Applications of Potential Theory in Mechanics PDF Download
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Author: V. I. Fabrikant
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 492
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Book Description
Author: V. I. Fabrikant
Publisher: Dordrecht ; Boston : Kluwer Academic Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 492
Get Book Here
Book Description
Author: Nikolaĭ Maksimovich Gi︠u︡nter
Publisher: Burns & Oates
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: Oliver Dimon Kellogg
Publisher: Springer Science & Business Media
ISBN: 3642908500
Category : Mathematics
Languages : en
Pages : 392
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Book Description
The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, in order that the book may present sound ideals to the student, and also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.
Author: D. E. Rutherford
Publisher: Courier Corporation
ISBN: 048615453X
Category : Mathematics
Languages : en
Pages : 148
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Book Description
This text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. 1957 edition.
Author: Philippe Biane
Publisher: Springer
ISBN: 3540693653
Category : Mathematics
Languages : en
Pages : 467
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Book Description
This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Author: K. GowriSankaran
Publisher: Springer Science & Business Media
ISBN: 9401111383
Category : Mathematics
Languages : en
Pages : 467
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Book Description
Proceedings of the NATO Advanced Research Workshop, Château de Bonas, France, July 25--31, 1993
Author: Nikolaĭ Maksimovich Gi︠u︡nter
Publisher:
ISBN:
Category : Mathematical physics
Languages : en
Pages : 338
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Book Description
Author: D. E. Rutherford
Publisher: Courier Corporation
ISBN: 9780486439037
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Designed to familiarize undergraduates with the methods of vector algebra and vector calculus, this text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. A chapter on differential geometry introduces readers to the study of this subject by the methods of vector algebra. The next section explores the many aspects of the theory of mechanics adaptable to the use of vectors, and a full discussion of the vector operator "nabla" proceeds to a treatment of potential theory and Laplace's equation. This includes applications to the theories of gravitation, hydrodynamics, and electricity. A brief chapter on four-dimensional vectors concludes the text.
Author: Lester L. Helms
Publisher: Springer Science & Business Media
ISBN: 1447164229
Category : Mathematics
Languages : en
Pages : 494
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Book Description
Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible. The subject matter is developed from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem, the author develops methods for constructing solutions of Laplace's equation on a region with prescribed values on the boundary of the region. The latter half of the book addresses more advanced material aimed at those with the background of a senior undergraduate or beginning graduate course in real analysis. Starting with solutions of the Dirichlet problem subject to mixed boundary conditions on the simplest of regions, methods of morphing such solutions onto solutions of Poisson's equation on more general regions are developed using diffeomorphisms and the Perron-Wiener-Brelot method, culminating in application to Brownian motion. In this new edition, many exercises have been added to reconnect the subject matter to the physical sciences. This book will undoubtedly be useful to graduate students and researchers in mathematics, physics and engineering.
Author: Richard J. Blakely
Publisher: Cambridge University Press
ISBN: 9780521575478
Category : Mathematics
Languages : en
Pages : 468
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Book Description
This text bridges the gap between the classic texts on potential theory and modern books on applied geophysics. It opens with an introduction to potential theory, emphasising those aspects particularly important to earth scientists, such as Laplace's equation, Newtonian potential, magnetic and electrostatic fields, and conduction of heat. The theory is then applied to the interpretation of gravity and magnetic anomalies, drawing on examples from modern geophysical literature. Topics explored include regional and global fields, forward modeling, inverse methods, depth-to-source estimation, ideal bodies, analytical continuation, and spectral analysis. The book includes numerous exercises and a variety of computer subroutines written in FORTRAN. Graduate students and researchers in geophysics will find this book essential.
