The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.
Author: B. M. Budak
A Collection of Problems on Mathematical Physics is a translation from the Russian and deals with problems and equations of mathematical physics. The book contains problems and solutions. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations. The book considers the statement and solutions of boundary value problems pertaining to equations of parabolic types when the physical processes are described by functions of two, three or four independent variables such as spatial coordinates or time. The book then discusses dynamic problems pertaining to the mechanics of continuous media and problems on electrodynamics. The text also discusses hyperbolic and elliptic types of equations. The book is intended for students in advanced mathematics and physics, as well as, for engineers and workers in research institutions.
Author: Vasilij S. VladimirovPublish On: 2013-11-09
This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem.
Author: Vasilij S. Vladimirov
Publisher: Springer Science & Business Media
The extensive application of modern mathematical teehniques to theoretical and mathematical physics requires a fresh approach to the course of equations of mathematical physics. This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem. The concept of a generalized solution considerably broadens the field of problems and enables solving from a unified position the most interesting problems that cannot be solved by applying elassical methods. To this end two new courses have been written at the Department of Higher Mathematics at the Moscow Physics anrl Technology Institute, namely, "Equations of Mathematical Physics" by V. S. Vladimirov and "Partial Differential Equations" by V. P. Mikhailov (both books have been translated into English by Mir Publishers, the first in 1984 and the second in 1978). The present collection of problems is based on these courses and amplifies them considerably. Besides the classical boundary value problems, we have ineluded a large number of boundary value problems that have only generalized solutions. Solution of these requires using the methods and results of various branches of modern analysis. For this reason we have ineluded problems in Lebesgue in tegration, problems involving function spaces (especially spaces of generalized differentiable functions) and generalized functions (with Fourier and Laplace transforms), and integral equations.
Teachers will also find this text useful as a supplement, since important concepts and techniques are developed in the problems. The material was tested in the author's lectures given around the world.The book is divided into two volumes.
In the present edition I have included "Supplements and Problems" located at the end of each chapter.
Author: O.A. Ladyzhenskaya
Publisher: Springer Science & Business Media
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.
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.
Author: Willi-Hans Steeb
Publisher: World Scientific
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 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, ...
Author: V. I. Agoshkov
Publisher: Cambridge Int Science Publishing
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.
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 ...
Author: A. A. Samarskii
Publisher: Walter de Gruyter
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.
Series Solutions of the Legendre Equation As pointed out in the preceding
section, the Legendre equation (VI.l) is of the type (VI.3) and the coefficients a(x)
and b(x) can be expanded into Taylor series at x = 0 which converge in |x| < 1.
Author: Hans Sagan
Publisher: Courier Corporation
Well-known text uses a few basic concepts to solve such problems as the vibrating string, vibrating membrane, and heat conduction. Problems and solutions. 31 illustrations.
The Book Is Intended As A Text For Students Of Physics At The Master S Level.
Author: P. K. Chattopadhyay
Publisher: New Age International
Category: Mathematical physics
The Book Is Intended As A Text For Students Of Physics At The Master S Level. It Is Assumed That The Students Pursuing The Course Have Some Knowledge Of Differential Equations And Complex Variables. In Addition, A Knowledge Of Physics Upto At Least The B.Sc. (Honours) Level Is Assumed. Throughout The Book The Applications Of The Mathematical Techniques Developed, To Physics Are Emphasized. Examples Are, To A Large Extent, Drawn From Various Branches Of Physics. The Exercises Provide Further Extensions To Such Applications And Are Often ``Chosen`` To Illustrate And Supplement The Material In The Text. They Thus Form An Essential Part Of The TextDistinguishing Features Of The Book: * Emphasis On Applications To Physics. The Examples And Problems Are Chosen With This Aspect In Mind. * More Than One Hundred Solved Examples And A Large Collection Of Problems In The Exercises. * A Discussion On Non-Linear Differential Equations-A Topic Usually Not Found In Standard Texts. There Is Also A Section Devoted To Systems Of Linear, First Order Differential Equations. * One Full Chapter On Linear Vector Spaces And Matrices. This Chapter Is Essential For The Understanding Of The Mathematical Foundations Of Quantum Mechanics And The Material Can Be Used In A Course Of Quantum Mechanics. * Parts Of Chapter-6 (Greens Function) Will Be Useful In Courses On Electrodynamics And Quantum Mechanics. * One Complete Chapter Is Devoted To Group Theory Within Special Emphasis On The Applications In Physics. The Subject Matter Is Treated In Fairly Great Detail And Can Be Used In A Course On Group Theory.
This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems.
Author: S. L. Sobolev
Publisher: Courier Corporation
This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.
VARIATIONAL METHODS Gould, S. H., Variational Methods for Eigenvalue Problems, University of Toronto Press, Toronto, ... A. A. Samarski, and A. N.
Tychonov, A Collection of Problems on Mathematical Physics, Pergamon,
Author: Ivar Stakgold
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.
The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers. ------------ [A] manual for future engineers must strongly differ from the textbook for pure ...
Author: Victor P. Pikulin
Publisher: Springer Science & Business Media
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. 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. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.
An eigenvalue problem is introduced for a simple differential equation.
Author: George H. Pimbley
Category: Differential equations
An eigenvalue problem is introduced for a simple differential equation. This equation, however, contains a nonlinear term with definitely states properties. It is shown, and the methods of proof are described, that instead of getting the familiar properties of the eigenvalues and eigenfunctions of classical linear systems, one obtains rather interesting patterns of finite multiplicity of the solutions.