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A0BA8379CD23345070B2BD8649B14C20C63C688D
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April 22, 2026, 9:18 a.m.
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(Last updated: April 22, 2026, 9:18 a.m.)
| File | Size |
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| ['Readme.txt'] | 0 bytes |
| ['Thron W. Introduction to The Theory of Functions of A Complex Variable 1953.djvu'] | 0 bytes |
| ['Thron W. Introduction to The Theory of Functions of A Complex Variable 1953.pdf'] | 0 bytes |
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2025-07-27
| Uploaded by XXXClub | Size 462.4 MB | Health [ 18 /20 ] | Added 2025-07-27 |
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NOTE
SOURCE: Thron W. Introduction to The Theory of Functions of A Complex Variable 1953
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COVER
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MEDIAINFO
Textbook in PDF and DJVU formats
A definite need exists for an introduction to functions of complex variables in which all results are derived from a simple set of axioms. Since no such book is available I have attempted to fill the gap by writing a text in which occur neither “intuitiveproofs” nor theorems for whose proofs the reader is referred to other sources. The only intentional exception to this rule is the omission of those proofs that seemed to be simple enough to be left as exercises for the reader. In certain borderline cases outlines of proofs are given. Thus the statement that no previous mathematical knowledge is required of the reader is literally true.
It is hoped that this book will be useful as a text. I have used preliminary drafts of it in a two-semester course at Washington University in the academic years 1946-47 and 1948-49. It also is intended to serve as a reference book to which instructors and interested students may want to turn for complete derivations in many instances not to be found elsewhere.
Fundamental concepts
Real numbers
Cardinal numbers
Complex numbers
Sums and products
Hausdorff spaces
Metric spaces
The plane of complex numbers
Limits, continuity, differentiability
Real functions of real variables
Curves and regions in the plane of complex numbers
Some combinatorial topology
Jordan curves
Rectifiable and directed curves
Integration
The Cauchy integral theorem
Sequences of functions
Infinite series
Power series
Function spaces
Elementary transcendental functions
Inverse functions
Analytic continuation and singular points
The extended plane
Classification of some single-valued analytic functions
Residues
Conformal maps
Linear fractional transformations and inversions
Simple functions and the Riemann mapping theorem
The elliptic modular function and Picard’s theorems
Riemann surfaces
Index
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