An edition of An introduction to the theory of complex variables
(2013)
An introduction to the theory of complex variables
by R. S. Johnson
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Last edited by Tom Morris
February 4, 2018 | History
The theory of complex variables is significant in pure mathematics, and the basis for important applications in applied mathematics (e.g. fluids).
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Publish Date
2013
Publisher
Bookboon
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Book Details
Table of Contents
Innhold
Part I: An introduction to complex variables
Preface
Introduction
Complex Numbers
Elementary properties
Inequalities
Roots
Exercises 1
Functions
Elementary functions
Exercises 2
Differentiability
Definition
The derivative in detail
Analyticity
Harmonic functions
Exercises 3
Integration in the complex plane
The line integral
The fundamental theorem of calculus
Closed contours
Exercises 4
The Integral Theorems
Cauchy’s Integral Theorem (1825)
Cauchy’s Integral Formula (1831)
An integral inequality
An application to the evaluation of real integrals
Exercises 5
Power Series
The Laurent expansion (1843)
Exercises 6
The Residue Theorem
The (Cauchy) Residue Theorem (1846)
Application to real integrals
Using a different contour
Exercises 7
The Fourier Transform
FTs of derivatives
Exercises 8
Answers
Part II: The integral theorems of complex analysis with applications to the evaluation of real integrals
List of Integrals
Preface
Introduction
Complex integration
Exercises 1
The integral theorems
Green’s theorem
Cauchy’s integral theorem
Cauchy’s integral formula
The (Cauchy) residue theorem
Exercises 2
Evaluation of simple, improper real integrals
Estimating integrals on semi-circular arcs
Real integrals of type 1
Real integrals of type 2
Exercises 3
Indented contours, contours with branch cuts and other special contours
Cauchy principal value
The indented contour
Contours with branch cuts
Special contours
Exercises 4
Integration of rational functions of trigonometric functions
Exercises 5
Answers
Biographical Notes
Index
ID Numbers
Links outside Open Library
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| February 4, 2018 | Edited by Tom Morris | merge authors |
| January 12, 2016 | Edited by Alice Kirk | Edited without comment. |
| January 12, 2016 | Created by Alice Kirk | Added new book. |