Theory of Functions of Two Complex Variable by Andrew Forsyth
Theory of Functions of Two Complex Variable - Table of Contents
1. Geometrical Representation of the Variables
2. Lineo-Linear Transformations; Invariants and Covariants
3. Uniform Analytic Functions
4. Uniform Functions in Restricted Domains
5. Functions Without Essential Singularities in the Finite Part of the Field of Variation
6. Integrals; In Particular, Double Integrals
7. Level Places of Two Simultaneous Functions
8. Uniform Periodic Functions
What You Will Learn in Theory of Functions of Two Complex Variable
"Lectures Introductory to the Theory of Functions of Two Complex Variables" by "Andrew Russell Forsyth" is a classical text that extends "complex analysis" from one variable to "functions of two complex variables". Forsyth systematically introduces the concept of regular (analytic) functions in two variables, explaining conditions for analyticity, uniformity, and convergence of "double power series". He emphasizes rigorous proofs while providing examples that illustrate the geometric and analytic behavior of these functions in higher dimensions.
The book explores advanced topics such as "multiform functions", algebraic functions in two variables, branch points, and surfaces. Forsyth also discusses conditions for meromorphicity, the behavior of double integrals, and doubly periodic or homoperiodic functions. His approach combines classical analytic methods with geometric intuition, helping readers understand how functions of one variable generalize to the more complex two-variable setting.
Forsyth’s lectures were historically significant as one of the earliest systematic English-language treatments of several complex variables. The text remains valuable for understanding the classical foundations of "function theory" in higher dimensions. It provides a bridge between single-variable complex analysis and modern developments in multi-variable theory, offering insights into double series expansions, branch structures, and the analytic continuation of functions in two complex variables.
Book Details & Specifications
Title:
Theory of Functions of Two Complex Variable by Andrew Forsyth
Publisher:
University Press
Year:
1914
Pages:
312
Type:
PDF
Language:
English
ISBN-10 #:
1371174423
ISBN-13 #:
978-1371174422
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 "functions of several variables". Educated at Cambridge, he focused on extending classical single-variable theory to multi-variable settings, emphasizing clarity, rigor, and geometric intuition. Forsyth authored influential works, including "Theory of Functions of Two Complex Variables", which presents double power series, multiform functions, and analytic continuation. His systematic approach to "function theory" helped shape the teaching and development of several complex variables, bridging classical analysis with modern multi-variable mathematics, and leaving a lasting impact on both research and education.
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