伯克利數學問題集（第3版）

內容介紹

本書為美國加州大學伯克利分校數學系歷屆攻讀數學連棵白博雅提腿項士學位者第店嫌才一學年水平測試的試題彙編。分問題和題解兩部分，章套微承節劃分按分抹立捆設支漏乘放學科重求進行，包括實分析，多元微積分，微分方程，度量空間，複分析，代數和線性代數等內容。

作品目錄

Preface

Ⅰ Real Analysis

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

7 Linear Algebra

Ⅱ Solutions

1 Real Analysis

2 Multivariable Calculus

3 Differential Equations

4 Metric Spaces

5 Complex Analysis

6 Algebra

7 Linear Algebra

Ⅲ Appendices

A How to Get the Exams

B Passing Scores

C The Syllabus

References

Index

Ⅳ

伯克利數學問題集（第3版）

基本介紹

內容介紹

作品目錄

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