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
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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