J. C. Burkill, H. BurkillCambridge University PressEdition: New Ed, 10/24/2002EAN 9780521523431, ISBN10: 0521523435Paperback, 536 pages, 22.8 x 15.2 x 3 cmLanguage: EnglishThe classic analysis textbook from Burkill and Burkill, now available in the Cambridge Mathematical Library. This straightforward course, based on the idea of a limit, is intended for students of mathematics and physics who have acquired a working knowledge of the calculus and are ready for a more systematic treatment. 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. This, combined with the large number of examples included, ensure that this book will appeal to students of analysis.1. Sets and functions2. Metric spaces3. Continuous functions on metric spaces4. Limits in the spaces R and Z5. Uniform convergence6. Integration7. Functions from Rm to Rn8. Integrals in Rn9. Fourier series10. Complex function theory11. Complex integrals, Caucy's theorem12. Expansions, singularities, residues13. General theorems, analytic functions14. Applications to special functions.
