現(xiàn)代分析及其應(yīng)用教程（英文）
定 價：58 元
叢書名：國外優(yōu)秀數(shù)學(xué)著作原版系列
- 作者：[澳] 格雷姆·L.科（Graeme L.Cohen） 著
- 出版時間：2021/1/1
- ISBN：9787560391021
- 出 版 社：哈爾濱工業(yè)大學(xué)出版社
- 中圖法分類：O177
- 頁碼：340
- 紙張：膠版紙
- 版次：1
- 開本：16開
《現(xiàn)代分析及其應(yīng)用教程（英文）》通過度量空間中序列的收斂性討論了完備性和緊性等問題，并給出了解決相關(guān)問題的方法，還闡述了現(xiàn)代分析中的另一種拓撲方法。
《現(xiàn)代分析及其應(yīng)用教程（英文）》可應(yīng)用到微分方程和積分方程、線性代數(shù)方程組、近似理論、數(shù)值分析和量子力學(xué)等領(lǐng)域，適合數(shù)學(xué)本科生、數(shù)學(xué)教師和其他需要學(xué)習(xí)一些數(shù)學(xué)分析知識用于其他領(lǐng)域的讀者參考使用。
This book offers an introduction to some basic aspects of modern analysis. It is designed for students who are majoring in some area of mathematics but who do not necessarily intend to continue their studies at a graduate level.
The choice of material and the method of presentation are both aimed at as wide a readership as possible. Future teachers of high school mathematics should be given an introduction to the mathematical future as much as they must be given some knowledge of the mathematical past; students of mathematical engineering， biology or finance may need to read current literature without desiring to contribute to it. These are perhaps the extremes in the type of student to whom this book is directed. At the same time， students who do need to go on to courses in measure theory and functional analysis will find this book an easy introduction to the initial concepts in those areas.
Preface
1 Prelude to Modern Analysis
1．1 Introduction
1．2 Sets and numbers
1．3 Functions or mappings
1．4 Countability
1．5 Point sets
1．6 Open and closed sets
1．7 Sequences
1．8 Series
1．9 Functions of a real variable
1．10 Uniform convergence
1．11 Some linear algebra
1．12 Setting off
2 Metric Spaces
2．1 Definition of a metric space
2．2 Examples of metric spaces
2．3 Solved problems
2．4 Exercises
2．5 Convergence in a metric space
2．6 Examples on completeness
2．7 Subspace of a metric space
2．8 Solved problems
2．9 Exercises
3 The Fixed Point Theorem and its Applications
3．1 Mappings between metric spaces
3．2 The fixed point theorem
3．3 Applications
3．4 Perturbation mappings
3．5 Exercises
4 Compactness
4．1 Compact sets
4．2 Ascoli's theorem
4．3 Application to approximation theory
4．4 Solved problems
4．5 Exercises
5 Topological Spaces
5．1 Definitions and examples
5．2 Closed sets
5．3 Compact sets
5．4 Continuity in topological spaces
5．5 Homeomorphisms; connectedness
5．6 Solved problems
5．7 Exercises
……
6 Normed Vector Spaces
7 Mappings on Normed Spaces
8 Inner Product Spaces
9 Hilbert Space
Bibliography
Selected Solutions
Index
編輯手記
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