数学分析原理_PDF下载[102MB-百度云]巴舍沃夫

本书特色

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《数学分析原理(英文)》是数学分析方面的经典著作，主要介绍了数列的收敛性、点集拓扑、黎曼积分、超越函数、傅里叶级数等内容。它也可以作为实数分析，泛函分析，谐波分析等课程的课外读物。对于需要学习微积分的非数学专业的学生，这本书是一个好的选择。

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内容简介

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《数学分析原理(英文)》由哈尔滨工业大学出版社出版。

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Preface1 Sets and Proofs1．1 Sets， Elements， and Subsets1．2 Operations on Sets1．3 Language of Logic1．4 Techniques of Proof1．5 Relations1．6 Functions1．7 Axioms of Set TheoryExercises2 Numbers2．1 SystemN2．2 Systems Z and Q2．3 Least Upper Bound Property and Q2．4 System R2．5 Least Upper Bound Property and R2．6 Systems R， C， and *R2．7 CardinalityExercises3 Convergence3．1 Convergence ofNumerical Sequences3．2 Cauchy Criterion for Convergence3．3 Ordered Field Structure and Convergence3．4 Subsequences3．5 NumericalSeries3．6 Some Series of Particular Interest3．7 AbsoluteConvergence3．8 Number eExercises4 Point Set Topology4．1 MetricSpaces4．2 Open and Closed Sets4．3 Completeness4．4 Separability4．5 TotaIBoundedness4．6 Compactness4．7 Perfectness4．8 Connectedness4．9* Structure of Open and Closed SetsExercises5 Continuity5．1 Definition and Examples5．2 Continuity and Limits5．3 Continuity and Compactness5．4 Continuity and Connectedness5．5 Continuity and Oscillation5．6 Continuity of Rk-valued FunctionsExercises6 Space C(E， E’)6．1 UniformContinuity6．2 UniformConvergence6．3 Completeness of C(E， E)6．4 Bernstein and Weierstrass Theorems6．5* Stone and Weierstrass Theorems6．6* Ascoli-Arzela TheoremExercises7 Differentiation7．1 Derivative7．2 Differentiation and Continuity7．3 Rules of Differentiation7．4 Mean-ValueTheorems7．5 Taylor’sTheorem7．6* DifferentialEquations7．7* Banach Spaces and the Space C1 (a，b)7．8 A View to Differentiation in RkExercises8 Bounded Variation8．1 Monotone Functions8．2 CantorFunction8．3 Functions ofBoundedVariation8．4 Space BV(a， b)8．5 Continuous Functions of Bounded Variation……