A Course in Mathematical Analysis 2-1 (Complex Variable) by Edouard Goursat
A Course in Mathematical Analysis 2-1 (Complex Variable) - Table of Contents
1. Elements of the Theory
I. General Principles: Analytic Functions
II. Power Series with Complex Terms & Elementary Transcendental Functions
III. Conformal Representation
2. The General Theory of Analytic Functions (according to Cauchy)
I. Definite Integrals Taken Between Imaginary Limits
II. Cauchy's Integral; Taylor's and Laurent's Series; Singular Points; Residues
III. Applications of the General Theorems
IV. Periods of Definite Integrals
3. Single-Valued Analytic Functions
I. Weierstrass's Primary Functions; Mittag-Leffler's Theorem
II. Doubly Periodic Functions; Elliptic Functions
III. Inverse Functions; Curves of Deficiency One
4. Analytic Extension
I. Definition of an Analytic Function by Means of One of Its Elements
II. Natural Boundaries
5. Analytic Functions of Several Variables
I. General Properties
II. Implicit Functions; Algebraic Functions
What You Will Learn in A Course in Mathematical Analysis 2-1 (Complex Variable)
"A Course in Mathematical Analysis Volume 2 Part 1 (FUNCTIONS OF A COMPLEX VARIABLE)" by Édouard Goursat is a classic text in "complex analysis" that has shaped the study of functions of a complex variable for over a century. Designed for advanced undergraduate and graduate students, this volume introduces the rigorous foundation of the subject while maintaining clarity and precision. The book systematically develops key concepts, making it ideal for both learning and reference.
The text explores "analytic functions", including their general properties, power series expansions, and the behavior of singularities. Goursat also presents conformal mappings and geometric interpretations, providing readers with intuitive insights alongside formal proofs. Important topics like Laurent series, residues, and applications of "Cauchy’s theorem" are explained in detail, demonstrating the power of these methods in solving complex variable problems.
In addition, the book covers multi-valued functions, analytic extension, and the groundwork for elliptic functions. Goursat’s careful treatment ensures a deep understanding of both theory and application, making this work a timeless resource for mathematicians, physicists, and engineers. With its structured approach and rigorous proofs, this volume remains a cornerstone in the study of "complex analysis".
Book Details & Specifications
Title:
A Course in Mathematical Analysis 2-1 (Complex Variable) by Edouard Goursat
Publisher:
Ginn & Company
Year:
1916
Pages:
280
Type:
PDF
Language:
English
ISBN-10 #:
1141798077
ISBN-13 #:
978-1141798070
License:
Public Domain Work
Amazon:
Amazon
About the Author: Edouard Goursat
The author Edouard Goursat
(1858–1936) was a renowned French mathematician known for his pioneering work in "complex analysis" and "mathematical analysis". He developed rigorous foundations for "analytic functions" and advanced the study of complex variables, differential equations, and elliptic functions. Goursat taught at the University of Paris and authored "A Course in Mathematical Analysis", a classic text celebrated for its clarity, precision, and logical structure. His contributions continue to influence mathematicians and students worldwide, making his work essential for anyone studying "complex analysis", "analytic functions", or advanced mathematics.
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