Excursions in classical analysis : pathways to advanced problem solving and undergraduate research
QA301 .C43 2010
- Unknown QA301 .C43 2010
- Mathematical Association of America.
- Includes bibliographical references and index.
- Preface-- 1. Two classical inequalities-- 2. A new approach for proving inequalities-- 3. Means generated by an integral-- 4. The L'Hopital monotone rule-- 5. Trigonometric identities via complex numbers-- 6. Special numbers-- 7. On a sum of cosecants-- 8. The gamma products in simple closed forms-- 9. On the telescoping sums-- 10. Summation of subseries in closed form-- 11. Generating functions for powers of Fibonacci numbers-- 12. Identities for the Fibonacci powers-- 13. Bernoulli numbers via determinants-- 14. On some finite trigonometric power sums-- 15. Power series-- 16. Six ways to sum zeta(2)-- 17. Evaluations of some variant Euler sums-- 18. Interesting series involving binomial coefficients-- 19. Parametric differentiation and integration-- 20. Four ways to evaluate the Poisson integral-- 21. Some irresistible integrals-- Solutions to selected problems.
- (source: Nielsen Book Data)
- Publisher's Summary
- Excursions in Classical Analysis introduces undergraduate students to advanced problem solving and undergraduate research in two ways. Firstly, it provides a colourful tour of classical analysis which places a wide variety of problems in their historical context. Secondly, it helps students gain an understanding of mathematical discovery and proof. In demonstrating a variety of possible solutions to the same sample exercise, the reader will come to see how the connections between apparently inapplicable areas of mathematics can be exploited in problem-solving. This book will serve as excellent preparation for participation in mathematics competitions, as a valuable resource for undergraduate mathematics reading courses and seminars and as a supplement text in a course on analysis. It can also be used in independent study, since the chapters are free-standing.
(source: Nielsen Book Data)
- Publication date
- Hongwei Chen.
- Classroom resource materials series