Real Infinite Series.实数无穷级数
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作者： Daniel D. Bonar等著
出 版 社：
出版时间： 2006-1-1字数：版次： 1页数： 263印刷时间： 2006/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780883857458包装： 精装编辑推荐
作者简介：
Daniel Donald Bonar did his Ph.D. work in complex analysis at Ohio State University where he graduated in 1968. In 1965 he joined the faculty of Denison University in Granville, OH where he has been teaching mathematics, statistics, and computer science. In 1995 he was appointed to the newly created George R. Stibitz Distinguished Professorship in Mathematics and Computer Science. He is the author of a book entitled "On Annular Functions", and is co-author on several research papers. He has published joint work with the internationally acclaimed Hungarian mathematician Paul Erdos.
内容简介
This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.
目录
1 Introduction to Infinite Series
1.1 Definitions
1.2 Special Series
1.3 Intuition and Infinity
1.4 Basic Convergence Tests
1.5 General Series
2 More Sophisticated Techniques
2.1 The Work of Cauchy
2.2 Kummer's Results
2.3 The Tests of Raabe and Gauss
2.4 Logarithmic Scales
2.5 Tests of Abel
Appendix: Proofs of Bertrand's Tests
3 The Harmonic Series and Related Results
3.1 Divergence Proofs
3.2 Rate of Growth
3.3 The Alternating Harmonic Series
3.4 Selective Sums
3.5 Unexpected Appearances
4 Intriguing Results
4.1 Gems
5 Series and the Putnam Competition
5.1 The Problems
5.2 The Solutions
6Final Diversions
6.1 Puzzles
6.2 Visuals
6.3 Fallacious Proofs
6.4 Fallacies, Flaws and Flimflam
6.5 Answers to Puzzles
Appendix A: 101 True or False Questions
Appendix B: Harmonic Series Article
Appendix C: References
Books on Infinite Series
Books with Excellent Material on Infinite Series
Sources for Excellent Problems Related to Infinite Series
Pleasurable Reading
Journal Articles
Index
About the Authors