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首页 分析txt,chm,pdf,epub,mobi下载作者:阿莫恩 (Herbert Amann) 出版社: 世界图书出版公司北京公司 原作名: Analysis I 出版年: 2012-9-1 页数: 426 定价: 89.00元 装帧: 平装 ISBN: 9787510048005 内容简介 · · · · · ·《分析(第1卷)(英文)》内容简介：This reprint has been authorized by Springer Science & Busincss Media for distribution in China Mainland only and not for export therefrom. 目录 · · · · · ·PrefaceChapter Ⅰ Foundations 1 Fundamentals of Logic 2 Sets Elementary Facts The Power Set · · · · · ·() Preface Chapter Ⅰ Foundations 1 Fundamentals of Logic 2 Sets Elementary Facts The Power Set Complement, Intersection and Union Products Families of Sets 3 Functions Simple Examples Composition of Functions Commutative Diagrams Injections, Surjections and Bijections Inverse Functions Set Valued Functions 4 Relations and Operations Equivalence R;elations Order Relations Operations 5 The Natural Numbers The Peano Axioms The Arithmetic of Natural Numbers The Division Algorithm The Induction Principle Recursive Definitions 6 Countab:ility Permutations Equinumerous Sets Countable Sets Infinite Products 7 Groups and Homomorphisms Groups Subgroups Cosets Homomorphisms Isomorphisms 8 Rings, Fields and Polynomials Rings The Binomial Theorem The Multinomial Theorem Fields Ordered Fields Formal Power Series Polynomials Polynomial Functions Division of Polynomials Linear Factors Polynomials in Several Indeterminates 9 The Rational Numbers The Integers The Rational Numbers Rational Zeros of Polynomials Square Roots 10 The Real Numbers Order Completeness Dedekind's Construction of the Real Numbers The Natural Order on R The Extended Number Line A Characterization of Supremum and Infimum The Archimedean Property The Density of the Rational Numbers in R nth Roots The Density of the Irrational Numbers in R Intervals 11 The Complex Numbers Constructing the Complex Numbers Elementary Properties Computation with Complex Numbers Balls in K 12 Vector Spaces, Affine Spaces and Algebras Vector Spaces Linear Functions Vector Space Bases Affine Spaces Affine Functions Polynomiallnterpolation Algebras Difference Operators and Summation Formulas Newton Interpolation Polynomials Chapter Ⅱ Convergence 1 Convergence of Sequences Sequences Metric Spaces Cluster Points Convergence Bounded Sets Uniqueness of the Limit Subsequences 2 Real and Complex Sequences Null Sequences Elementary Rules The Comparison Test Complex Sequences 3 Normed Vector Spaces Norms Balls Bounded Sets Examples The Space of Bounded Functions Inner Product Spaces The Cauchy-Schwarz Inequality Euclidean Spaces Equivalent Norms Convergence in Product Spaces 4 Monotone Sequences Bounded Monotone Sequences Some Important Limits 5 Infinite Limits Convergence to ±∞ The Limit Superior and Limit Inferior The Bolzano-Weierstrass Theorem 6 Completeness Cauchy Sequences Banach Spaces Cantor's Construction of the Real Numbers 7 Series Convergence of Series Harmonic and Geometric Series Calculating with Series Convergence Tests Alternating Series Decimal, Binary and Other Representations of Real Numbers The Uncountability of R 8 Absolute Convergence Majorant, Root and Ratio Tests The Exponential Function Rearrangements of Series Double Series Cauchy Products 9 Power Series The Radius of Convergence Addition and Multiplication of Power Series The Uniqueness of Power Series Representations Chapter Ⅲ Continuous Functions 1 Contimuty Elementary Properties and Examples Sequential Continuity Addition and Multiplication of Continuous Functions One-Sided Continuity 2 The Fndamentals of Topology OpenSets ClosedSets The Closure of a Set The Interior of a Set The Boundary ofa Set The Hausdorff Condition Examples A Characterization of Continuous Functions Continuous Extensions Relative Topology General Topological Spaces 3 Compactness Covers A Characterization of Compact Sets Sequential Compactness Continuous Functions on Compact Spaces The Extreme Value Theorem Total Boundedness Uniform Continuity Compactness in General Topological Spaces 4 Connectivity Definition and Basic Properties Connectivity in R The Generalized Intermediate Value Theorem Path Connectivity Connectivity in General Topological Spaces 5 Functions on R Bolzano's Intermediate Value Theorem Monotone Functions Continuous Monotone Functions 6 The Exponential and Related Functions Euler's Formula The Real Exponential Function The Logarithm and Power Functions The Exponential Function on iR The Definition of 7r and its Consequences The Tangent and Cotangent Functions The Complex Exponential Function Polar Coordinates Complex Logarithms Complex Powers A Further Representation of the Exponential Function …… Chapter Ⅳ Differentiation in One Variable Chapter Ⅴ Sequences of Functions Appendix Introduction to Mathematical Logic Bibliography Index · · · · · · () |
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