3.4    Loci in the complex plane

3.5    Functions of a complex variable

3.6    Engineering application: alternating currents in electrical networks

3.7    Review exercises

 

Chapter 4: Vector Algebra

4.1    Introduction

4.2    Basic definitions and results

4.3    The vector treatment of the geometry of lines and planes

4.4    Engineering application: spin-dryer suspension

4.5    Engineering application: cable stayed bridge

4.6    Review exercises

 

Chapter 5: Matrix Algebra

5.1    Introduction

5.2    Definitions and properties

5.3    Determinants

5.4    The inverse matrix

5.5    Linear equations

5.6    Rank

5.7    The eigenvalue problem

5.8    Engineering application: spring systems

5.9    Engineering application: steady heat transfer through composite materials

5.10    Review exercises 

 

Chapter 6: An Introduction to Discrete Mathematics

6.1    Introduction

6.2    Set theory

6.3    Switching and logic circuits

6.4    Propositional logic and methods of proof

6.5    Engineering application: expert systems

6.6    Engineering application: control

6.7    Review exercises

 

Chapter 7: Sequences, Series and Limits

7.1    Introduction

7.2    Sequences and series

7.3    Finite sequences and series

7.4    Recurrence relations

7.5    Limit of a sequence

7.6    Infinite series

7.7    Power series

7.8    Functions of a real variable

7.9    Continuity of functions of a real variable

7.10    Engineering application: insulator chain

7.11    Engineering application: approximating functions and Padé approximants

7.12    Review exercises

 

Chapter 8: Differentiation and Integration

8.1    Introduction

8.2    Differentiation

8.3    Techniques of differentiation

8.4 Higher derivatives

8.5    Applications of optimization problems

8.6    Numerical differentiation

8.7    Integration

8.8    Techniques of integration

8.9    Applications of integration

8.10    Numerical evaluation of integrals

8.11    Engineering application: design of prismatic channels