Understanding Analysis
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed t...
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| Định dạng: | Sách |
| Ngôn ngữ: | English |
| Được phát hành: |
Springer
2015
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| Những chủ đề: | |
| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57457 |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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oai:scholar.dlu.edu.vn:DLU123456789-574572023-11-11T05:45:47Z Understanding Analysis Abbott, Stephen Mathematical analysis Analyse mathématique Analyse This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. 2015-08-14T03:30:04Z 2015-08-14T03:30:04Z 2015 Book 978-1-4939-2712-8 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57457 en application/pdf Springer |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| topic |
Mathematical analysis Analyse mathématique Analyse |
| spellingShingle |
Mathematical analysis Analyse mathématique Analyse Abbott, Stephen Understanding Analysis |
| description |
This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.
Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. |
| format |
Book |
| author |
Abbott, Stephen |
| author_facet |
Abbott, Stephen |
| author_sort |
Abbott, Stephen |
| title |
Understanding Analysis |
| title_short |
Understanding Analysis |
| title_full |
Understanding Analysis |
| title_fullStr |
Understanding Analysis |
| title_full_unstemmed |
Understanding Analysis |
| title_sort |
understanding analysis |
| publisher |
Springer |
| publishDate |
2015 |
| url |
https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/57457 |
| _version_ |
1782548820778811392 |