The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

> Contains all the mathematical material likely to be needed for any undergraduate course in the physical sciences > Maintains the method and clarity of presentation that has been much praised in earlier editions > Over 800 exercises: half with complete solutions available; half suitable for unaided homework - the only book at this level to have fully-worked solutions to ALL of its problems

Table of Contents

Prefaces 1. Preliminary algebra 2. Preliminary calculus 3. Complex numbers and hyperbolic functions 4. Series and limits 5. Partial differentiation 6. Multiple integrals 7. Vector algebra 8. Matrices and vector spaces 9. Normal modes 10. Vector calculus 11. Line, surface and volume integrals 12. Fourier series 13. Integral transforms 14. First-order ordinary differential equations 15. Higher-order ordinary differential equations 16. Series solutions of ordinary differential equations 17. Eigenfunction methods for differential equations 18. Special functions 19. Quantum operators 20. Partial differential equations: general and particular 21. Partial differential equations: separation of variables 22. Calculus of variations 23. Integral equations 24. Complex variables 25. Application of complex variables 26. Tensors 27. Numerical methods 28. Group theory 29. Representation theory 30. Probability 31. Statistics Index.