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Basic Complex Analysis

Basic Complex Analysis Cover

 

Synopses & Reviews

Publisher Comments:

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.
.

Book News Annotation:

This textbook introduces complex numbers, analytic functions, Cauchy's Theorem, the calculus of residues, conformal mappings, asymptotic methods, and Laplace transforms. For the third edition, the evaluation of integrals has been rewritten to make the treatment less encyclopedic.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

The intuitive approach taken by this text allows theorems to be understood by science and engineering students. There is an extensive range of examples, exercises and applications, and there is more coverage of the theoretical aspects studied within the context of the development of maths.

Table of Contents

1. Analytic Functions

    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

    1.6 Differentiation of the Elementary Functions
    

2. Cauchy's Theorem

    2.1 Contour Integrals

    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

    4.4 Evaluation of Infinite Series and Partial-Fraction Expansions

    

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

     8.1 Basic Properties of Laplace Transforms
     8.2 Complex Inversion Formula
     8.3 Application of Laplace Transforms to Ordinary Differential Equations

  Answers to Odd-Numbered Exercises

  Index

Product Details

ISBN:
9780716728771
Other:
Hoffman, Michael J.
Publisher:
W. H. Freeman
Author:
Marsden, Jerrold E.
Author:
Hoffman, Michael J.
Location:
New York
Subject:
General
Subject:
Mathematical Analysis
Subject:
Functions of complex variables
Subject:
Analise complexa
Subject:
General Mathematics
Subject:
Mathematics - General
Edition Number:
3
Edition Description:
Third Edition
Publication Date:
19981215
Binding:
Hardback
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
600
Dimensions:
9.38 x 7.63 in

Related Subjects


Reference » Science Reference » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Complex Analysis
Science and Mathematics » Mathematics » General
Textbooks » General

Basic Complex Analysis
0 stars - 0 reviews
$ In Stock
Product details 600 pages W.H. Freeman & Company - English 9780716728771 Reviews:
"Synopsis" by , The intuitive approach taken by this text allows theorems to be understood by science and engineering students. There is an extensive range of examples, exercises and applications, and there is more coverage of the theoretical aspects studied within the context of the development of maths.
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