Basic complex analysis /
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| Author / Creator: | |
|---|---|
| Format: | Book |
| Language: | English |
| Imprint: | San Francisco : W. H. Freeman, [1973] |
| Subjects: |
Table of Contents:
- Preface
- 1. Analytic Functions
- 1.1. Introduction to Complex Numbers
- 1.2. Properties of Complex Numbers
- 1.3. Some Elementary Functions
- 1.4. Continuous Functions
- 1.5. Basic Properties of Analytic Functions
- 1.6. Differentiation of the Elementary Functions
- 2. Cauchy's Theorem
- 2.1. Contour Integrals
- 2.2. Cauchy's Theorem--A First Look
- 2.3. A Closer Look at Cauchy's Theorem
- 2.4. Cauchy's Integral Formula
- 2.5. Maximum Modulus Theorem and Harmonic Functions
- 3. Series Representation of Analytic Functions
- 3.1. Convergent Series of Analytic Functions
- 3.2. Power Series and Taylor's Theorem
- 3.3. Laurent Series and Classification of Singularities
- 4. Calculus of Residues
- 4.1. Calculation of Residues
- 4.2. Residue Theorem
- 4.3. Evaluation of Definite Integrals
- 4.4. Evaluation of Infinite Series and Partial-Fraction Expansions
- 5. Conformal Mappings
- 5.1. Basic Theory of Conformal Mappings
- 5.2. Fractional Linear and Schwarz-Christoffel Transformations
- 5.3. Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
- 6. Further Development of the Theory
- 6.1. Analytic Continuation and Elementary Riemann Surfaces
- 6.2. Rouche's Theorem and Principle of the Argument
- 6.3. Mapping Properties of Analytic Functions
- 7. Asymptotic Methods
- 7.1. Infinite Products and the Gamma Function
- 7.2. Asymptotic Expansions and the Method of Steepest Descent
- 7.3. Stirling's Formula and Bessel Functions
- 8. Laplace Transform and Applications
- 8.1. Basic Properties of Laplace Transforms
- 8.2. Complex Inversion Formula
- 8.3. Application of Laplace Transforms to Ordinary Differential Equations
- Answers to Odd-Numbered Exercises
- Index