分析中的問題與定理（第1卷）

內(nèi)容概要

這套兩卷集的教科書主要面向工程科學和應用數(shù)學領(lǐng)域的本科生和研究生，因此書中主要強調(diào)偏微分程在力學中的應用等內(nèi)容，各章中的實例研究和每章后的習題均從工程應用中提煉而成。書中還全面討論了唯一性定理，以及極大值原理和極小值原理。本書的根本目的在于引導學生運用力學中的偏微分方程理論建立工程問題模型。

書籍目錄

Part One Infinite Series and Infinite Sequences  Chapter 1 One peratios with Power Series    Additive Unmber Theory,Combinatorial problems,and Applications    Binomial Coefficitents and Related Problem    Differentiation of Power Series    Functional Equations and Power Series    Gaussian Binomial Coefficients    Majorant Series  Chapter 2 Linear Transformations of Series.A Theorem of Cesaro    Triangular Transformations of Sequences into Sequences    More General Transformations of Sequences into Sequences    Transformations of Sequences into Functions,Theorem of Cesaro  Chapter 3 The Structuue of Real Sequences and Series    The Structure of Infinite Sequences    Convergence Exponent    The Maximum Term of a Power Series    Subseries    Rearrangement of the Terms    Distribution of the Sings of the Terms  Chapter 4 Miscellaneous Problems    Evneloping Series    Various Propositions on Real Series and Sequences    Partitions of Sets,Cycles in PermutationsPart Two Integration  Chapter 1 The Integral as the Limit of a Sum of Rectangles  Chapter 2 Inequalities  Chapter 3 Some Propertries of Real Functions  Chapter 4 Various Types of Equidistribution  Chapter 5 Functions of Large NumbersPart Three Functions of One Complex Variable,General Part  Chapter 1 Complex Numbers and Number Sequences  Chapter 2 Mappings and Vector Fields  Chapter 3 Some Geometrical Aspects of Complex Vriables  Chapter 4 Cauchy's Theorem·The Argument Principle  Chapter 5 Sequences of Analytic Functions  Chapter 6 The Maximum PrincipleAuthor IndexSubject Idex

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