Complex analysis and applications /
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| Author / Creator: | Jeffrey, Alan. |
|---|---|
| Edition: | 2nd ed. |
| Imprint: | Boca Raton, FL : Taylor & Francis, 2006. |
| Description: | 581 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/5891804 |
Table of Contents:
- Chapter 1. Analytic Functions
- 1.1. Review of Complex Numbers
- 1.2. Curves, Domains, and Regions
- 1.3. Analytic Functions
- 1.4. The Cauchy-Riemann Equations: Proof and Consequences
- 1.5. Elementary Functions
- Chapter 2. Complex Integration
- 2.1. Contours and Complex Integrals
- 2.2. The Cauchy Integral Theorem
- 2.3. Antiderivatives and Definite Integrals
- 2.4. The Cauchy Integral Formula
- 2.5. The Cauchy Integral Formula for Derivatives
- 2.6. Useful Results Deducible from the Cauchy Integral Formulas
- 2.7. Evaluation of Improper Definite Integrals by Contour Integration
- 2.8. Proof of the Cauchy-Goursat Theorem (Optional)
- Chapter 3. Taylor and Laurent Series: Residue Theorem and Applications
- 3.1. Sequences, Series, and Convergence
- 3.2. Uniform Convergence
- 3.3. Power Series
- 3.4. Taylor Series
- 3.5. Laurent Series
- 3.6. Classification of Singularities and Zeros
- 3.7. Residues and the Residue Theorem
- 3.8. Applications of the Residue Theorem
- 3.9. The Laplace Inversion Integral
- Chapter 4. Conformal Mapping
- 4.1. Geometrical Aspects of Analytic Functions: Mapping
- 4.2. Conformal Mapping
- 4.3. The Linear Fractional Transformation
- 4.4. Mappings by Elementary Functions
- 4.5. The Schwarz-Christoffel Transformation
- Chapter 5. Boundary Value Problems, Potential Theory, and Conformal Mapping
- 5.1. Laplace's Equation and Conformal Mapping: Boundary Value Problems
- 5.2. Standard Solutions of the Laplace Equation
- 5.3. Steady-State Temperature Distribution
- 5.4. Steady Two-Dimensional Fluid Flow
- 5.5. Two-Dimensional Electrostatics
- Solutions to Selected Odd-Numbered Exercises
- Bibliography and Suggested Reading List
- Index
