Foundation Mathematics for the Physical Sciences

This tutorial-style textbook develops the basic mathematical tools needed by first and second year undergraduates to solve problems in the physical sciences. Students gain hands-on experience through hundreds of worked examples, self-test questions and homework problems. Each chapter includes a summary of the main results, definitions and formulae. Over 270 worked examples show how to put the tools into practice. Around 170 self-test questions in the footnotes and 300 end-of-section exercises give students an instant check of their understanding. More than 450 end-of-chapter problems allow students to put what they have just learned into practice. Hints and outline answers to the odd-numbered problems are given at the end of each chapter. Complete solutions to these problems can be found in the accompanying Student Solutions Manual. Fully-worked solutions to all problems, password-protected for instructors, are available at www.cambridge.org/foundation.

Table of Contents

Chapter 1 Arithmetic And Geometry
Chapter 2 Preliminary Algebra
Chapter 3 Differential Calculus
Chapter 4 Integral Calculus
Chapter 5 Complex Numbers And Hyperbolic Functions
Chapter 6 Series And Limits
Chapter 7 Partial Differentiation
Chapter 8 Multiple Integrals
Chapter 9 Vector Algebra
Chapter 10 Matrices And Vector Spaces
Chapter 11 Vector Calculus
Chapter 12 Line, Surface And Volume Integrals
Chapter 13 Laplace Transforms
Chapter 14 Ordinary Differential Equations
Chapter 15 Elementary Probability
Appendix A: The base for natural logarithms
Appendix B: Sinusoidal definitions
Appendix C: Leibnitz’s theorem
Appendix D: Summation convention
Appendix E: Physical constants
Appendix F: Footnote answers