伯克利数学问题集 Berkeley Problems in Mathematics 第三版[DJVU]

游客，本帖隐藏的内容需要积分高于 1 才可浏览，您当前积分为 0

资源信息： 中文名: 伯克利数学问题集 原名: Berkeley Problems in Mathematics 作者: (美)Paulo Ney de Souza Jorge-Nuno Silva 资源格式: DJVU 版本: 第三版 出版社: Springer 书号: 0387008926 发行时间: 2004年 地区: 美国 语言: 英文 概述:

内容简介: 1977年，为考查一年级的博士研究生是否已经成功掌握为攻读数学博士学位所需的基本数学知识和技能，加州大学伯克利分校数学系设立了一项书面考试，作为获得博士学位的首要要求之一。该项考试自其创设以来，已成为研究生获得博士学位必须克服的一个主要障碍。本书的目的即为出版这些考试材料，以期对本科生准备该项考试有所帮助。 全书收录最近25年的1250余道伯克利数学考试试题，对所有计划攻读数学博士学位的学生，本书中的试题和解答都颇具价值；读者研读完本书，在诸如实分析、多变量微积分、微分方程、度量空间、复分析、代数学及线性代数等学科的解题能力都将得到提高。 这些问题按学科及难易程度编排，每道试题均注明相应的考试年月，读者可以依此方便地整理出各套试题。附录介绍如何得到电子版试题，考试大纲以及各次考试的及格线。 新版已包含直至2003秋季学期的最近考试试题和解答，增添了以前版本未收录的许多新的试题及题解。

目录: Preface I Problems. 1 Real Analysis 1.1 Elementary Calculus 1.2 Limits and Continuity 1.3 Sequences, Series, and Products 1.4 Differential Calculus 1.5 Integral Calculus 1.6 Sequences of Functions 1.7 Fourier Series 1.8 Convex Functions 2 Multivariable Calculus 2.1 Limits and Continuity 2.2 Differential Calculus 2.3 Integral Calculus 3 Differential Equations 3.1 First Order Equations 3.2 Second Order Equations 3.3 Higher Order Equations 3.4 Systems of Differential Equations 4 Metric Spaces 4.1 Topology of Rn 4.2 General Theory 4.3 Fixed Point Theorem 5 Complex Analysis 5.1 Complex Numbers 5.2 Series and Sequences of Functions 5.3 Conformal Mappings 5.4 Functions on the Unit Disc 5.5 Growth Conditions 5.6 Analytic and Meromorphic Functions 5.7 Cauchy's Theorem 5.8 Zeros and Singularities 5.9 Harmonic Functions 5.10 Residue Theory 5.11 Integrals Along the Real Axis 6 Algebra 6.1 Examples of Groups and General Theory 6.2 Homomorphisms and Subgroups 6.3 Cyclic Groups 6.4 Normality, Quotients, and Homomorphisms 6.5 Sn, An, Dn, ... 6.6 Direct Products 6.7 Free Groups, Generators, and Relations 6.8 Finite Groups 6.9 Rings and Their Homomorphisms 6.10 Ideals 6.11 Polynomials 6.12 Fields and Their Extensions 6.13 Elementary Number Theory 7 Linear Algebra 7.1 Vector Spaces 7.2 Rank and Determinants 7.3 Systems of Equations 7.4 Linear Transformations 7.5 Eigenvalues and Eigenvectors 7.6 Canonical Forms 7.7 Similarity 7.8 Bilinear, Quadratic Forms, and Inner Product Spaces 7.9 General Theory of Matrices.. II Solutions 1 Real Analysis 1.1 Elementary Calculus 1.2 Limits and Continuity 1.3 Sequences, Series, and Products 1.4 Differential Calculus 1.5 Integral Calculus 1.6 Sequences of Functions 1.7 Fourier Series 1.8 Convex Functions 2 Multivariable Calculus 2.1 Limits and Continuity 2.2 Differential Calculus 2.3 Integral Calculus 3 Differential Equations 3.1 First Order Equations 3.2 Second Order Equations 3.3 Higher Order Equations 3.4 Systems of Differential Equations 4 Metric Spaces 4.1 Topology of Rn 4.2 General Theory 4.3 Fixed Point Theorem 5 Complex Analysis 5.1 Complex Numbers 5.2 Series and Sequences of Functions 5.3 Conformal Mappings 5.4 Functions on the Unit Disc 5.5 Growth Conditions 5.6 Analytic and Meromorphic Functions 5.7 Cauchy's Theorem 5.8 Zeros and Singularities 5.9 Harmonic Functions 5.10 Residue Theory 5.11 Integrals Along the Real Axis 6 Algebra 6.1 Examples of Groups and General Theory 6.2 Homomorphisms and Subgroups 6.3 Cyclic Groups 6.4 Normality, Quotients, and Homomorphisms 6.5 Sn, An, Dn, ... 6.6 Direct Products 6.7 Free Groups, Generators, and Relations 6.8 Finite Groups 6.9 Rings and Their Homomorphisms 6.10 Ideals 6.11 Polynomials 6.12 Fields and Their Extensions 6.13 Elementary Number Theory 7 Linear Algebra 7.1 Vector Spaces 7.2 Rank and Determinants 7.3 Systems of Equations 7.4 Linear Transformations 7.5 Eigenvalues and Eigenvectors 7.6 Canonical Forms 7.7 Similarity 7.8 Bilinear, Quadratic Forms, and Inner Product Spaces 7.9 General Theory of Matrices III Appendices A How to Get the Exams A.1 On-line A.2 Off-line, the Last Resort B Passing Scores C The Syllabus References Index