Methods For Solving Mathematical Physics Problems

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Methods for Solving Mathematical Physics Problems :

Science

Author - V. I. Agoshkov, P. B. Dubovski, V. P. Shutiayev
Publisher - Cambridge Int Science Publishing
Pages - 320
ISBN - 1904602053


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Detail - The book examines the classic and generally accepted methods for solving mathematical physics problems (method of the potential theory, the eigenfunction method, integral transformation methods, discretisation characterisation methods, splitting methods). A separate chapter is devoted to methods for solving nonlinear equations. The book offers a large number of examples of how these methods are applied to the solution of specific mathematical physics problems, applied in the areas of science and social activities, such as energy, environmental protection, hydrodynamics, theory of elasticity, etc.

Methods for Solving Inverse Problems in Mathematical Physics :

Mathematics

Author - Global Express Ltd. Co., Aleksey I. Prilepko, Dmitry G. Orlovsky, Igor A. Vasin
Publisher - CRC Press
Pages - 744
ISBN - 9780824719876


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Detail - Developing an approach to the question of existence, uniqueness and stability of solutions, this work presents a systematic elaboration of the theory of inverse problems for all principal types of partial differential equations. It covers up-to-date methods of linear and nonlinear analysis, the theory of differential equations in Banach spaces, applications of functional analysis, and semigroup theory.

Numerical Methods for Solving Inverse Problems of Mathematical Physics :

Mathematics

Author - A. A. Samarskii, Petr N. Vabishchevich
Publisher - Walter de Gruyter
Pages - 452
ISBN - 3110205793


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Detail - The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

A Collection of Problems in Mathematical Physics :

Science

Author - Boris Mikha?lovich Budak, Aleksandr Andreevich Samarski?, Andre? Nikolaevich Tikhonov
Publisher - Courier Corporation
Pages - 768
ISBN - 0486658066


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Detail - Outstanding, wide-ranging material on classification and reduction to canonical form of second-order differential equations; hyperbolic, parabolic, elliptic equations, more. Bibliography.

Methods of Mathematical Physics :

Science

Author - Richard Courant, D. Hilbert
Publisher - John Wiley & Sons
Pages - 575
ISBN - 3527617221


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Detail - Since the first volume of this work came out in Germany in 1924, this book, together with its second volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's second and final revision of 1953.

Equations in Mathematical Physics : A practical course

Science

Author - V.P. Pikulin, Stanislav I. Pohozaev
Publisher - Birkhäuser
Pages - 207
ISBN - 3034882858


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Detail - The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type.

The Boundary Value Problems of Mathematical Physics :

Science

Author - O.A. Ladyzhenskaya
Publisher - Springer Science & Business Media
Pages - 322
ISBN - 1475743173


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Detail - In the present edition I have included "Supplements and Problems" located at the end of each chapter. This was done with the aim of illustrating the possibilities of the methods contained in the book, as well as with the desire to make good on what I have attempted to do over the course of many years for my students-to awaken their creativity, providing topics for independent work. The source of my own initial research was the famous two-volume book Methods of Mathematical Physics by D. Hilbert and R. Courant, and a series of original articles and surveys on partial differential equations and their applications to problems in theoretical mechanics and physics. The works of K. o. Friedrichs, which were in keeping with my own perception of the subject, had an especially strong influence on me. I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space. This desire was successfully realized thanks to the introduction of various classes of general solutions and to an elaboration of the methods of proof for the corresponding uniqueness theorems. This was accomplished on the basis of comparatively simple integral inequalities for arbitrary functions and of a priori estimates of the solutions of the problems without enlisting any special representations of those solutions.

Stochastic Numerics for Mathematical Physics :

Science

Author - Grigori Noah Milstein, Michael V. Tretyakov
Publisher - Springer Science & Business Media
Pages - 596
ISBN - 3662100630


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Detail - Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

Problems & Solutions in Theoretical & Mathematical Physics: Advanced level :

Science

Author - Willi-Hans Steeb
Publisher - World Scientific
Pages - 362
ISBN - 9789812389879


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Detail - This book is a collection of problems with detailed solutions which will prove valuable to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers will find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the author's lectures given around the world. The book is divided into two volumes. Volume I presents the introductory problems, for undergraduate and advanced undergraduate students. In Volume II, the more advanced problems, together with detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics, such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang -- Baxter relation, chaos, fractals, complexity, etc.

The Theory of Difference Schemes :

Mathematics

Author - Alexander A. Samarskii
Publisher - CRC Press
Pages - 786
ISBN - 9780203908518


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Detail - The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."

Inverse Problems of Mathematical Physics :

Mathematics

Author - Viatcheslav I. Priimenko, Mikhail M. Lavrent'ev, Alexander V. Avdeev
Publisher - Walter de Gruyter
Pages - 281
ISBN - 3110915529


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Detail - This monograph deals with the theory of inverse problems of mathematical physics and applications of such problems. Besides it considers applications and numerical methods of solving the problems under study. Descriptions of particular numerical experiments are also included.

Introduction to Mathematical Physics : Methods & Concepts

Science

Author - Chun Wa Wong
Publisher - Oxford University Press
Pages - 716
ISBN - 0199641390


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Detail - Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, ithelps the student master these necessary mathematical skills.