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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1999 Hardback NEAR FINE Hardback, 600pp., This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. This highly respected text is designed f...show moreor mathematics, physical science and engineering students familiar with calculus, but new to complex analysis. A major feature is the clearly written text, which motivates students to study by themselves, and this new edition has been revised to make the material even more accessible. Many examples and applications have been rewritten and clarified, and certain non-core topics have been moved to the Instructor's Supplement or Student Guide, both new to the Third Edition. *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** ...show less
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