Introduction to the Theory of Analytic Functions by James Harkness
Introduction to the Theory of Analytic Functions - Table of Contents
- 1. The Ordinal Number System
- 2. Geometric Representation of Complex Numbers
- 3. The Bilinear Transformation
- 4. Geometric Theory of Logarithm and Exponential
- 5. Bilinear Transformation of a Plane into Itself
- 6. Limits and Continuity
- 7. The Rational Algebraic Function
- 8. Convergence of Infinite Series
- 9. Uniform Convergence of Real Series
- 10. Theory of Power Series
- 11. Operations with Power Series
- 12. Continuation of Power Series
- 13. Analytic Theory of Exponential and Logarithm
- 14. Singular Points of Analytic Functions
- 15. Weierstrass’s Factor Theorem
- 16. Principles of Integration
- 17. Laurent’s Theorem and Theta Functions
- 18. Functions Arising from a Network
- 19. Foundations of Elliptic Functions
- 20. Simple Algebraic Functions on Riemann Surfaces
- 21. Theory of Algebraic Functions
- 22. Cauchy’s Theory and the Potential
What You Will Learn in Introduction to the Theory of Analytic Functions
Introduction to the Theory of Analytic Functions by James Harkness is an authoritative classic designed to build a rigorous foundation in higher-level complex variable theory. Developed as a foundational reference for university scholars, this analytic functions textbook for graduate students focuses on power series expansions, Cauchy’s integral theorem, Riemann surfaces, and Weierstrass’s factorization methods.
Harkness and Morley’s approach is thorough, structured, and geometrically intuitive. Each concept is presented with precise analytical derivations, allowing readers to learn analytic functions concepts step-by-step—from infinite products and double series to conformal representation and elliptic functions. This clear methodology makes the volume an essential theory of analytic functions harkness pdf resource for understanding classical complex analysis.
Ideal for mathematics major students, theoretical physicists, and research historians, this landmark text serves as an outstanding free complex analysis textbook for advanced students. Available as an accessible educational reference, it remains a reliable analytic functions study guide for self-learners aiming to master the foundational framework powering modern geometric analysis.
Book Details & Specifications
Title:
Introduction to the Theory of Analytic Functions by James Harkness
Publisher:
Macmillan and Co.
Year:
1898
Pages:
362
Type:
PDF
Language:
English
ISBN-10 #:
1436563984
ISBN-13 #:
978-1436563987
License:
Public Domain Work
Amazon:
Amazon
About the Author: James Harkness
The author James Harkness
(1864–1923) was a distinguished British-Canadian mathematician and Redpath Professor of Mathematics at McGill University, celebrated for co-authoring pioneering English-language textbooks on complex variable theory with Frank Morley.
His classic monograph Theory of Analytic Functions PDF by James Harkness remains a historical landmark in the exposition of Cauchy, Riemann, and Weierstrass function theory.
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