分析基礎(chǔ)

內(nèi)容概要

　　《分析基礎(chǔ)：微積分理論》旨在為對嚴(yán)格的證明不熟悉的讀者，提供一本學(xué)習(xí)標(biāo)準(zhǔn)積分教程的后繼教程。對于學(xué)習(xí)高等分析教程，復(fù)變量、微分方程、傅里葉分析、數(shù)值分析、多變量微積分以及統(tǒng)計的人來說讀《分析基礎(chǔ)：微積分理論》是很有必要的。同樣也可以作為將來中學(xué)老師的參考教科書。　　有關(guān)實線的概念《分析基礎(chǔ)：微積分理論》研究不多，許多抽象概念，如矩陣空間和有序系，在《分析基礎(chǔ)：微積分理論》中都避免討論；最小上界的性質(zhì)在《分析基礎(chǔ)：微積分理論》中拿來即用，實線的有序性貫穿于書的始終；數(shù)字序列的透徹講解作為學(xué)習(xí)標(biāo)準(zhǔn)微積分的基礎(chǔ)；選修部分可以讓學(xué)生學(xué)習(xí)矩陣空間和Riemann-Stieltjes積分。

書籍目錄

Preface1 Introduction  1 TheSet N of Natural Numbers  2 The Set Q of Rational Numbers  3 The Set R of Real Numbers  4 The Completeness Axiom  5 The Symbols +oo and -oo  6 * A Development of R2 Sequences  7 Limits of Sequences  8 A Discussion.about Proofs  9 Limit Theorems for Sequences  10 Monotone Sequences and Cauchy Sequences  11 Subsequences  12 lim sap's and lim inf's  13 * Some Topological Concepts in Metric spaces  14 Series  15 Aternatin4g Series and Integral Tests  16 * Decimal Expansions of Real Numbers3 Continuity  17 Continuous Functions   18 Properties of Continuous Functions    19 Uniform Continuity  20 Limits of Functions  21 * More on Metric Spaces: Continuity  22 * More on Metric Spaces: Connectedness4 Sequences and Series of Functions  23 Power Series  24 Uniform Convergence  25 More on Uniform Convergence  26 Differentiation and Integration of Power series  27 * weierstrass's Approximation Theorem5 Differentiation  28 Basic Properties of the Derivative  29 The Mean Value Theorem  30 * UHospital's Rule  31 Taylor s Theorem6 Integration  32 The Riemann Integral   33 Properties of the Riemann Integral   34 Fundamental Theorem of Calctflus  35 * Riemann-Stieltjes Integrals  36 * Improper Integrals  37 * A Discussion of Exponents and Logarithms Appendix on Set NotationSelected Hints and AnswersReferencesSymbols IndexIndex

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