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| Preface | p. vii |
| Analytic Functions | p. 1 |
| Introduction to Complex Numbers | p. 1 |
| Properties of Complex Numbers | p. 12 |
| Some Elementary Functions | p. 25 |
| Continuous Functions | p. 41 |
| Basic Properties of Analytic Functions | p. 60 |
| Differentiation of the Elementary Functions | p. 81 |
| Cauchy's Theorem | p. 95 |
| Contour Integrals | p. 95 |
| Cauchy's Theorem--A First Look | p. 111 |
| A Closer Look at Cauchy's Theorem | p. 123 |
| Cauchy's Integral Formula | p. 144 |
| Maximum Modulus Theorem and Harmonic Functions | p. 164 |
| Series Representation of Analytic Functions | p. 183 |
| Convergent Series of Analytic Functions | p. 184 |
| Power Series and Taylor's Theorem | p. 203 |
| Laurent Series and Classification of Singularities | p. 222 |
| Calculus of Residues | p. 243 |
| Calculation of Residues | p. 243 |
| Residue Theorem | p. 256 |
| Evaluation of Definite Integrals | p. 269 |
| Evaluation of Infinite Series and Partial-Fraction Expansions | p. 304 |
| Conformal Mappings | p. 319 |
| Basic Theory of Conformal Mappings | p. 319 |
| Fractional Linear and Schwarz-Christoffel Transformations | p. 327 |
| Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics | p. 345 |
| Further Development of the Theory | p. 365 |
| Analytic Continuation and Elementary Riemann Surfaces | p. 365 |
| Rouche's Theorem and Principle of the Argument | p. 384 |
| Mapping Properties of Analytic Functions | p. 398 |
| Asymptotic Methods | p. 409 |
| Infinite Products and the Gamma Function | p. 409 |
| Asymptotic Expansions and the Method of Steepest Descent | p. 427 |
| Stirling's Formula and Bessel Functions | p. 446 |
| Laplace Transform and Applications | p. 457 |
| Basic Properties of Laplace Transforms | p. 457 |
| Complex Inversion Formula | p. 471 |
| Application of Laplace Transforms to Ordinary Differential Equations | p. 476 |
| Answers to Odd-Numbered Exercises | p. 481 |
| Index | p. 506 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
Basic Complex Analysis
by Marsden, Jerrold E.Edition: 2nd
Format: Hardcover
Pub. Date: 1987-03-01
Publisher(s): W H Freeman & Co
List Price: $94.21
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