A Collection of Problems on the Equations of Mathematical Physics

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.

Author: Vasilij S. Vladimirov

Publisher: Springer

ISBN: 3662055600

Category: Science

Page: 288

View: 860

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.
Categories: Science

A Collection of Problems on Mathematical Physics

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.

Author: B. M. Budak

Publisher: Elsevier

ISBN: 9781483184869

Category: Science

Page: 782

View: 156

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.
Categories: Science

Theoretical and Mathematical Physics

Theoretical and Mathematical Physics

'This is an excellent, well-written and very comprehensive book covering many topics of mathematics and physics.

Author: Steeb Willi-hans

Publisher: World Scientific

ISBN: 9789813275393

Category: Science

Page: 736

View: 958

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.
Categories: Science

Methods for Solving Mathematical Physics Problems

Methods for Solving Mathematical Physics Problems

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.

Author: V. I. Agoshkov

Publisher: Cambridge Int Science Publishing

ISBN: 9781904602057

Category: Science

Page: 320

View: 548

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.
Categories: Science

Problems And Solutions In Theoretical And Mathematical Physics Volume Ii Advanced Level Third Edition

Problems And Solutions In Theoretical And Mathematical Physics   Volume Ii  Advanced Level  Third Edition

This book provides a comprehensive collection of problems together with their detailed solutions in the field of Theoretical and Mathematical Physics.

Author: Steeb Willi-hans

Publisher: World Scientific Publishing Company

ISBN: 9789813101043

Category: Science

Page: 428

View: 222

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.
Categories: Science

Problems Solutions in Theoretical Mathematical Physics Introductory level

Problems   Solutions in Theoretical   Mathematical Physics  Introductory 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.

Author: W.-H. Steeb

Publisher: World Scientific

ISBN: 981238989X

Category: Science

Page: 213

View: 695

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.
Categories: Science

Problems Solutions in Theoretical Mathematical Physics Advanced level

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.

Author: Willi-Hans Steeb

Publisher: World Scientific

ISBN: 9812389873

Category: Science

Page: 362

View: 434

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.
Categories: Science

Equations of Mathematical Physics

Equations of Mathematical Physics

At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.

Author: Andrej Nikolaevi? Tikhonov (Mathematician)

Publisher: Courier Corporation

ISBN: 9780486664224

Category: Mathematics

Page: 765

View: 149

Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendices that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.
Categories: Mathematics

Direct and Inverse Problems of Mathematical Physics

Direct and Inverse Problems of Mathematical Physics

This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.

Author: R.P. Gilbert

Publisher: Springer Science & Business Media

ISBN: 9781475732146

Category: Mathematics

Page: 453

View: 909

This volume consists of papers presented in the special sessions on "Wave Phenomena and Related Topics", and "Asymptotics and Homogenization" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT -9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the 'participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of the ISAAC Congresses. We decided to include with the papers presented in the ISAAC Congress and the U.S.-Japan Seminar several very good papers by colleagues from the former Soviet Union. These participants in the ISAAC Congress attended at their own expense. This volume has the title Direct and Inverse Problems of Mathematical Physics which consists of the papers on scattering theory, coefficient identification, uniqueness and existence theorems, boundary controllability, wave propagation in stratified media, viscous flows, nonlinear acoustics, Sobolev spaces, singularity theory, pseudo differential operators, and semigroup theory.
Categories: Mathematics

Problems and Solutions in Theoretical and Mathematical Physics Introductory level

Problems and Solutions in Theoretical and Mathematical Physics  Introductory level

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.

Author: W.-H. Steeb

Publisher: World Scientific Publishing Company Incorporated

ISBN: 9810229410

Category: Science

Page: 240

View: 387

Categories: Science

Advanced Level

Advanced Level

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.

Author: Willi-Hans Steeb

Publisher:

ISBN: 9810229429

Category:

Page: 323

View: 403

Categories:

Boundary Value Problems of Mathematical Physics

Boundary Value Problems of Mathematical Physics

VARIATIONAL METHODS Gould, S. H., Variational Methods for Eigenvalue
Problems, University of Toronto Press, Toronto, 1966. Mikhlin, S. G., Variational
Methods in Mathematical Physics, Macmillan, New York, 1964. COLLECTIONS
OF ...

Author: Ivar Stakgold

Publisher: SIAM

ISBN: 9781611972382

Category:

Page: 748

View: 251

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.
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