Discrete Fourier analysis, Cauchy integrals, construction of conformal maps, univalent functions
著者
書誌事項
Discrete Fourier analysis, Cauchy integrals, construction of conformal maps, univalent functions
（Pure and applied mathematics, . Applied and computational complex analysis / Peter Henrici ; Vol. 3）
Wiley, c1986
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注記
"A Wiley-Interscience publication."
Includes bibliographies and index
内容説明・目次
内容説明
At a mathematical level accessible to the non-specialist, the third of a three-volume work shows how to use methods of complex analysis in applied mathematics and computation. The book examines two-dimensional potential theory and the construction of conformal maps for simply and multiply connected regions. In addition, it provides an introduction to the theory of Cauchy integrals and their applications in potential theory, and presents an elementary and self-contained account of de Branges' recently discovered proof of the Bieberbach conjecture in the theory of univalent functions. The proof offers some interesting applications of material that appeared in volumes 1 and 2 of this work. It discusses topics never before published in a text, such as numerical evaluation of Hilbert transform, symbolic integration to solve Poisson's equation, and osculation methods for numerical conformal mapping.
目次
- Discrete Fourier Analysis
- Cauchy Integrals
- Potential Theory in the Plane
- Construction of Conformal Maps. Simply Connected Regions
- Construction of Conformal Maps: Multiply Connected Regions
- Polynomial Expansions and Conformal Maps
- Univalent Functions
- Bibliography
- Index.
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