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.
Over 270 worked examples show how to put the tools into practice, and more than 450 end-of-chapter problems allow students to apply the tools themselves
Around 170 self-test questions and 300 end-of-section exercises help students check their understanding as they work through the text
Fully-worked solutions to all problems, password-protected for instructors, are available at www.cambridge.org/foundation
Table of Contents 1. Arithmetic and geometry 2. Preliminary algebra 3. Differential calculus 4. Integral calculus 5. Complex numbers and hyperbolic functions 6. Series and limits 7. Partial differentiation 8. Multiple integrals 9. Vector algebra 10. Matrices and vector spaces 11. Vector calculus 12. Line, surface and volume integrals 13. Laplace transforms 14. Ordinary differential equations 15. Elementary probability
K. F. Riley, University of Cambridge M. P. Hobson, University of Cambridge