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Table of contents:
An understanding of functions of a complex variable, together with the importance of their applications, form an essential part of the study of mathematics. Complex Variables and their Applications assumes as little background knowledge of the reader as is practically possible, a sound knowledge of calculus and basic real analysis being the only essential pre-requisites. With an emphasis on clear and careful explanation, the book covers all the essential topics covered in a first course on Complex Variables, such as differentiation, integration and applications, Laurent series, residue theory and applications, and elementary conformal mappings. The reader is also introduced to the Schwarz-Christoffel transformation, Dirchlet problems, harmonic functions, analytic continuation, infinite products, asymptotic series and elliptic functions. Applications of complex variable theory to linear ordinary differential equations and integral transforms are also included. Complex Variables and their Applications is an ideal textbook and resource for second and final year students of mathematics, engineering and physics.
Contents:
*Functions of a Complex
*Differentiation and the Cauchy-Riemann Equations
*Integration, Cauchy's Theorems and Related Results
*Infinite Series, Taylor Series and Laurent Series
*The Residue Theorems and its Applications
*Conformal Transformations
*Linear Ordinary Differential
*Fourier and Laplace Transforms
*Laplace's Equations and Other Partial Differential Equations
*Analytical Functions
*Elliptic Functions.
Brief Description:
This book is concerned with the study of functions of a complex variable. It is a clear exposition of the fundamental areas of complex analysis, together with applications directed mainly to differential equations.
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