The Cauchy method of residues : theory and applications
著者
書誌事項
The Cauchy method of residues : theory and applications
（Mathematics and its applications, . East European series ; v. 259）
D. Reidel, c1984-c1993
English ed
- [v. 1]
- v. 2
- タイトル別名
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Cauchyjev račun ostataka sa primenama
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注記
v. 2 published by Kluwer Academic Publishers
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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v. 2 ISBN 9780792323112
内容説明
This volume is a sequel to "The Cauchy Method of Residues" published in 1984 (also by Kluwer under the D. Reidel imprint). Volume 1 surveyed the main results published in the period 1814-1982. The present volume contains various results which were omitted from the first volume, some results mentioned briefly in Volume 1 and discussed here in greater detail, and new results published since 1982. It also contains short expositions, by various authors, dealing with new and interesting aspects of the theory and applications of residues. This volume should be of interest to researchers and graduate students in complex analysis, and also physicists and engineers whose work involves the application of complex functions.
目次
- 1. Introduction. 2. Evaluation of Residues 3. Applications of Calculus of Residues in the Theory of Functions. 4. Evaluation of Real Define Integrals by Means of Residues. 5. Evaluation of Finite and Infinite Sums byResidues. 6. Applications of Calculus of Residues to Special functions. 7 Master's Dissertation of J.V Sohocki. 8. On the Principal and the Generalized Value of Improper Integrals-, D.S. Ditnitrov ski. 9. Applications of the Calculus of Residues to Numerical Evaluation of Integrals
- D.D. Tosic.. 10. Inclusive Calculus of Residues: MS. Petkovic. 11. Complex Polynomials Orthogonal on the Semicircle: G. V Milovanovic, 12. A Representation of Half Plane Meromorphic Functions
- D. Mirovic 13. Calculus of Residues and Distributions: D. Mitrovic.
- 巻冊次
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[v. 1] ISBN 9789027716231
内容説明
Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not' grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory arid the struc ture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-5cale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exampla gratia: - a central concept which plays an important role in several different mathe matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific en deavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.
目次
1. Introduction.- 2. Definition and Evaluation of Residues.- 3. Contour Integration.- 4. Applications of the Calculus of Residues in the Theory of Functions.- 5. Evaluation of Real Definite Integrals by Means of Residues.- 6. Evaluation of Finite and Infinite Sums by Residues.- 7. Differential and Integral Equations.- 8. Applications of Calculus of Residues to Special Functions.- 9. Calculus of Finite Differences.- 10. Augustin-Louis Cauchy.- Notes Added in Proof.- Name Index.
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