Berkeley Problems in Mathematics / Edition 3

Berkeley Problems in Mathematics / Edition 3

by Paulo Ney de Souza, Jorge-Nuno Silva, J. N. Silva
     
 

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ISBN-10: 0387204296

ISBN-13: 9780387204291

Pub. Date: 01/08/2004

Publisher: Springer New York

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex

Overview

This book collects approximately nine hundred problems that have appeared on the preliminary exams in Berkeley over the last twenty years. It is an invaluable source of problems and solutions. Readers who work through this book will develop problem solving skills in such areas as real analysis, multivariable calculus, differential equations, metric spaces, complex analysis, algebra, and linear algebra.

Product Details

ISBN-13:
9780387204291
Publisher:
Springer New York
Publication date:
01/08/2004
Series:
Problem Books in Mathematics Series
Edition description:
3rd ed. 2004
Pages:
593
Product dimensions:
9.21(w) x 6.14(h) x 1.31(d)

Table of Contents

Contents
Preface
I Problems
1 Real Analysis
1.1 Elementary Calculus
1.2 Limitsand 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 Limitsand Continuity
2.2 Differential Calculus
2.3 Integral Calculus 3 Differential Equations
3.1 First Order Equations
3.2 SecondOrder 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 Ringsand 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 Rankand 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 ofMatrices 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
1.6Sequences of Functions
1.7 Fourier Series
1.8 Convex Functions 2 Multivariable Calculus
2.1 Limitsand 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 Rankand 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

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