Amazing and Aesthetic Aspects of Analysis / by Paul Loya
| データ種別 | 電子書籍 |
|---|---|
| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 2017 |
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| 書誌ID | OB01037643 |
|---|---|
| 本文言語 | 英語 |
| 一般注記 | Preface -- Some of the most beautiful formulæ in the world -- Part 1. Some standard curriculum -- 1. Very naive set theory, functions, and proofs -- 2. Numbers, numbers, and more numbers -- 3. Infinite sequences of real and complex numbers -- 4. Limits, continuity, and elementary functions -- 5. Some of the most beautiful formulæ in the world I-III -- Part 2. Extracurricular activities -- 6. Advanced theory of infinite series -- 7. More on the infinite: Products and partial fractions -- 8. Infinite continued fractions -- Bibliography -- Index . License restrictions may limit access Summary: Lively prose and imaginative exercises draw the reader into this unique introductory real analysis textbook. Motivating the fundamental ideas and theorems that underpin real analysis with historical remarks and well-chosen quotes, the author shares his enthusiasm for the subject throughout. A student reading this book is invited not only to acquire proficiency in the fundamentals of analysis, but to develop an appreciation for abstraction and the language of its expression. In studying this book, students will encounter: the interconnections between set theory and mathematical statements and proofs; the fundamental axioms of the natural, integer, and real numbers; rigorous ε-N and ε-δ definitions; convergence and properties of an infinite series, product, or continued fraction; series, product, and continued fraction formulæ for the various elementary functions and constants. Instructors will appreciate this engaging perspective, showcasing the beauty of these fundamental results |
| 著者標目 | *Loya, Paul SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Functions of real variables LCSH:Sequences (Mathematics) FREE:Mathematics FREE:Sequences, Series, Summability FREE:Real Functions |
| 分 類 | LCC:QA292 LCC:QA295 DC23:515.24 |
| 巻冊次 | ISBN:9781493967957 RefWorks出力（各巻） print ; ISBN:9781493967933 RefWorks出力（各巻） |
| 資料種別 | 機械可読データファイル |
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