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. The Geometric Representation of Complex Numbers
3. The Bilinear Transformation
4. Geometric Theory of the Logarithm and the Exponential
5. The 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. Power Series
11. Operations with Power Series
12. Continuation of Power Series
13. Analytic Theory of the Exponential and Logarithm
14. Singular Points of Analytic Functions
15. Weierstrass’s Factor Theorem
16. Integration
17. Laurent’s Theorem and the Theta Functions
18. Functions Arising from a Network
19. Elliptic Functions
20. Simple Algebraic Functions on Riemann Surfaces
21. 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" (with Frank Morley) is a classical text that provides a thorough foundation in "complex analysis". The book systematically introduces the concept of "analytic functions", starting from basic definitions such as limits, continuity, and convergence, and gradually building up to more advanced topics. It emphasizes a clear, structured approach, making complex ideas accessible to readers encountering analytic function theory for the first time.
The text covers essential topics like "power series", analytic continuation, singularities, and bilinear transformations. Harkness and Morley carefully explain how these functions behave, how they can be represented, and the conditions under which they are valid. Detailed examples and step-by-step proofs help illustrate the concepts, bridging the gap between elementary calculus and more sophisticated complex-variable techniques. The book also explores the geometric aspects of analytic functions, helping readers understand their mapping properties and behavior under transformations.
This text remains influential for its clarity and classical approach to "function theory". It serves as a foundational guide for students and researchers seeking to understand the historical development of complex analysis and the rigorous treatment of "analytic functions". Its combination of theory, examples, and structured exposition ensures it remains a valuable resource in both teaching and research contexts.
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
(1854–1923) was a British mathematician known for his work in "complex analysis" and "analytic functions". He focused on teaching and writing with clarity, bridging elementary calculus and advanced function theory, making challenging concepts accessible to students and researchers. Harkness co-authored "Introduction to the Theory of Analytic Functions", a classical text covering "power series", singularities, analytic continuation, and geometric properties of functions. His systematic approach and rigorous proofs helped shape the study and teaching of function theory, leaving a lasting influence on the development of complex analysis and the understanding of analytic functions.
Read or Downloadable Introduction to the Theory of Analytic Functions
Free Complex Analysis Books PDF | Download University Textbooks