Modern Engineering Mathematics

Prentice Hall
Glyn James
Prentice Hall
total pages
August 2007
Related Titles


A rigorous, applications-focused introduction to the field of Engineering Mathematics. Suitable for a first year course in the subject area, the book presents the key mathematical concepts that engineers will be expected to know. The applications focus allows the student to see the mathematics in action and helps to contextualise what they are actually learning. As such, it is also well suited to maths courses within the physical sciences and applied mathematics. Incorporates many exercises throughout the chapters so students can reinforce their learning. This edition will be accompanied by online bridging chapters – refresher units in core subjects to bring students up to speed with what they’ll need to know before taking the engineering mathematics course.



  • Comprehensive coverage of first year engineering maths
  • Thorough approach emphasising the applicability of maths to solving engineering problems
  • Excellent coverage of applications
  • Numerous fully worked examples
  • Matlab and Maple integrated throughout the text


New to this Edition


    • More than 100 new worked examples

    • Over 200 new exercises to help test your learning and provide a more progressive level of difficulty

    • Online ‘bridging’ chapters offer a refresher in fundamental topic areas
    • Matlab fully integrated, showing you how to use this powerful tool to support your work in mathematics

Table of Contents

James: Modern Engineering Mathematics 4e

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

8.12            Engineering application: harmonic analysis of periodic functions

8.13            Review exercises


Chapter 9: Further Calculus

9.1               Introduction

9.2               Improper integrals

9.3               Some theorems with applications to numerical methods

9.4               Taylor’s theorem and related results

9.5               Calculus of vectors

9.6               Functions of several variables

9.7               Taylor’s theorem for functions of two variables

9.8               Engineering application: deflection of built-in column

9.9               Engineering application: streamlines in fluid dynamics

9.10            Review exercises


Chapter 10: Introduction to Ordinary Differential Equations

10.1            Introduction

10.2            Engineering examples

10.3            The classification of differential equations

10.4            Solving differential equations

10.5            first-order ordinary differential equations

10.6            Numerical solution of first-order ordinary differential equations

10.7            Engineering application: analysis of damper performance

10.8            Linear differential equations

10.9            Linear constant-coefficient differential equations

10.10        Engineering application: second-order linear constant-coefficient differential   equations

10.11        Numerical solution of second-and higher-order differential equations

10.12        Qualitative analysis of second-order differential equations

10.13        Review exercises


Chapter 11: Introduction to Laplace Transforms

11.1            Introduction

11.2            The Laplace transform

11.3            Solution of differential equations

11.4            Engineering applications: electrical circuits and mechanical vibrations

11.5            Review exercises


Chapter 12: Introduction to Fourier Series

12.1            Introduction

12.2            Fourier series expansion

12.3            Functions defined over a finite interval

12.4            Differentiation and integration of Fourier series

12.5            Engineering application: analysis of a slider-crank mechanism

12.6            Review exercises


Chapter 13: Data Handling and Probability Theory

13.1            Introduction

13.2            The raw material of statistics

13.3            Probabilities of random events

13.4            Random variables

13.5            Important practical distributions

13.6            Engineering application: quality control

13.7            Engineering application: clustering of rare events

13.8            Review exercises


Appendix I Tables


Answers to Exercises



Back Cover

This book provides a complete course for first-year engineering mathematics. Whichever field of engineering you are studying, you will be most likely to require knowledge of the mathematics presented in this textbook. Taking a thorough approach, the authors put the concepts into an engineering context, so you can understand the relevance of mathematical techniques presented and gain a fuller appreciation of how to draw upon them throughout your studies.

Key features

  • Comprehensive coverage of first-year engineering mathematics
  • Fully worked examples and exercises provide relevance and reinforce the role of mathematics in the various branches of engineering

§         Excellent coverage of engineering applications

New to this edition

  • More than 100 new worked examples
  • Over 200 new exercises to help monitor progress with your learning and provide a more progressive level of difficulty
  • Online ‘refresher units' covering topics you should have encountered at school but may not have used for some time

§         MATLAB and MAPLE fully integrated, showing you how these powerful tools can be used to support your work in mathematics

Professor Glyn James is Emeritus Professor within the Department of Mathematical Sciences at Coventry University, having previously been Dean of the School of Mathematical and Information Science.

As in previous editions he has drawn upon the knowledge and experience of his co-authors to provide an excellent revision of the book.