數(shù)學(xué)分析（第1卷）

前言

　　An entire generation of mathematicians has grown up during the time between the appearance of the first edition of this textbook and the publication of the fourth edition， a translation of which is before you. The book is familiar to many people， who either attended the lectures on which it is based or studied out of it， and who now teach others in universities all over the world.I am glad that it has become accessible to English-speaking readers. . This textbook consists of two parts. It is aimed primarily at university students and teache..

內(nèi)容概要

這是一套完整介紹數(shù)學(xué)分析的教材，內(nèi)容涉及從實數(shù)到流形上的微分形式，其中包括漸近方法、傅立葉分析、拉普拉斯變換、勒讓德變換、橢圓函數(shù)以及頻率分布。本書語言通俗，表達(dá)清晰，各章有大量的練習(xí)、思考題以及最新應(yīng)用實例。

作者簡介

佐里奇，是莫斯科國立大學(xué)教授。主要從事分析、保角幾何、擬共形映照方面的研究工作。近期從事熱力學(xué)中的數(shù)學(xué)問題的研究。他解決了空間擬共形映照下的球面同胚問題，并因該研究成果獲得了“青年數(shù)學(xué)家國家獎”（National Prize for Young Mathematicians）。同時還擁有一項技術(shù)專利。
    作為莫斯科國立大學(xué)數(shù)學(xué)力學(xué)系高級實驗課程的組織者之一，他在一些大學(xué)中開設(shè)并教授現(xiàn)代分析學(xué)課程，并發(fā)表了大量的數(shù)學(xué)研究成果。

書籍目錄

1 Some General Mathematical Concepts and Notation. 　1.1 Logical Symbolism  　1.2 Sets and Elementary Operations on them 　1.3 Functions 　1.4 Supplementary Material 2 The Real Numbers  　2.1 Axioms and Properties of Real Numbers 　2.2 Classes of Real Numbers and Computations 　2.3 Basic Lemmas on Completeness 　2.4 Countable and Uncountable Sets 3 Limits  　3.1 The Limit of a Sequence 　3.2 The Limit of a Function 4 Continuous Functions  　4.1 Basic Definitions and Examples 　4.2 Properties of Continuous Functions 5 Differential Calculus  　5.1 Differentiable Functions 　5.2 The Basic Rules of Differentiation 　5.3 The Basic Theorems of Differential Calculus  5.4 Differential Calculus Used to Study Functions  5.5 Complex Numbers and Elementary Functions  5.6 Examples of Differential Calculus in Natural Science  5.7 Primitives 6 Integration  6.1 Definition of the Integral  6.2 Linearity, Additivity and Monotonicity of the Iuntegral  6.3 The Integral and the Derivative  6.4 Some Applications of Integration  6.5 Improper Integrals7 Functions of Several Variables  7.1 The Space Rm and its Subests  7.2 Limits and Continuity of Functions of Several Variables8 Differential Calculus in Several Variables  8.1 The Linear Structure on Rm……Some Problems from the Midterm ExaminationsExamination TopicsReferencesSubject IndexName Index

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