Excursions in Classical Analysis
Mathematical Association of America (Verlag)
978-0-88385-768-7 (ISBN)
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.
Hongwei Chen was born in China, and received his PhD from North Carolina State University in 1991. He is currently a Professor of Mathematics at Christopher Newport University. He has published more than fifty research articles in classical analysis and partial differential equations.
Preface; 1. Two classical inequalities; 2. A new approach for proving inequalities; 3. Means generated by an integral; 4. The L'Hôpital 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 ζ(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.
| Reihe/Serie | Classroom Resource Materials |
|---|---|
| Verlagsort | Washington |
| Sprache | englisch |
| Maße | 183 x 262 mm |
| Gewicht | 710 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| ISBN-10 | 0-88385-768-5 / 0883857685 |
| ISBN-13 | 978-0-88385-768-7 / 9780883857687 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
