Generous in the number of examples, exercises, and applications provided
Applications include electric potentials, heat conduction, and hydrodynamics-studied with the aid of harmonic functions, conformal mappings, Laplace transforms, asymptotic expansions, and Gamma and Bessel functions
Intuitive approach enables application-oriented students to skip the more technical parts without sacrificing ...show more an understanding of the main theoretical points
Highly readable text motivates students and encourages self-study
Edition/Copyright:3RD 99 Cover: Hardcover Publisher:W.H. Freeman Published: 12/15/1998 International: No
View Table of Contents
1. Analytic Functions
Introduction to Complex Numbers Properties of Complex Numbers Some Elementary Functions Continuous Functions Analytic Functions Differentiation of the Elementary Functions Review Exercises for Chapter 1
2. Cauchy's Theorem
Contour Integrals Supplement: Riemann Sums Cauchy's Theorem: Intuitive Version Cauchy's Theorem: Precise Version Supplement A: Integrals Along Continuous Curves Supplement B: Relationship of Cauchy's Theorem to the Jordan Curve Theorem Cauchy's Integral Formula Maximum Modulus Theorem and Harmonic Function Review Exercises for Chapter 2
3. Series Representation of Analytic Functions
Convergent Series of Analytic Functions Power Series and Taylor's Theorem Laurent's Series and Classification of Singularities Review Exercises for Chapter 3
4. Calculus of Residues
Calculation of Residues The Residue Theorem Evaluation of Definite Integrals Evaluation of Infinite Series and Partial-Fraction Expansions Review Exercises for Chapter 4
5. Conformal Mappings
Basic Theory of Conformal Mappings Fractional Linear and Schwarz-Christoffel Transformations Applications of Conformal Mapping to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics Review Exercises for Chapter 5
6. Further Development of the Theory
Analytic Continuation and Elementary Riemann Surfaces Rouché's Theorem and the Principle of the Argument Mapping Properties of Analytic Functions Supplement A: Normal Families and The Riemann Mapping Theorem Supplement B: The Dynamics of Complex Analytic Mappings Review Exercises for Chapter 6
7. Asymptotic Methods
Infinite Products and the Gamma Function Asymptotic Expansions and the Method of Steepest Descent Supplement: Bounded Variation and the Proof of the Stationary Phase Formula Stirling's Formula and Bessel Functions Review Exercises for Chapter 7
8. The Laplace Transform and Applications
Basic Properties of LaPlace Transforms The Complex Inversion Formula Application of Laplace Transforms to Ordinary Differential Equations Supplement: The Fourier Transform and the Wave Equation Review Exercises for Chapter 8
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