The Cauchy Method of Residues: Theory and Applications
Springer Science & Business Media, Apr 30, 1984 - Mathematics - 361 pages
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.
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The Cauchy Method of Residues: Volume 2: Theory and Applications
Dragoslav S. Mitrinovic,J.D. Keckic
No preview available - 2012
Acad analytic function applications arbitrary becomes belong bounded calculus of residues called Cauchy circle closed contour coefficients complex Compt conclude considered constant contains continuous Contour Integration convergent defined Definite Integrals denoted determine difference equal equation evaluated EXAMPLE exists expansion expressed f is regular Figure formula function f Furthermore give given hand Hence implies important inside integral intégrales Let f limit Math Mathematical means mentioned method neighbourhood obtain Oeuvres origin Paris particular period plane polynomial positive problem Proof proved published real axis REFERENCE region region G regular function REMARK Rend replaced Res f(z respect result Russian satisfies side simple poles singularities solution Suppose taken Theorem theory transform variables written zeros
Page 7 - ... into another ; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another. The Mathematics and Its Applications programme tries to make available a careful selection of books which fit the philosophy outlined above. With such books, which are stimulating rather than definitive, intriguing rather than encyclopaedic, we hope to contribute something towards better communication among the practitioners in diversified fields.
Page 8 - ... available a careful selection of books which fit the philosophy outlined above. With such books, which are stimulating rather than definitive, intriguing rather than encyclopaedic, we hope to contribute something towards better communication among the practitioners in diversified fields. Because of the wealth of scholarly research being undertaken in the Soviet Union, Eastern Europe, and Japan, it was decided to devote special attention to the work emanating from these particular regions. Thus...
Page 8 - The unreasonable effectiveness of mathe- As long as algebra and geometry promatics in science ... ceeded along separate paths, their advance was slow and their applications limited.