A Collection of Problems on Mathematical Physics

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.

A Collection of Problems on Mathematical Physics

Author: B. M. Budak

Publisher: Elsevier

ISBN: 1483184862

Page: 782

View: 900

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.

A Collection of Problems on the Equations of Mathematical Physics

This is especially true with regards to such a fundamental concept as the 80lution of a boundary value problem.

A Collection of Problems on the Equations of Mathematical Physics

Author: Vasilij S. Vladimirov

Publisher: Springer Science & Business Media

ISBN: 3662055589

Page: 288

View: 853

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.

Problems and Solutions in Theoretical and Mathematical Physics

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.

Problems and Solutions in Theoretical and Mathematical Physics

Author: Willi-Hans Steeb

Publisher: World Scientific

ISBN: 9789810229443

Page: 323

View: 579

The purpose of this book is to supply a collection of problems together with their detailed solution which will prove to be valuable to students as well as to research workers in the fields of mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. 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. Volume I presents the introductory problems for undergraduate and advanced undergraduate students. In volume II, the more advanced problems, together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover most of the new fields in theoretical and mathematical physics such as Lax representation. Bäcklund transformation, soliton equations, Lie algebra valued differential forms, Hirota technique, Painlevé test, the Bethe ansatz, the Yang-Baxter relation, chaos, fractals, complexity, etc.

The Boundary Value Problems of Mathematical Physics

In the present edition I have included "Supplements and Problems" located at the end of each chapter.

The Boundary Value Problems of Mathematical Physics

Author: O.A. Ladyzhenskaya

Publisher: Springer Science & Business Media

ISBN: 1475743173

Page: 322

View: 479

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.

Problems Solutions in Theoretical Mathematical Physics Advanced level

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.

Problems   Solutions in Theoretical   Mathematical Physics  Advanced level

Author: Willi-Hans Steeb

Publisher: World Scientific

ISBN: 9789812389879

Page: 362

View: 134

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.

Methods for Solving Mathematical Physics Problems

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, ...

Methods for Solving Mathematical Physics Problems

Author: V. I. Agoshkov

Publisher: Cambridge Int Science Publishing

ISBN: 1904602053

Page: 320

View: 899

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.

Mathematical Physics

Overall this book will be a valuable resource for a wide spectrum of students and instructors of mathematical physics.

Mathematical Physics

Author: V. Balakrishnan

Publisher: Springer Nature

ISBN: 3030396800

Page:

View: 727

Partial Differential Equations of Mathematical Physics

This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems.

Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev

Publisher: Courier Corporation

ISBN: 9780486659640

Page: 427

View: 455

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.

Boundary and Eigenvalue Problems in Mathematical Physics

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.
Hence ...

Boundary and Eigenvalue Problems in Mathematical Physics

Author: Hans Sagan

Publisher: Courier Corporation

ISBN: 0486150925

Page: 399

View: 662

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.

Numerical Methods for Solving Inverse Problems of Mathematical Physics

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 ...

Numerical Methods for Solving Inverse Problems of Mathematical Physics

Author: A. A. Samarskii

Publisher: Walter de Gruyter

ISBN: 3110205793

Page: 452

View: 995

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.

Contemporary Problems In Mathematical Physics Proceedings Of The Fourth International Workshop

The contributions in this volume address a variety of contemporary problems in mathematical and theoretical physics.

Contemporary Problems In Mathematical Physics   Proceedings Of The Fourth International Workshop

Author: Jan Govaerts

Publisher: World Scientific

ISBN: 9814477648

Page: 456

View: 546

The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their applications can be conceived, developed and disseminated. The contributions in this volume address a variety of contemporary problems in mathematical and theoretical physics.

Mathematical Physics

The Book Is Intended As A Text For Students Of Physics At The Master S Level.

Mathematical Physics

Author: P. K. Chattopadhyay

Publisher: New Age International

ISBN: 9788122402834

Page: 352

View: 738

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.

Boundary Value Problems of Mathematical Physics

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,
London, 1964.

Boundary Value Problems of Mathematical Physics

Author: Ivar Stakgold

Publisher: SIAM

ISBN: 1611972388

Page: 748

View: 256

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.

A Collection of Problems on a Course of Mathematical Analysis

This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric ...

A Collection of Problems on a Course of Mathematical Analysis

Author: G. N. Berman

Publisher: Elsevier

ISBN: 1483137341

Page: 602

View: 863

A Collection of Problems on a Course of Mathematical Analysis is a collection of systematically selected problems and exercises (with corresponding solutions) in mathematical analysis. A common instruction precedes a group of problems of the same type. Problems with a physics content are preceded by the necessary physical laws. In the case of more or less difficult problems, hints are given in the answers. This book is comprised of 15 chapters and begins with an overview of functions and methods of specifying them; notation for and classification of functions; elementary investigation of functions; and trigonometric and inverse trigonometric functions. The following chapters deal with limits and tests for their existence; differential calculus, with emphasis on derivatives and differentials; functions and curves; definite and indefinite integrals; and methods of evaluating definite integrals. Some applications of the integral in geometry, statics, and physics are also considered; along with functions of several variables; multiple integrals and iterated integration; line and surface integrals; and differential equations. The final chapter is devoted to trigonometric series. This monograph is intended for students studying mathematical analysis within the framework of a technical college course.

Equations in Mathematical Physics

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 ...

Equations in Mathematical Physics

Author: Victor P. Pikulin

Publisher: Springer Science & Business Media

ISBN: 3034802684

Page: 207

View: 347

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.