Enhanced descriptions from Syndetics:

Suitable for a first year course in the subject, this book is an introduction to the field of engineering mathematics. The book is 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.

Table of contents provided by Syndetics

• 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 Hiderivatives
• 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
• Index

Author notes provided by Syndetics

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.