Fundamentals of University Mathematics

3rd Edition

Authors: Colin McGregor Jonathan Nimmo Wilson Stothers
Paperback ISBN: 9780857092236
eBook ISBN: 9780857092243
Imprint: Woodhead Publishing
Published Date: 20th October 2010
Page Count: 568
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The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.

Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.

The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.

Key Features

  • One volume, unified treatment of essential topics
  • Clearly and comprehensively covers material beyond standard textbooks
  • Worked examples, challenges and exercises throughout


University students

Table of Contents

Preface to the Third Edition


Chapter 1: Preliminaries

1.1 Number Systems

1.2 Intervals

1.3 The Plane

1.4 Modulus

1.5 Rational Powers

1.6 Inequalities

1.7 Divisibility and Primes

1.8 Rationals and Irrationals

1.X Exercises

Chapter 2: Functions and Inverse Functions

2.1 Functions and Composition

2.2 Real Functions

2.3 Standard Functions

2.4 Boundedness

2.5 Inverse Functions

2.6 Monotonic Functions

2.X Exercises

Chapter 3: Polynomials and Rational Functions

3.1 Polynomials

3.2 Division and Factors

3.3 Quadratics

3.4 Rational Functions

3.X Exercises

Chapter 4: Induction and the Binomial Theorem

4.1 The Principle of Induction

4.2 Picking and Choosing

4.3 The Binomial Theorem

4.X Exercises

Chapter 5: Trigonometry

5.1 Trigonometric Functions

5.2 Identities

5.3 General Solutions of Equations

5.4 The t-formulae

5.5 Inverse Trigonometric Functions

5.X Exercises

Chapter 6: Complex Numbers

6.1 The Complex Plane

6.2 Polar Form and Complex Exponentials

6.3 De Moivre’s Theorem and Trigonometry

6.4 Complex Polynomials

6.5 Roots of Unity

6.6 Rigid Transformations of the Plane

6.X Exercises

Chapter 7: Limits and Continuity

7.1 Function Limits

7.2 Properties of Limits

7.3 Continuity

7.4 Approaching Infinity

7.X Exercises

Chapter 8: Differentiation—Fundamentals

8.1 First Principles

8.2 Properties of Derivatives

8.3 Some Standard Derivatives

8.4 Higher Derivatives

8.X Exercises

Chapter 9: Differentiation—Applications

9.1 Critical Points

9.2 Local and Global Extrema

9.3 The Mean Value Theorem<


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© Woodhead Publishing 2010
Woodhead Publishing
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About the Author

Colin McGregor

Colin McGregor is an Honorary Research Fellow in the Department of Mathematics, University of Glasgow, UK.

Affiliations and Expertise

Glasgow University, UK

Jonathan Nimmo

Jonathan Nimmo is a Reader in Mathematics in the Department of Mathematics, University of Glasgow, UK.

Affiliations and Expertise

Glasgow University

Wilson Stothers

Wilson Stothers was formerly a member in the Department of Mathematics, University of Glasgow, UK.

Affiliations and Expertise

formerly Glasgow University, UK


I found this book to be extremely helpful over a wide range of topics. I must have used this to aid my revision for at least 7 or 8 exams and would probably have struggled without it. Particularly useful sections include those on Complex Numbers, Matrices, Vectors, and Differential Equations. If you can only afford to buy one or two books for your course or study, make sure this is one of them!, Rg Ellam "rob_ellam (review on
This book is excellent preparation for 2nd year undergraduate Mathematics courses. It is detailed and step-by-step, so you don't get lost on certain topics. The proofs are complex, but then that's Mathematics for you!, Jon Baldie (review on
If you are looking for a first year university text you should carefully look at this, a unifier of mathematical ideas at this level. I found it most valuable., The Mathematical Gazette (review of a previous edition)