This set consists of the third edition of this highly acclaimed undergraduate textbook and its solutions manual containing complete worked solutions to half of the problems. Suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences, the text provides lucid descriptions of all the topics, many worked examples, and 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, 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.

• 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 provided; the remainder for unaided homework - the only book at this level to have complete solutions to ALL of its problems

• Preliminary algebra
• Preliminary calculus
• Complex numbers and hyperbolic functions
• Series and limits
• Partial differentiation
• Multiple integrals
• Vector algebra
• Matrices and vector spaces
• Normal modes
• Vector calculus
• Line, surface and volume integrals
• Fourier series
• Integral transforms
• First-order ordinary differential equations
• Higher-order ordinary differential equations
• Series solutions of ordinary differential equations
• Eigenfunction methods for differential equations
• Special functions
• Quantum operators
• Partial differential equations: general and particular
• Partial differential equations: separation of variables
• Calculus of variations
• Integral equations
• Complex variables
• Application of complex variables
• Tensors
• Numerical methods
• Group theory
• Representation theory
• Probability
• Statistics