<電子ブック>
A Short Book on Long Sums : Infinite Series for Calculus Students / by Fernando Q. Gouvêa
(Readings in Mathematics. ISSN:29455847)
版 | 1st ed. 2023. |
---|---|
出版者 | Cham : Springer Nature Switzerland : Imprint: Springer |
出版年 | 2023 |
本文言語 | 英語 |
大きさ | XI, 145 p. 48 illus., 41 illus. in color : online resource |
著者標目 | *Gouvêa, Fernando Q author SpringerLink (Online service) |
件 名 | LCSH:Sequences (Mathematics) LCSH:Mathematical analysis LCSH:Functions of real variables FREE:Sequences, Series, Summability FREE:Analysis FREE:Real Functions |
一般注記 | - To the reader -- Getting close with lines -- Getting closer with polynomials -- Going all the way: Convergence -- Power series -- Distant mountains -- Appendix A: SageMath: A (very) short introduction -- Appendix B: Why I do it this way -- Bibliography This concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor’s guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis HTTP:URL=https://doi.org/10.1007/978-3-031-37557-6 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
|
Springer eBooks | 9783031375576 |
|
電子リソース |
|
EB00226059 |
類似資料
この資料の利用統計
このページへのアクセス回数:2回
※2017年9月4日以降