书籍详情
复分析与几何引论（影印版）
作者：（美）约翰·P·迪·安格罗（John,P.D'Angelo）
出版社：高等教育出版社
出版时间：2017-04-01
ISBN：9787040469981
定价：¥99.00
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内容简介
《美国数学会经典影印系列：复分析与几何引论（影印版）》提供给读者一个对复分析的深刻理解以及这门学科是如何融入数学的。《美国数学会经典影印系列：复分析与几何引论（影印版）》是从伊利诺伊大学香槟分校的校园荣誉计划中的讲座发展起来的。这些课程的目标是让学生体会到当以复分析的观点对待许多数学和物理问题时，问题便被神奇地简化了。《美国数学会经典影印系列：复分析与几何引论（影印版）》从初等的水平出发。《美国数学会经典影印系列：复分析与几何引论（影印版）》的前四章给出了对复分析及其许多初等但非寻常应用的一个导引，第5到第7章发展了Cauchy理论，包括一些引人注目的对于微积分的应用。第8章则探讨了一些吸引人的论题，使全书连成一个有机的整体并为深入研究打开了大门。280个习题囊括了从简单计算到难解之题。这种多样性使得此书的吸引力。只阅读前四章的读者将能够在初等情形中应用复数。研读整《美国数学会经典影印系列：复分析与几何引论（影印版）》将能了解基本的单复变论并将目睹它作为一个整体融合进数学中。数学研究工作者也会发现许多新的观点。
作者简介
暂缺《复分析与几何引论（影印版）》作者简介
目录
Preface
Chapter 1．From the Real Numbers to the Complex Numbers
1．Introduction
2．Number systems
3．Inequalities and ordered fields
4．The complex numbers
5．Alternative definitions of C
6．A glimpse at metric spaces
Chapter 2．Complex Numbers
1．Complex conjugation
2．Existence of square roots
3．Limits
4．Convergent infinite series
5．Uniform convergence and consequences
6．The unit circle and trigonometry
7．The geometry of addition and multiplication
8．Logarithms
Chapter 3．Complex Numbers and Geometry
1．Lines， circles， and balls
2．Analytic geometry
3．Quadratic polynomials
4．Linear fractional transformations
5．The Riemann sphere
Chapter 4．Power Series Expansions
1．Geometric series
2．The radius of convergence
3．Generating functions
4．Fibonacci numbers
5．An application of power series
6．Rationality
Chapter 5．Complex Differentiation
1．Definitions of complex analytic function
2．Complex differentiation
3．The Cauchy-Riemann equations
4．Orthogonal trajectories and harmonic functions
5．A glimpse at harmonic functions
6．What is a differential form?
Chapter 6．Complex Integration
1．Complex-valued functions
2．Line integrals
3．Goursat's proof
4．The Cauchy integral formula
5．A return to the definition of complex analytic function
Chapter 7．Applications of Complex Integration
1．Singularities and residues
2．Evaluating real integrals using complex variables methods
3．Fourier transforms
4．The Gamma function
Chapter 8．Additional Topics
1．The minimum-maximum theorem
2．The fundamental theorem of algebra
3．Winding numbers， zeroes， and poles
4．Pythagorean triples
5．Elementary mappings
6．Quaternions
7．Higher-dimensional complex analysis
Fhrther reading
Bibliography
Index
Chapter 1．From the Real Numbers to the Complex Numbers
1．Introduction
2．Number systems
3．Inequalities and ordered fields
4．The complex numbers
5．Alternative definitions of C
6．A glimpse at metric spaces
Chapter 2．Complex Numbers
1．Complex conjugation
2．Existence of square roots
3．Limits
4．Convergent infinite series
5．Uniform convergence and consequences
6．The unit circle and trigonometry
7．The geometry of addition and multiplication
8．Logarithms
Chapter 3．Complex Numbers and Geometry
1．Lines， circles， and balls
2．Analytic geometry
3．Quadratic polynomials
4．Linear fractional transformations
5．The Riemann sphere
Chapter 4．Power Series Expansions
1．Geometric series
2．The radius of convergence
3．Generating functions
4．Fibonacci numbers
5．An application of power series
6．Rationality
Chapter 5．Complex Differentiation
1．Definitions of complex analytic function
2．Complex differentiation
3．The Cauchy-Riemann equations
4．Orthogonal trajectories and harmonic functions
5．A glimpse at harmonic functions
6．What is a differential form?
Chapter 6．Complex Integration
1．Complex-valued functions
2．Line integrals
3．Goursat's proof
4．The Cauchy integral formula
5．A return to the definition of complex analytic function
Chapter 7．Applications of Complex Integration
1．Singularities and residues
2．Evaluating real integrals using complex variables methods
3．Fourier transforms
4．The Gamma function
Chapter 8．Additional Topics
1．The minimum-maximum theorem
2．The fundamental theorem of algebra
3．Winding numbers， zeroes， and poles
4．Pythagorean triples
5．Elementary mappings
6．Quaternions
7．Higher-dimensional complex analysis
Fhrther reading
Bibliography
Index
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