A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

Author: B. M. Budak

Publisher: Elsevier

ISBN:

Category: Science

Page: 782

View: 608

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

Author: Vasilij S. Vladimirov

Publisher: Springer Science & Business Media

ISBN:

Category: Science

Page: 288

View: 312

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

Author: Willi-Hans Steeb

Publisher: World Scientific

ISBN:

Category: Science

Page: 323

View: 831

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

Author: O.A. Ladyzhenskaya

Publisher: Springer Science & Business Media

ISBN:

Category: Science

Page: 322

View: 996

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.

Boundary and Eigenvalue Problems in Mathematical Physics

Author: Hans Sagan

Publisher: Courier Corporation

ISBN:

Category: Science

Page: 399

View: 253

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.

Mathematical Physics and Complex Analysis

Collection of Survey Papers 4 [i.e. [4th]] on the 50th Anniversary of the Institute

Author: L. D. Faddeev

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 326

View: 539

Methods for Solving Mathematical Physics Problems

Author: V. I. Agoshkov

Publisher: Cambridge Int Science Publishing

ISBN:

Category: Science

Page: 320

View: 483

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.

Theoretical and Mathematical Physics

Problems and Solutions

Author: Steeb Willi-hans

Publisher: World Scientific

ISBN:

Category: Science

Page: 736

View: 299

This updated and extended edition of the book combines the topics provided in the two parts of the previous editions as well as new topics. It is a comprehensive compilation covering most areas in mathematical and theoretical physics. The book provides a collection of problems together with their detailed solutions which will prove to be valuable to students as well as to researchers in the fields of mathematics, physics, engineering and other sciences. Each chapter provides a short introduction with the relevant definitions and notations. All relevant definitions are given. The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Stimulating supplementary problems are also provided in each chapter. 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. Introductory problems for both undergraduate and advanced undergraduate students are provided. More advanced problems together with their detailed solutions are collected, to meet the needs of graduate students and researchers. Problems included cover new fields in theoretical and mathematical physics such as tensor product, Lax representation, Bäcklund transformation, soliton equations, Hilbert space theory, uncertainty relation, entanglement, spin systems, Lie groups, Bose system, Fermi systems differential forms, Lie algebra valued differential forms, metric tensor fields, Hirota technique, Painlevé test, Bethe ansatz, Yang-Baxter relation, wavelets, gauge theory, differential geometry, string theory, chaos, fractals, complexity, ergodic theory, etc. A number of software implementations are also provided.

Problems And Solutions In Theoretical And Mathematical Physics - Volume I: Introductory Level (Third Edition)

Author: Steeb Willi-hans

Publisher: World Scientific Publishing Company

ISBN:

Category: Science

Page: 260

View: 630

The articles in the proceedings are closely related to the lectures presented at the topology conference held at the University of Hawaii, August 12-18, 1990. These cover recent results in algebraic topology, algebraic transformation groups, real algebraic geometry, low-dimensional topology, and Nielsen Fixed Point Theory.

Problems & Solutions in Theoretical & Mathematical Physics: Advanced level

Author: Willi-Hans Steeb

Publisher: World Scientific

ISBN:

Category: Science

Page: 362

View: 498

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.

Problems And Solutions In Theoretical And Mathematical Physics - Volume Ii: Advanced Level (Third Edition)

Author: Steeb Willi-hans

Publisher: World Scientific Publishing Company

ISBN:

Category: Science

Page: 428

View: 391

This book is devoted to the theory and phenomenology of transverse-spin effects in high-energy hadronic physics. Contrary to common past belief, it is now rather clear that such effects are far from irrelevant. A decade or so of intense theoretical work has shed much light on the subject and brought to surface an entire class of new phenomena, which now await thorough experimental investigation. Over the next few years a number of experiments world-wide (at BNL, CERN, DESY and JLAB) will run with transversely polarised beams and targets, providing data that will enrich our knowledge of the transverse-spin structure of hadrons. It is therefore timely to assess the state of the art, and this is the principal aim of the volume.An outline of the book is as follows. After a few introductory remarks (Chapter 1), attention is directed in Chapter 2 to transversely polarised deeply-inelastic scattering (DIS), which probes the transverse spin structure function g2. This existing data are reviewed and discussed (for completeness, a brief presentation of longitudinally polarised DIS is also provided). In Chapter 3 the transverse-spin structure of the proton is illustrated in detail, with emphasis on the transversity distribution and the twist-three parton distribution contributing to g2. Model calculations of these quantities are also presented. In Chapter 4, the QCD evolution of transversity is studied at leading and next-to-leading order. Chapter 5 illustrates the g2 structure function and its related sum rules within the framework of perturbative QCD. The last three chapters are devoted to the phenomenology of transversity, in the context of Drell-Yan processes (Chapter 6), inclusive leptoproduction (Chapter 7) and inclusive hadroproduction (Chapter 8). The interpretation of some recent single-spin asymmetry data is discussed and the prospects for future measurements are reviewed.

Mathematical Physics

Author: P. K. Chattopadhyay

Publisher: New Age International

ISBN:

Category: Mathematical physics

Page: 352

View: 923

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.

Problems & Solutions in Theoretical & Mathematical Physics: Introductory level

Author: W.-H. Steeb

Publisher: World Scientific

ISBN:

Category: Science

Page: 213

View: 311

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.

Mathematical Physics

Applications and Problems

Author: V. Balakrishnan

Publisher: Springer Nature

ISBN:

Category:

Page:

View: 924