The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. This up-to-date volume provides the essential mathematical and computational education for students, researchers, and practicing engineers. The author begins with a review of computation, and then deals with a range of key concepts including sets, fields, matrix theory, and vector spaces. He then goes on to cover more advanced subjects such as linear mappings, group theory, and special functions. He concentrates exclusively on the most important topics for the working physical scientist or engineer with the aim of helping them to make intelligent use of the latest computational and analytical methods. The book contains well over 400 homework problems and covers many topics not dealt with in other textbooks. It will be ideal for senior undergraduate and graduate students in the physical sciences and engineering, as well as a valuable reference for working engineers.
Preface; 1. Foundations of computation; 2. Sets and mappings; 3. Evaluation of functions; 4. Groups, rings and fields; 5. Vector spaces; 6. Linear mappings I; 7. Linear functionals; 8. Inner products and norms; 9. Linear mappings II; 10. Convergence in normed vector spaces; 11. Group representations; 12. Special functions; Appendices.