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正版新书]复分析及其应用初级教程 第3版DennisG.Zill(D.G.齐尔
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Preface
Chapter 1. Complex Numbers and the Complex Plane
1.1 Complex Numbers and Their Properties
1.2 Complex Plane
1.3 Polar Form of Complex Numbers
1.4 Powers and Roots
1.5 Sets of Points in the Complex Plane
1.6 Applications
Chapter 1 Review Quiz
Chapter 2. Complex Functions and Mappings
2.1 Complex Functions
2.2 Complex Functions as Mappings
2.3 Linear Mappings
2.4 Special Power Functions
2.4.1 The Power Function z
2.4.2 The Power Function zl
2.5 Reciprocal Function
2.6 Applications
Chapter 2 Review Quiz
Chapter 3. Analytic Functions
3.1 Limits and Continuity
3.1.1 Limits
3.1.2 Continuity
3.2 Differentiability and Analyticity
3.3 Cauchy-Riemann Equations
3.4 Harmonic Functions
3.5 Applications
Chapter 3 Review Quiz
Chapter 4. Elementary Functions
4.1 Exponential and Logarithmic Functions
4.1.1 Complex Exponential Function
4.1.2 Complex Logarithmic Function
4.2 Complex Powers
4.3 Trigonometric and Hyperbolic Functions
4.3.1 Complex Trigonometric Functions
4.3.2 Complex Hyperbolic Functions
4.4 Inverse Trigonometric and Hyperbolic Functions
4.5 Applications
Chapter 4 Review Quiz
Chapter 5. Integration in the Complex Plane
5.1 Real Integrals
5.2 Complex Integrals
5.3 Cauchy-Goursat Theorem
5.4 Independence of Path
5.5 Cauchy's Integral Formulas and Their
Consequences
5.5.1 Cauchy's Two Integral Formulas
5.5.2 Some Consequences of the Integral
Formulas
5.6 Applications
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