Complex Analytic Methods for Partial Differential Equations
Complex Analytic Methods for Partial Differential Equations

Author: Heinrich G. W. Begehr

Publisher: World Scientific

Published: 1994

Total Pages: 288

ISBN-13: 9789810215507

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This is an introductory text for beginners who have a basic knowledge of complex analysis, functional analysis and partial differential equations. Riemann and Riemann-Hilbert boundary value problems are discussed for analytic functions, for inhomogeneous Cauchy-Riemann systems as well as for generalized Beltrami systems. Related problems such as the Poincar‚ problem, pseudoparabolic systems and complex elliptic second order equations are also considered. Estimates for solutions to linear equations existence and uniqueness results are thus available for related nonlinear problems; the method is explained by constructing entire solutions to nonlinear Beltrami equations. Often problems are discussed just for the unit disc but more general domains, even of multiply connectivity, are involved.

Handbook of Differential Equations: Ordinary Differential Equations
Handbook of Differential Equations: Ordinary Differential Equations

Author: Flaviano Battelli

Publisher: Elsevier

Published: 2008-08-19

Total Pages: 719

ISBN-13: 0080559468

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This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience. Covers a variety of problems in ordinary differential equations Pure mathematical and real-world applications Written for mathematicians and scientists of many related fields

Mathematics-II (Calculus, Ordinary Differential Equations and Complex Variable)
Mathematics-II (Calculus, Ordinary Differential Equations and Complex Variable)

Author: Bhui, Bikas Chandra & Chatterjee Dipak

Publisher: Vikas Publishing House

Published:

Total Pages:

ISBN-13: 9353381312

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Mathematics-II (Calculus, Ordinary Differential Equations and Complex Variable) for the paper BSC-104 of the latest AICTE syllabus has been written for the second semester engineering students of Indian universities. Paper BSC-104 is common for all streams except CS&E students. The book has been planned with utmost care in the exposition of concepts, choice of illustrative examples, and also in sequencing of topics. The language is simple, yet accurate. A large number of worked-out problems have been included to familiarize the students with the techniques to solving them, and to instil confidence. Authors’ long experience of teaching various grades of students has helped in laying proper emphasis on various techniques of solving difficult problems.

Complex Variables
Complex Variables

Author: Steven G. Krantz

Publisher: CRC Press

Published: 2019-04-16

Total Pages: 351

ISBN-13: 1000000354

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The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.

Singular Partial Differential Equations
Singular Partial Differential Equations

Author: Abduhamid Dzhuraev

Publisher: CRC Press

Published: 1999-11-29

Total Pages: 220

ISBN-13: 9781584881445

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Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equations and systems in a class of bounded functions with complex coefficients having singularities at the inner points or boundary of the domain. Using complex variable techniques, the author considers a variety of problems, including the Dirichlet, Neumann, and other problems for first order systems. He also explores applications to singular equations, degenerate, high-dimensional Beltrami systems in Cn,, and others. Singular Partial Differential Equations fills a gap in the literature on degenerate and singular partial differential equations and significantly contributes to the theory of boundary value problems for these equations and systems. It will undoubtedly stimulate further research in the field. Practical applications in analysis and physics make this important reading for researchers and students in physics and engineering, along with mathematicians.

Partial Differential Equations
Partial Differential Equations

Author: Lipman Bers

Publisher: American Mathematical Soc.

Published: 1964-12-31

Total Pages: 372

ISBN-13: 9780821896983

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This book consists of two main parts. The first part, "Hyperbolic and Parabolic Equations", written by F. John, contains a well-chosen assortment of material intended to give an understanding of some problems and techniques involving hyperbolic and parabolic equations. The emphasis is on illustrating the subject without attempting to survey it. The point of view is classical, and this serves well in furnishing insight into the subject; it also makes it possible for the lectures to be read by someone familiar with only the fundamentals of real and complex analysis. The second part, "Elliptic Equations", written by L. Bers and M. Schechter, contains a very readable account of the results and methods of the theory of linear elliptic equations, including the maximum principle, Hilbert-space methods, and potential-theoretic methods. It also contains a brief discussion of some quasi-linear elliptic equations. The book is suitable for graduate students and researchers interested in partial differential equations.