Download or read book Potential Theory and Its Applications to Basic Problems of Mathematical Physics written by Nikolaĭ Maksimovich Gi︠u︡nter and published by Burns & Oates. This book was released on 1968 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Potential theory and its applications to basic problems of mathematical physics written by Nikolaĭ Maksimovich Gi︠u︡nter and published by . This book was released on 1967 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Foundations of Potential Theory written by Oliver Dimon Kellogg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundations of Modern Potential Theory written by Naum Samoĭlovich Landkof and published by Springer. This book was released on 1972 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods for Solving Mathematical Physics Problems written by Valeriĭ Ivanovich Agoshkov and published by Cambridge Int Science Publishing. This book was released on 2006 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. The book is of the handbook-teaching type. On the one hand, the book describes the main definitions, the concepts of the examined methods and approaches used in them, and also the results and claims obtained in every specific case. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.
Download or read book Potential Theory written by Josef Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal with applications in physics and engineering, other concern potential theoretic aspects of function theory and complex analysis. Numerous papers are devoted to the theory of partial differential equations. Included are also many articles on axiomatic and abstract potential theory with its relations to probability theory. The present volume may thus be of intrest to mathematicians speciali zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.
Download or read book Potential Theory written by Lester Helms and published by Springer Science & Business Media. This book was released on 2009-05-27 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ?rst six chapters of this book are revised versions of the same chapters in the author’s 1969 book, Introduction to Potential Theory. Atthetimeof the writing of that book, I had access to excellent articles,books, and lecture notes by M. Brelot. The clarity of these works made the task of collating them into a single body much easier. Unfortunately, there is not a similar collection relevant to more recent developments in potential theory. A n- comer to the subject will ?nd the journal literature to be a maze of excellent papers and papers that never should have been published as presented. In the Opinion Column of the August, 2008, issue of the Notices of the Am- ican Mathematical Society, M. Nathanson of Lehman College (CUNY) and (CUNY) Graduate Center said it best “. . . When I read a journal article, I often ?nd mistakes. Whether I can ?x them is irrelevant. The literature is unreliable. ” From time to time, someone must try to ?nd a path through the maze. In planning this book, it became apparent that a de?ciency in the 1969 book would have to be corrected to include a discussion of the Neumann problem, not only in preparation for a discussion of the oblique derivative boundary value problem but also to improve the basic part of the subject matter for the end users, engineers, physicists, etc.
Download or read book Applications of Potential Theory in Mechanics written by V. I. Fabrikant and published by Dordrecht ; Boston : Kluwer Academic Publishers. This book was released on 1989 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Singular Integral Equations written by N. I. Muskhelishvili and published by Courier Corporation. This book was released on 2013-02-19 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVHigh-level treatment of one-dimensional singular integral equations covers Holder Condition, Hilbert and Riemann-Hilbert problems, Dirichlet problem, more. 1953 edition. /div
Download or read book Multiscale Potential Theory written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.
Download or read book Potential Theory written by Lester L. Helms and published by Springer Science & Business Media. This book was released on 2014-04-10 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory And Applications In Mathematical Physics In Honor Of B Tirozzi s 70th Birthday written by Giovanni Montani and published by World Scientific. This book was released on 2015-10-13 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to make a connection among advanced mathematical tools and application to real problems. There are many different mathematical structures analyzed in the book and all of them are in important applications, like statistics and biology, neural networks and financial markets, asymptotic methods for partial differential equations and the problem of tsunami propagation. Plasma physics has been given a new approach, using focal points in analogy to the theory of tsunami waves.
Download or read book Potential Theory Surveys and Problems written by Josef Kral and published by Springer. This book was released on 2007-02-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.
Download or read book Mathematical Physics written by Shigeji Fujita and published by John Wiley & Sons. This book was released on 2010-02-01 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Going beyond standard mathematical physics textbooks by integrating the mathematics with the associated physical content, this book presents mathematical topics with their applications to physics as well as basic physics topics linked to mathematical techniques. It is aimed at first-year graduate students, it is much more concise and discusses selected topics in full without omitting any steps. It covers the mathematical skills needed throughout common graduate level courses in physics and features around 450 end-of-chapter problems, with solutions available to lecturers from the Wiley website.
Download or read book Potential Theory in Applied Geophysics written by Kalyan Kumar Roy and published by Springer Science & Business Media. This book was released on 2007-11-15 with total page 661 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.
Download or read book Problems in Classical Potential Theory with Applications to Mathematical Physics written by Erik Lundberg and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters. Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem). Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain. Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.
Download or read book Boundary Value Problems of Mathematical Physics written by Ivar Stakgold and published by SIAM. This book was released on 2000-06-30 with total page 1156 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.
