A Second Course in Mathematical Analysis

Description

Description The classic analysis textbook from Burkill and Burkill is now available in the Cambridge Mathematical Library. This straightforward course, based on the idea of a limit, is for students of mathematics and physics who have acquired a working knowledge of calculus and are ready for a more systematic approach. The treatment given here also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter. Classic text in analysis, now re-issued in the Cambridge Mathematical Library. Clear exposition and a great number of examples make this ideal for use by students Authors J. C. Burkill, University of Cambridge H. Burkill, University of Sheffield Reviews & endorsements 'Books of this quality are rare enough to be hailed enthusiastically… it is so fresh in conception and so lucid in style that it will appeal to anyone who has a genuine interest in mathematics.' The Times Literary Supplement 'It is a pleasure to be able to welcome a book on analysis written by an author who has a sense of style.' Proceedings of the Edinburgh Mathematical Society 'This is an excellent book … If I were teaching a course for honours students of the type described, this book would rank high as a possible choice of text.' Canadian Mathematical Bulletin Table of Contents Chapter 1. Sets and functions Chapter 2. Metric spaces Chapter 3. Continuous functions on metric spaces Chapter 4. Limits in the spaces R and Z Chapter 5. Uniform convergence Chapter 6. Integration Chapter 7. Functions from Rm to Rn Chapter 8. Integrals in Rn Chapter 9. Fourier series Chapter 10. Complex function theory Chapter 11. Complex integrals, Caucy's theorem Chapter 12. Expansions, singularities, residues Chapter 13. General theorems, analytic functions Chapter 14. Applications to special functions.