Real Analysis via Sequences and Series / by Charles H.C. Little, Kee L. Teo, Bruce van Brunt
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 2015 |
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| 書誌ID | OB01016867 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Preface -- 1. Introduction -- 2. Sequences -- 3. Series -- 4. Limits of Functions -- 5. Continuity -- 6. Differentiability -- 7. The Riemann Integral -- 8. Taylor Polynomials and Taylor Series -- 9. The Fixed Point Problem -- 10. Sequences of Functions -- Bibliography -- Index. License restrictions may limit access Summary: This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results, and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e, and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions |
| 著者標目 | *Little, Charles H.C Teo, Kee L van Brunt, Bruce SpringerLink (Online service) |
| 統一書名標目 | Undergraduate Texts in Mathematics, |
| 件 名 | LCSH:Mathematics LCSH:Sequences (Mathematics) FREE:Real Functions FREE:Sequences, Series, Summability |
| 分 類 | LCC:QA331.5 DC23:515.8 |
| 巻冊次 | ISBN:9781493926510 RefWorks出力（各巻） print ; ISBN:9781493926527 RefWorks出力（各巻） print ; ISBN:9781493926503 RefWorks出力（各巻） print ; ISBN:9781493941810 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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※2020年8月16日以降