The elements of complex analysis
著者
書誌事項
The elements of complex analysis
John Wiley & Sons, 1992
2nd ed
- : Wiley Eastern
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注記
Originally published: New Delhi, India : Wiley Eastern, 1992
Includes bibliographical references (p. [326]) and index
内容説明・目次
- 巻冊次
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ISBN 9780470221167
内容説明
This introduction to the field features proofs and motivation, gives examples and exercises at various levels of difficulty to illustrate the concepts, details uniform approximation and elliptic functions, and provides ordinary linear homogeneous differential equations of the second order and conformal mapping. Diagrams are provided whenever feasible to help develop the ability to visualize abstract ideas. The solutions to selected exercises provide ideas and theoretical considerations.
目次
- Sets, Functions and Complex Numbers
- Metric Spaces
- Elementary Properties of Analytic Functions
- Line Integral and Cauchy's Theorem
- Applications of Cauchy's Theorem
- Power Series
- Laurent Series, Singularities
- Residue Theorem and Its Applications
- Conformal Mapping
- Harmonic Functions
- Weierstrass Factorization Theorem
- Extension of the Maximum Modulus Principle
- Elliptic Functions
- Analytic Continuation, Differential Equations
- Approximation by Rational Functions and Polynomials.
- 巻冊次
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: Wiley Eastern ISBN 9788122403992
内容説明
Some of the welcome features of the book are: proofs and motivation for the theory: examples are provided to illustrate the concepts; exercises of various levels of difficulty are given at the end of every chapter: keeping in view the applied nature of the subject, ordinary linear homogeneous differential equations of the second order and conformal mapping and its applications are given more attention than most other books: uniform approximation and elliptic functions are treated in great detail; there is also a detailed treatment of Harmonic Functions, Weierstrass approximation theorem, analytic continuation, Riemann mapping theorem, homological version of Cauchys theorem and its applications; diagrams are provided whenever feasible to help the reader develop skill in using imagination to visualise abstract ideas; and, solutions to some selected exercises which involve lot of new ideas and theoretical considerations have been provided at the end.
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