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Fundamentals of University Mathematics
3rd Edition - October 20, 2010
Authors: Colin McGregor, Jonathan Nimmo, Wilson Stothers
Paperback ISBN:
9 7 8 - 0 - 8 5 7 0 9 - 2 2 3 - 6
eBook ISBN:
9 7 8 - 0 - 8 5 7 0 9 - 2 2 4 - 3
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… Read more
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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.
- One volume, unified treatment of essential topics
- Clearly and comprehensively covers material beyond standard textbooks
- Worked examples, challenges and exercises throughout
University students
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
9.4 More on Monotonic Functions
9.5 Rates of Change
9.6 L’Hôpital’s Rule
9.X Exercises
Chapter 10: Curve Sketching
10.1 Types of Curve
10.2 Graphs
10.3 Implicit Curves
10.4 Parametric Curves
10.5 Conic Sections
10.6 Polar Curves
10.X Exercises
Chapter 11: Matrices and Linear Equations
11.1 Basic Definitions
11.2 Operations on Matrices
11.3 Matrix Multiplication
11.4 Further Properties of Multiplication
11.5 Linear Equations
11.6 Matrix Inverses
11.7 Finding Matrix Inverses
11.X Exercises
Chapter 12: Vectors and Three Dimensional Geometry
12.1 Basic Properties of Vectors
12.2 Coordinates in Three Dimensions
12.3 The Component Form of a Vector
12.4 The Section Formula
12.5 Lines in Three Dimensional Space
12.X Exercises
Chapter 13: Products of Vectors
13.1 Angles and the Scalar Product
13.2 Planes and the Vector Product
13.3 Spheres
13.4 The Scalar Triple Product
13.5 The Vector Triple Product
13.6 Projections
13 X Exercises
Chapter 14: Integration—Fundamentals
14.1 Indefinite Integrals
14.2 Definite Integrals
14.3 The Fundamental Theorem of Calculus
14.4 Improper Integrals
14.X Exercises
Chapter 15: Logarithms and Exponentials
15.1 The Logarithmic Function
15.2 The Exponential Function
15.3 Real Powers
15.4 Hyperbolic Functions
15.5 Inverse Hyperbolic Functions
15 X Exercises
Chapter 16: Integration - Methods and Applications
16.1 Substitution
16.2 Rational Integrals
16.3 Trigonometric Integrals
16.4 Integration by Parts
16.5 Volumes of Revolution
16.6 Arc Lengths
16.7 Areas of Revolution
16.X Exercises
Chapter 17: Ordinary Differential Equations
17.1 Introduction
17.2 First Order Separable Equations
17.3 First Order Homogeneous Equations
17.4 First Order Linear Equations
17.5 Second Order Linear Equations
17.X Exercises
Chapter 18: Sequences and Series
18.1 Reed Sequences
18.2 Sequence Limits
18.3 Series
18.4 Power Series
18.5 Taylor’s Theorem
18.X Exercises
Chapter 19: Numerical Methods
19.1 Errors
19.2 The Bisection Method
19.3 Newton’s Method
19.4 Definite Integrals
19.5 Euler’s Method
19.X Exercises
Appendix A: Answers to Exercises
Appendix B: Solutions to Problems
Appendix C: Limits and Continuity - A Rigorous Approach
Appendix D: Properties of Trigonometric Functions
Appendix E: Table of Integrals
Appendix F: Which Test for Convergence?
Appendix G: Standard Maclaurin Series
Index
- No. of pages: 568
- Language: English
- Published: October 20, 2010
- Imprint: Woodhead Publishing
- Paperback ISBN: 9780857092236
- eBook ISBN: 9780857092243
CM
Colin McGregor
Colin McGregor is an Honorary Research Fellow in the Department of Mathematics, University of Glasgow, UK.
Affiliations and expertise
Glasgow University, UKJN
Jonathan Nimmo
Jonathan Nimmo is a Reader in Mathematics in the Department of Mathematics, University of Glasgow, UK.
Affiliations and expertise
Glasgow UniversityWS
Wilson Stothers
Wilson Stothers was formerly a member in the Department of Mathematics, University of Glasgow, UK.
Affiliations and expertise
formerly Glasgow University, UK