Introduction to complex analysis
著者
書誌事項
Introduction to complex analysis
Clarendon Press , Oxford University Press, 1990
Rev. ed
- : pbk
大学図書館所蔵 件 / 全16件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Bibliography: p. [207]-208
内容説明・目次
内容説明
This book presents a concise introduction to elementary complex analysis. The theory is treated rigorously, but no prior knowledge of topology is assumed. The emphasis throughout is on those aspecsts of the theory which are important in other branches of mathematics. The basic techniques are explained, and the major theorems are presented in such a way as to enable the reader to appreciate both the practical and the theoretical applications of the subject. In this revised edition, the author has included numerous new exercises to help and consolidate a firm understanding of complex analysis.
目次
- Part 1 The complex plane: complex numbers
- open and closed sets in the complex plane
- limits and continuity. Part 2 Holomorphic function and power series: complex power series
- elementary functions. Part 3 Prelude to Cauchy's theorem: paths
- integration along paths
- connectedness and simple connectedness
- properties of paths and contours. Part 4 Cauchy's theorem: Cauchy's theorem, level I and II
- logarithms, argument and index
- Cauchy's theorem revisited. Part 5 Consequences of Cauchy's theorem: Cauchy's formulae
- power series representation
- zeros of holomorphic functions
- the maximum-modulus theorem. Part 6 Singularities and multifunctions: Laurent's theorem
- singularities
- meromorphic functions
- multifunctions. Part 7 Cauchy's residue theorem: counting zeroes and poles
- claculation of residues
- estimation of integrals. Part 8 Applications of contour integration: improper and principal-values integrals
- integrals involving functions with a finite number of poles and infinitely many poles
- deductions from known integrals
- integrals involving multifunctions
- evaluation of definite integrals. Part 9 Fourier and Laplace tranforms: the Laplace tranform - basic properties and evaluation
- the inversion of Laplace tranforms
- the Fourier tranform
- applications to differential equations
- proofs of the Inversion and Convolution theorems. Part 10 Conformal mapping and harmonic functions: circles and lines revisited
- conformal mapping
- mobius tranformations
- other mappings - powers, exponentials, and the Joukowski transformation
- examples on building conformal mappings
- holomorphic mappings - some theory
- harmonic functions.
「Nielsen BookData」 より
