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1. Introduction 2. Geometric Representation of Imaginary Quantities 3. Functions of a Complex Variable in General 4. Multiform Functions 5. Integrals with Complex Variables 6. The Logarithmic and Exponential Functions 7. General Properties of Functions 8. Infinite and Infinitesimal Values of Functions 9. Integrals 10. Simply and Multiply Connected Surfaces 11. Moduli of Periodicity
"Elements of the Theory of Functions of a Complex Variable with Especial Reference to the Methods of Riemann" by Heinrich Durège is a classic 19th-century text that introduces the foundations of "complex analysis". The book explains how complex functions behave and how they can be studied using geometric and analytical ideas. Inspired by Bernhard Riemann’s approach, it presents mathematics not just as formulas, but as a deeper conceptual system. Durège carefully develops topics such as analytic functions, conformal mapping, and the structure of complex variables. A major focus is on "Riemann surfaces", which provide a powerful way to understand multi-valued functions. By combining algebra with geometry, the book strengthens understanding of "function theory" and advanced mathematical reasoning. Historically, this work helped spread "Riemann’s methods" across Europe and influenced university-level teaching of higher mathematics. It became an important reference for students studying "mathematical analysis", shaping the development of modern complex function theory and its applications in science and engineering.
Title: Theory of Functions & Riemann's Methods by H. Durège Publisher: Macmillan Year: 1896 Pages: 308 Type: PDF Language: English ISBN-10 #: 1110352093 ISBN-13 #: 9781110352098 License: Public Domain Work Amazon: Amazon
The author Heinrich Durege was a German mathematician known for his work in "complex analysis" and the "theory of functions". He wrote "Theory of Functions & Riemann's Methods" to explain and organize the ideas of Bernhard Riemann for students and scholars. His writing helped make advanced topics in "analytic functions" clearer and more structured. Durège played an important role in spreading "Riemann’s methods" across Europe. His textbooks supported higher "mathematics education", guiding learners through the geometric and analytical foundations of modern function theory.
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