Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable
by Lars V. Ahlfors
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A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of show more Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals. show lessTags
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A beautiful exposition of complex analysis. One warning, though: you should have a good understanding of complex algebra and calculus before reading this text, as it is dense.
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- Canonical title
- Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable
- Original title
- Complex Analysis
- Dedication
- To Erna
- First words
- It is fundamental that the real and complex numbers obey the same basic laws of arithmetic.
- Last words
- (Click to show. Warning: May contain spoilers.)Finally, if Ω is not simply connected, then (f,Ω)∊F₀ is the analytic continuation of a restriction to a simply connected subregion of Ω, and since the restriction belongs to F so does (f,Ω) because of property 1.
- Original language
- English US
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Statistics
- Members
- 275
- Popularity
- 116,887
- Reviews
- 1
- Rating
- (4.32)
- Languages
- Chinese, English
- Media
- Paper
- ISBNs
- 8
- ASINs
- 7
