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[资源] Problems and Theorems in Analysis【 George Polya】【两卷全】【已搜索，无置重】

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
Problems and Theorems in Analysis【 George Polya】【两卷全】【已搜索，无置重】
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