Theory of Functions of a Complex Variable by A.R. Forsyth

Book Contents :-
1. General Introduction 2. Integration of Uniform Functions 3. Expansion of Functions into Power Series 4. Uniform Functions, Particularly Those without Essential Singularities 5. Transcendental Integral Functions 6. Functions with a Limited Number of Essential Singularities 7. Functions with Unlimited Essential Singularities and Expansion into Series of Functions 8. Multiform Functions 9. Periods of Definite Integrals and Periodic Functions in General 10. Uniform Simply Periodic and Doubly Periodic Functions 11. Doubly Periodic Functions of the Second Order 12. Pseudo-Periodic Functions 13. Functions Possessing an Algebraic Addition Theorem 14. Connectivity of Surfaces 15. Riemann Surfaces 16. Algebraic Functions and Their Integrals 17. Schwarz’s Proof of the Existence Theorem 18. Applications of the Existence Theorem 19. Conformal Representation: Introduction 20. Conformal Representation: General Theory 21. Groups of Linear Substitutions 22. Automorphic Functions 23. Supplementary Notes on Abel’s Theorem

About this book :-
"Theory of Functions of a Complex Variable" by "A. R. Forsyth" is a foundational textbook in "complex analysis" that explores the behavior of functions of a complex variable. It develops rigorous ideas of analytic functions, contour integration, and conformal mappings, providing mathematical tools essential for advanced analysis. The book reflects early twentieth-century precision and remains historically important in function theory. The text explains key concepts such as series expansions, singularities, and properties of analytic mappings. Forsyth’s systematic approach helps readers understand how complex functions behave and how analysis applies to mathematical modeling. Although written in a classical style, its ideas continue to influence modern mathematical theory. For students and researchers of "complex function theory", this book serves as a valuable reference. It contributes to the historical development of analysis and supports deeper understanding of mathematical structures. Its emphasis on logical rigor and analytic methods makes it significant for advanced mathematical study and scientific applications.

Book Detail :-
Title: Theory of Functions of a Complex Variable by A.R. Forsyth
Publisher: Cambridge University Press
Year: 1918
Pages: 896
Type: PDF
Language: English
ISBN-10 #: 1147415056
ISBN-13 #: 978-1147415056
License: Public Domain Work
Amazon: Amazon

About Author :-
The author Andrew Russell Forsyth was a leading mathematician known for his contributions to "complex analysis" and "differential equations". He wrote influential textbooks that shaped modern mathematical education and analytical thinking. His work emphasized rigorous proofs and systematic development of mathematical ideas, helping students understand advanced concepts with clarity. His book "Theory of Functions of a Complex Variable" became an important reference in "function theory" and mathematical research. It introduced structured explanations of analytic functions and complex methods. The text influenced generations of mathematicians and remains valuable for studying "mathematical analysis" and theoretical foundations.

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