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Fundamentals and applications of complex analysis

Author: Harold Cohen
Publisher: New York : Kluwer Academic/Plenum Publishers, ©2003.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Serves as a text for first and second year courses in single variable complex analysis. The concepts are illustrated with large numbers of examples, many of which involve problems students encounter  Read more...

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Document Type: Book
All Authors / Contributors: Harold Cohen
ISBN: 0306477483 9780306477485
OCLC Number: 52182574
Description: xv, 418 pages : illustrations ; 24 cm
Contents: A Brief History --
Complex Numbers --
Conjugation, Modulus, Argument and Arithemetic --
Cartesian, Trigonometric and Polar Forms --
Roots of Unity --
Complex Numbers and AC Circuits --
Complex Variables --
Derivatives, Cauchy-Riemann Conditions and Analyticity --
Integrals of Analytic Function --
Pole Singularities --
Cauchy's Residue Theorem --
Series, Limits and Residues --
Taylor Series for Analytic Functions --
Laurent Series for a Singular Function --
Arithmetic Combinations of Power Series --
Limits and L'Hospital's Rule --
Residues --
Evaluation of Integrals --
Integrals Along the Entire Real Axis --
Integrals of Functions of Sin[theta] and Cos[theta] --
Cauchy's Principal Value Integral and the Dirac [delta] Symbol --
Miscellaneous Integrals --
Multivalued Functions, Branch Points and Cuts --
Non-Integer Power, Logarithm Functions --
Riemann Sheets, Branch Points and Cuts --
Branch Structure --
Multiple Branch Points --
Evaluation of Integrals --
Singularities of Functions Defined by Integrals --
The Integrand is Analytic --
The Integrand is Singular --
Limits of the Integral are Variable --
Conformal Mapping --
Properties of a Mapping --
Linear and Bilinear Transformations --
Schwarz-Christoffel Transformation --
Applications --
Dispersion Relations --
Kramers-Kronig Dispersion Relations over the Entire Real Axis --
Kramers-Kronig Dispersion Relations Over Half the Real Axis --
Dispersion Relations for a Function with Branch Structure --
Subtracted Dispersion Relations.
Responsibility: Harold Cohen.

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"The textbook Fundamentals and Applications of Complex Analysis by Harold Cohen is an idiosyncratic treatment of the subject, written by a physicist, with lots of interesting insights and alternative Read more...

 
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