Pub. Date:
Freeman, W. H. & Company
Basic Complex Analysis / Edition 2

Basic Complex Analysis / Edition 2

by Jerrold E. Marsden, Michael Hoffman


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Basic Complex Analysis skillfully combines a clear exposition of core theory with a rich variety of applications.  Designed for undergraduates in mathematics, the physical sciences, and engineering who have completed two years of calculus and are taking complex analysis for the first time..

Product Details

ISBN-13: 9780716718147
Publisher: Freeman, W. H. & Company
Publication date: 04/28/1987
Series: Mathematics Series
Edition description: Older Edition
Pages: 620
Product dimensions: 7.09(w) x 8.66(h) x (d)

Table of Contents

1Analytic Functions1
1.1Introduction to Complex Numbers1
1.2Properties of Complex Numbers12
1.3Some Elementary Functions25
1.4Continuous Functions41
1.5Basic Properties of Analytic Functions60
1.6Differentiation of the Elementary Functions81
2Cauchy's Theorem95
2.1Contour Integrals95
2.2Cauchy's Theorem--A First Look111
2.3A Closer Look at Cauchy's Theorem123
2.4Cauchy's Integral Formula144
2.5Maximum Modulus Theorem and Harmonic Functions164
3Series Representation of Analytic Functions183
3.1Convergent Series of Analytic Functions184
3.2Power Series and Taylor's Theorem203
3.3Laurent Series and Classification of Singularities222
4Calculus of Residues243
4.1Calculation of Residues243
4.2Residue Theorem256
4.3Evaluation of Definite Integrals269
4.4Evaluation of Infinite Series and Partial-Fraction Expansions304
5Conformal Mappings319
5.1Basic Theory of Conformal Mappings319
5.2Fractional Linear and Schwarz-Christoffel Transformations327
5.3Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics345
6Further Development of the Theory365
6.1Analytic Continuation and Elementary Riemann Surfaces365
6.2Rouche's Theorem and Principle of the Argument384
6.3Mapping Properties of Analytic Functions398
7Asymptotic Methods409
7.1Infinite Products and the Gamma Function409
7.2Asymptotic Expansions and the Method of Steepest Descent427
7.3Stirling's Formula and Bessel Functions446
8Laplace Transform and Applications457
8.1Basic Properties of Laplace Transforms457
8.2Complex Inversion Formula471
8.3Application of Laplace Transforms to Ordinary Differential Equations476
Answers to Odd-Numbered Exercises481

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