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Problems and Theorems in Analysis【 George Polya】【两卷全】【已搜索，无置重】
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基本信息 原书名：Problems and Theorems in Analysis I:Series,Integral Calculus,Theory of Functions 原出版社： Springer-Verlag 作者： George Polya,Gabor Szego 丛书名： Classics in Mathematics 出版社：世界图书出版公司 ISBN：750626613X 上架时间：2004-9-30 出版日期：2004 年4月 开本：24开 页码：389 版次：1-1 所属分类：数学 > 分析 > 微积分 目录 Part One Infinite Series and Infinite Sequences Chapter 1 Problem Numbers Operations with Power Series 1 (1--31). Additive Number Theory, Combinatorial Problems,and Applications 2 (31.1--43.1). Binomial Coefficients and Related Problems 3 (44--49). Differentiation of Power Series 4 (50--60). Functional Equations and Power Series 5 (60.1--60.11). Gaussian Binomial Coefficients 6 (61--64.2). Majorant Series Chapter 2 Linear Transformations of Series. A Theorem of Cesaro 1 (65--78). Triangular Transformations of Sequences into Sequences 2 (79--82). More General Transformations of Sequences into Sequences 3 (83--97). Transformations of Sequences into Functions. Theorem of Cesaro Chapter 3 The Structure of Real Sequences and Series 1 (98--112). The Structure of Infinite Sequences 2 (113--116). Convergence Exponent 3 (117--123). The Maximum Term of a Power Series 4 (124--132). Subseries 5 (132.1--137). Rearrangement of the Terms 6 (138--139). Distribution of the Signs of the Terms Chapter 4 Miscellaneous Problems 1 (140--155). Enveloping Series 2 (156--185.2). Various Propositions on Real Series and Sequences 3 (186--210). Partitions of Sets, Cycles in Permutations Part Two Integration Chapter 1 Problem Numbers The Integral as the Limit of a Sum of Rectangles 1 (1--7). The Lower and the Upper Sum 2 (8--19.2). The Degree of Approximation 3 (20--29). Improper Integrals Between Finite Limits 4 (30--40). Improper Integrals Between Infinite Limits 5 (41--47). Applications to Number Theory 6 (48--59). Mean Values and Limits of Products 7 (60--68). Multiple Integrals Chapter 2 Inequalities 1 (69--94). Inequalities 2 (94.1--97). Some Applications of Inequalities Chapter 3 Some Properties of Real Functions 1 (98--111). Proper Integrals 2 (112--118.1). Improper Integrals 3 (119--127). Continuous, Differentiable, Convex Functions 4 (128--146). Singular Integrals. Weierstrass' Approximation Theorem Chapter 4 Various Types of Equidistribution 1 (147--161). Counting Function. Regular Sequences 2 (162--165). Criteria of Equidistribution 3 (166--173). Multiples of an Irrational Number 4 (174--184). Distribution of the Digits in a Table of Logarithms and Related Questions 5 (185--194). Other Types of Equidistribution Chapter 5 Functions of Large Numbers 1 (195--209). Laplace's Method 2 (210--217.1). Modifications of the Method 3 (218--222). Asymptotic Evaluation of Some Maxima 4 (223--226). Minimax and Maximin Part Three Functions of One Complex Variable. General Part Chapter 1 Complex Numbers and Number Sequences 1 (1--15). Regions and Curves. Working with Complex Variables 2 (16--27). Location of the Roots of Algebraic Equations Problem Numbers 3 (28--35). Zeros of Polynomials, Continued. A Theorem of Gauss 4 (36--43). Sequences of Complex Numbers 5 (44--50). Sequences of Complex Numbers, Continued: Transformation of Sequences 6 (51--54). Rearrangement of Infinite Series Chapter 2 Mappings and Vector Fields 1 (55--59). The Cauchy-Riemann Differential Equations 2 (60--84). Some Particular Elementary Mappings 3 (85--102). Vector Fields Chapter 3 Some Geometrical Aspects oi Complex Variables 1 (103--116). Mappings of the Circle. Curvature and Support Function 2 (117--123). Mean Values Along a Circle 3 (124--129). Mappings of the Disk. Area 4 (130--144). The Modular Graph. The Maximum Principle Chapter 4 Cauchy's Theorem ·The Argument Principle 1 (145--171). Cauchy's Formula 2 (172--178). Poisson's and Jensen's Formulas 3 (179--193). The Argument Principle 4 (194--206.2). Rouche's Theorem Chapter 5 Sequences of Analytic Functions 1 (207--229). Lagrange's Series. Applications 2 (230--240). The Real Part of a Power Series 3 (241--247). Poles on the Circle of Convergence 4 (248--250). Identically Vanishing Power Series 5 (251--258). Propagation of Convergence 6 (259--262). Convergence in Separated Regions 7 (263--265). The Order of Growth of Certain Sequences of Polynomials Chapter 6 The Maximum Principle 1 (266--279). The Maximum Principle of Analytic Functions 2 (280--298). Schwarz's Lemma 3 (299--310). Hadamard's Three Circle Theorem 4 (311--321). Harmonic Functions 5 (322--340). The Phragmen-Lindelof Method Author Index Subject Index 基本信息 原书名：Problems and Theorems in Analysis II:Theory of Functions,Zeros,Polynomials,Determinants,Number Theory,Geometry 原出版社： Springer-Verlag 作者： George Polya,Gabor Szego 丛书名： Classics in Mathematics 出版社：世界图书出版公司 ISBN：7506266024 上架时间：2004-9-30 出版日期：2004 年4月 开本：24开 页码：391 