Synopses & Reviews
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.
Review
"A sound beginning to mathematics degrees, and a reference book for anyone who uses maths regularly. If you seek a first year university text, certainly look at this one. I wish that I [had] had a copy as an undergraduate" Mathematics Today (review of a previous edition)
Synopsis
Provides, in a single volume, a unified treatment of first year topics fundamental to university mathematics. Successfully bridges the transitional gap between high school and university in a careful, thorough and unusually clear treatment. A valuable text for students majoring in mathematics.
About the Author
"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)
Table of Contents
Preliminaries; Functions and inverse functions; Polynomials and rational functions; Induction and the binomial theorem; Trigonometry; Complex numbers; Limits and continuity; Differentiation - fundamentals; Differentiation – applications; Curve sketching; Matrices and linear equations; Vectors and three-dimensional geometry; Products of vectors; Integration - fundamentals; Logarithms and exponentials; Integration - methods and applications; Ordinary differential equations; Sequences and series; Numerical methods; 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 Tables of integrals; Appendix F Standard Maclaurin series; Index.