Theory of Functions of A Complex Variable by H. Durege
Theory of Functions of A Complex Variable - Table of Contents
1. Geometric Representation of Imaginary Quantities
2. Functions of a Complex Variable in General
3. Multiform Functions
4. Integrals with Complex Variables
5. The Logarithmic and Exponential Functions
6. General Properties of Functions
7. Infinite and Infinitesimal Values of Functions
8. Integrals (further discussion)
9. Simply- and Multiply-Connected Surfaces
10. Moduli of Periodicity
What You Will Learn in Theory of Functions of A Complex Variable
Elements of the Theory of Functions of a Complex Variable, With Especial Reference To The Methods Of Riemann by H. Dürrège is a classic introduction to early "complex analysis", written in a clear but traditional 19th-century style. The book focuses on the foundations of complex numbers, the behavior of analytic functions, and the geometric intuition behind complex variables. Dürrège presents the subject through simple explanations and classical examples, making the material approachable while still mathematically solid.
A major part of the book discusses "power series", "analytic continuation", and the core results of Cauchy’s theory, including contour integration and the Cauchy integral formula. Dürrège also covers singularities, Laurent expansions, and early techniques that later evolved into the modern residue theory. While the language is old-fashioned, the structure clearly shows how complex analysis was taught before the modern formal era.
Today, the book is valued for its historical perspective rather than as a primary textbook. It appeals to students and historians interested in the development of mathematical ideas, offering insight into the early teaching of analytic functions and conformal mapping. Though not as rigorous as modern texts, Dürrège’s work remains a meaningful window into the evolution of "complex function theory".
Book Details & Specifications
Title:
Theory of Functions of A Complex Variable by H. Durege
Publisher:
Macmillan
Year:
1902
Pages:
312
Type:
PDF
Language:
English
ISBN-10 #:
1013174615
ISBN-13 #:
978-1013174612
License:
Public Domain Work
Amazon:
Amazon
About the Author: Heinrich Durège
The author Heinrich Durège
was a "19th-century German mathematician" best known for writing "Theory of Functions of a Complex Variable". His work focused on teaching and explaining the foundations of "complex analysis" during a period when the field was still taking shape. Although not widely recognized for major research breakthroughs, he played an important role in organizing and presenting early analytic function theory for students. Today, his work is valued for its historical insight into how mathematicians approached "analytic functions" in the early development of the subject.
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