版次：1-1 所属分类：数学 > 分析 > 微积分 目录 Part Four. Functions of One Complex Variable. Special Part Chapter 1. Maximum Term and Central Index, Maximum Modulus and Number of Zeros Problem Numbers 1 (1-40) Analogy between u(r) and M(r), v(r) and N (r) 2 (41-47) Further Results on u(r) and v(r) 3 (48-66) Connection between u(r), v(r), M(r) and N(r) 4 (67-76) u(r) and M(r) under Special Regularity Assumptions Chapter 2. Sehlicht Mappings 1 (77-83) Introductory Material 2 (84-87) Uniqueness Theorems 3 (88-96) Existence of the Mapping Function 4 (97-120) The Inner and the Outer Radius. The Normed Mapping Function 5 (121-135) Relations between the Mappings of Different Domains 6 (136-163) The Koebe Distortion Theorem and Related Topics Chapter 3. Miscellaneous Problems 1 (164-174.2) Various Propositions 2 (175-179) A Method of E. Landau 3 (180-187) Rectilinear Approach to an Essential Singularity 4 (188-194) Asymptotic Values of Entire Functions 5 (195-205) Further Applications of the Phragmen-Lindelof Method 6 (206-212) Supplementary Problems Part Five. The Location of Zeros Chapter 1. Rolle's Theorem and Descartes' Rule of Signs Problem Numbers 1 (1-21) Zeros of Functions, Changes of Sign of Sequences 2 (22-27) Reversals of Sign of a Function 3 (28-41) First Proof of Descartes' Rule.of Signs 4 (42-52) Applications of Descartes' Rule of Signs 5 (53-76) Applications of Rolle's Theorem 6 (77-86) Laguerre's Proof of Descartes' Rule of Signs 7 (87-91) What is the Basis of Descartes' Rule of Signs? 8 (92-100) Generalizations of Rolie's Theorem Chapter 2. The Geometry of the Complex Plane and the Zeros of Polynomials 1 (101-110) Center of Gravity of a System of Points with respect to a Point 2 (111-127) Center of Gravity of a Polynomial with respect to a Point. A Theorem of Laguerre 3 (128-156) Derivative ofaPolynomial with respect to a Point. A Theorem of Grace Chapter 3. Miscellaneous Problems 1 (157-182) Approximation of the Zeros of Transcendental Functions by the Zeros of Rational Functions 2 (183-189.3) Precise Determination of the Number of Zeros by Descartes' Rule of Signs 3 (190-196.1) Additional Problems on the Zeros of Polynomials Part Six. Polynomials and Trigonometric Polynomials 1 (1-7) Tchebychev Polynomials 2 (8-15) General Problems on Trigonometric Polynomials 3 (16-28) Some Special Trigonometric Polynomials 4 (29-38) Some Problems on Fourier Series 5 (39-43) Real Non-negative Trigonometric Polynomials 6 (44-49) Real Non-negative Polynomials 7 (50-61) Maximum-Minimum Problems on Trigonometric Polynomials 8 (62-66) Maximum-Minimum Problems on Polynomials 9 (67-76) The Lagrange Interpolation Formula 10 (77-83) The Theorems of S. Bernstein and A. Markov 11 (84-102) Legendre Polynomials and Related Topics 12 (103-113) Further Maximum-Minimum Problems on Polynomials Part Seven. Determinants and Quadratic Forms Problem Numbers 1 (1-16) Evaluation of Determinants. Solution of Linear Equations 2 (17-34) Power Series Expansion of Rational Functions 3 (35-43.2) Generation of Positive Quadratic Forms 4 (44-54.4) Miscellaneous Problems 5 (55-72) Determinants of Systems of Functions Part Eight. Number Theory Chapter 1. Arithmetical Functions 1 (1-11) Problems on the Integral Parts of Numbers 2 (12-20) Counting Lattice Points 3 (21-27.2) The Principle of Inclusion and Exclusion 4 (28-37) Parts and Divisors 5 (38-42) Arithmetical Functions, Power Series, Dirichlet Series 6 (43-64) Multiplicative Arithmetical Functions 7 (65-78) Lambert Series and Related Topics 8 (79-83) Further Problems on Counting Lattice Points Chapter 2. Polynomials with Integral Coefficients and Integral-Valued Functions 1 (84-93) Integral Coefficients and Integral-Valued Polynomials 2 (94-115) Integral-Valued Functions and their Prime Divisors 3 (116-129) Irreducibility of Polynomials Chapter 3. Arithmetical Aspects of Power Series 1 (130-137) Preparatory Problems on Binomial Coefficients 2 (138-148) On Eisenstein's Theorem 3 (149-154) On the Proof of Eisenstein's Theorem 4 (155-164) Power Series with Integral Coefficients Associated with Rational Functions 5 (165-173) Function-Theoretic Aspects of Power Series with Integral Coefficients 6 (174-187) Power Series with Integral Coefficients in the Sense of Hurwitz 7 (188-193) The Values at the Integers of Power Series that Converge about z= Chapter 4. Some Problems on Algebraic Integers Problem Numbers 1 (194-203) Algebraic Integers. Fields 2 (204-220) Greatest Common Divisor 3 (221-227.2) Congruences 4 (228-237) Arithmetical Aspects of Power Series Chapter 5. Miscellaneous Problems 1 (237.1-244.4) Lattice Points in Two and Three Dimensions 2 (245-266) Miscellaneous Problems Part Nine. Geometric Problems 1 (1-25) Some Geometric Problems Appendix 1 Additional Problems to Part One New Problems in English Edition Author Index Subject Index Topics Errata   |
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