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Basic Complex Analysis
Third Edition| ©1999 Jerrold E. Marsden, California Institute of Technology; Michael J. Hoffman, California State University, Los Angeles
ISBN:9781464152191
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Basic Complex Analysis
Third Edition| ©1999
Jerrold E. Marsden, California Institute of Technology; Michael J. Hoffman, California State University, Los Angeles
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Basic Complex Analysis
Third Edition| 1999
Jerrold E. Marsden, California Institute of Technology; Michael J. Hoffman, California State University, Los Angeles
Table of Contents
1.1 Introduction to Complex Numbers
1.2 Properties of Complex Numbers
1.3 Some Elementary Functions
1.4 Continuous Functions
1.5 Basic Properties of Analytic Functions
2. Cauchy's Theorem
2.2 Cauchy's Theorem-A First Look
2.3 A Closer Look at Cauchy's Theorem
2.4 Cauchy's Integral Formula
2.5 Maximum Modulus Theorem and Harmonic Functions
3. Series Representation of Analytic Functions
3.1 Convergent Series of Analytic Functions
3.2 Power Series and Taylor's Theorem
3.3 Laurent Series and Classification of Singularities
4. Calculus of Residues
4.1 Calculation of Residues
4.2 Residue Theorem
4.3 Evaluation of Definite Integrals
5. Conformal Mappings
5.1 Basic Theory of Conformal Mappings
5.2 Fractional Linear and Schwarz-Christoffel Transformations
5.3 Applications of Conformal Mappings to Laplace's Equation, Heat Conduction, Electrostatics, and Hydrodynamics
6. Further Development of the Theory
6.1 Analytic Continuation and Elementary Riemann Surfaces
6.2 Rouche Theorem and Principle of the Argument
6.3 Mapping Properties of Analytic Functions
7. Asymptotic Methods
7.1 Infinite Products and the Gamma Function
7.2 Asymptotic Expansions and the Method of Steepest Descent
7.3 Stirlings Formula and Bessel Functions
8. Laplace Transform and Applications
Answers to Odd-Numbered Exercises
Index

Basic Complex Analysis
Third Edition| 1999
Jerrold E. Marsden, California Institute of Technology; Michael J. Hoffman, California State University, Los Angeles
Authors

Jerrold E. Marsden

Michael J. Hoffman

Basic Complex Analysis
Third Edition| 1999
Jerrold E. Marsden, California Institute of Technology; Michael J. Hoffman, California State University, Los Angeles
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