Theory of Functions of Complex Variable by Andrew Forsyth
Theory of Functions of Complex Variable - Table of Contents
1. Preface
2. General Introduction
3. Integration of Uniform Functions
4. Expansions of Functions in Series of Powers
5. Uniform Functions, Particularly Those Without Essential Singularities
6. Transcendental Integral Uniform Functions
7. Functions with a Limited Number of Essential Singularities
8. Functions with Unlimited Essential Singularities, and Expansion in Series of Functions
9. Multiform Functions
10. Periods of Definite Integrals, and Periodic Functions in General
11. Simply-Periodic and Double-Periodic Functions
12. Double-Periodic Functions of the Second Order
13. Pseudo-Periodic Functions
14. Functions Possessing an Algebraical Addition-Theorem
15. Connectivity of Surfaces
16. Riemann’s Surfaces
17. Algebraic Functions and Their Integrals
18. Schwarz’s Proof of the Existence-Theorem
19. Applications of the Existence-Theorem; Supplementary Notes: Abel’s Theorem
20. Conformal Representation: Introductory
21. Conformal Representation: General Theory
22. Groups of Linear Substitutions
23. Automorphic Functions
24. Index / Glossary
What You Will Learn in Theory of Functions of Complex Variable
"Theory of Functions of a Complex Variable" by "Andrew Russell Forsyth" is a classical text offering a comprehensive study of "complex functions", systematically presenting both foundational and advanced concepts. The book begins with the basics of "analytic functions", exploring definitions, conditions for analyticity, convergence of "power series", and behavior near "singularities". Forsyth emphasizes rigorous proofs and clear exposition, making intricate concepts accessible to advanced students and researchers while maintaining mathematical precision.
Forsyth progresses to more advanced topics, including "multiform functions", algebraic functions, periodic and doubly periodic functions, and the study of integrals and transformations. He also discusses the geometric interpretation of complex functions, conformal mappings, and connections to algebraic curves, showing how these classical methods illuminate the structure and behavior of functions. Detailed examples, series expansions, and proofs provide a thorough understanding of both one-variable and multi-valued complex functions.
Historically, Forsyth’s work was one of the first systematic English-language treatments of complex function theory, influencing generations of mathematicians and forming a foundation for modern developments. The book bridges elementary analysis with advanced topics such as "Riemann surfaces", automorphic functions, and the theory of algebraic functions, providing a unified view of classical "function theory". Its rigorous yet accessible approach makes it a lasting resource in mathematical analysis and applied mathematics.
Book Details & Specifications
Title:
Theory of Functions of Complex Variable by Andrew Forsyth
Publisher:
University Press
Year:
1918
Pages:
893
Type:
PDF
Language:
English
ISBN-10 #:
1436600472
ISBN-13 #:
978-1436600477
License:
Public Domain Work
Amazon:
Amazon
About the Author: Andrew Russell Forsyth
The author Andrew Russell Forsyth
(1858–1942) was a British mathematician known for his contributions to "complex analysis" and "function theory". Educated at Cambridge, he focused on extending classical single-variable analysis to advanced topics, emphasizing clarity, rigor, and geometric understanding. Forsyth authored influential texts, including "Theory of Functions of a Complex Variable", covering "analytic functions", singularities, power series, and multiform behavior. His systematic approach helped shape the teaching and development of complex-variable mathematics, bridging classical analysis with modern theory and leaving a lasting impact on both mathematical research and education.
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