Essential Real Analysis / by Michael Field
| データ種別 | 電子書籍 |
|---|---|
| 版 | 1st ed. 2017. |
| 出版者 | Cham : Springer International Publishing : Imprint: Springer |
| 出版年 | 2017 |
書誌詳細を非表示
| 書誌ID | OB01038571 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | 1 Sets, functions and the real numbers -- 2 Basic properties of real numbers, sequences and continuous functions -- 3 Infinite series -- 4 Uniform convergence -- 5 Functions -- 6. Topics from classical analysis: The Gamma-function and the Euler-Maclaurin formula -- 7 Metric spaces -- 8 Fractals and iterated function systems -- 9 Differential calculus on Rm -- Bibliography. Index. License restrictions may limit access Summary: This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author's extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses |
| 著者標目 | *Field, Michael SpringerLink (Online service) |
| 統一書名標目 | Springer Undergraduate Mathematics Series, |
| 件 名 | LCSH:Functions of real variables LCSH:Sequences (Mathematics) LCSH:Topology LCSH:Fourier analysis FREE:Real Functions FREE:Sequences, Series, Summability FREE:Topology FREE:Fourier Analysis |
| 分 類 | LCC:QA331.5 DC23:515.8 |
| 巻冊次 | ISBN:9783319675466 RefWorks出力（各巻） print ; ISBN:9783319675459 RefWorks出力（各巻） print ; ISBN:9783319675473 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