Theory of functions of a complex variable
著者
書誌事項
Theory of functions of a complex variable
American Mathematical Society, 2001
2nd English ed
- v. 1
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注記
Includes index
"Reprinted with corrections by the American Mathematical Society, 2001"--T.p. verso
内容説明・目次
内容説明
Presents a translation of the last of Caratheodory's celebrated text books, ""Funktiontheorie, Volume 1"".
目次
- Part One: Complex Numbers: The complex numbers from the algebraic point of view The geometry of the complex numbers Euclidean, spherical, and non-Euclidean geometry
- Part Two: Some Results From Point Set Theory and From Topology: Convergent sequences of numbers and continuous complex functions Curves and regions Contour integration
- Part Three: Analytic Functions: Foundations of the theory The maximum-modulus principle The Poisson integral and harmonic functions Meromorphic functions
- Part Four: Analytic Functions Defined By Limiting Processes: Continuous convergence Normal families of meromorphic functions Power series Partial-fraction decomposition and the calculus of residues
- Part Five: Special Functions: The exponential and trigonometric functions The logarithmic function and the general power function The Bernoulli numbers and the gamma function Index.
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