Methods For Solving Mathematical Physics Problems

Author : Valeriĭ Ivanovich Agoshkov,P. B. Dubovsky,V. P. Shutiayev
Publisher : Cambridge Int Science Publishing
Page : 335 pages
File Size : 40,6 Mb
Release : 2006
Category : Science
ISBN : 9781904602057

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Methods for Solving Mathematical Physics Problems by Valeriĭ Ivanovich Agoshkov,P. B. Dubovsky,V. P. Shutiayev Pdf

The aim of the book is to present to a wide range of readers (students, postgraduates, scientists, engineers, etc.) basic information on one of the directions of mathematics, methods for solving mathematical physics problems. The authors have tried to select for the book methods that have become classical and generally accepted. However, some of the current versions of these methods may be missing from the book because they require special knowledge. 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. On the other hand, proofs of the majority of these results are not presented and they are given only in the simplest (methodological) cases. Another special feature of the book is the inclusion of many examples of application of the methods for solving specific mathematical physics problems of applied nature used in various areas of science and social activity, such as power engineering, environmental protection, hydrodynamics, elasticity theory, etc. This should provide additional information on possible applications of these methods. To provide complete information, the book includes a chapter dealing with the main problems of mathematical physics, together with the results obtained in functional analysis and boundary-value theory for equations with partial derivatives.

Author : Agoshkov
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 2008-01-01
Category : Electronic
ISBN : 8130909413

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Methods For Solving Mathematical Physics Problems by Agoshkov Pdf

Author : Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin
Publisher : CRC Press
Page : 736 pages
File Size : 53,5 Mb
Release : 2000-03-21
Category : Mathematics
ISBN : 0824719875

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Methods for Solving Inverse Problems in Mathematical Physics by Global Express Ltd. Co.,Aleksey I. Prilepko,Dmitry G. Orlovsky,Igor A. Vasin Pdf

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.

Author : Volodymyr Makarov,Nataliya Mayko
Publisher : John Wiley & Sons
Page : 356 pages
File Size : 55,6 Mb
Release : 2024-04-02
Category : Science
ISBN : 9781786309334

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Traditional Functional-Discrete Methods for the Problems of Mathematical Physics by Volodymyr Makarov,Nataliya Mayko Pdf

This book is devoted to the construction and study of approximate methods for solving mathematical physics problems in canonical domains. It focuses on obtaining weighted a priori estimates of the accuracy of these methods while also considering the influence of boundary and initial conditions. This influence is quantified by means of suitable weight functions that characterize the distance of an inner point to the boundary of the domain. New results are presented on boundary and initial effects for the finite difference method for elliptic and parabolic equations, mesh schemes for equations with fractional derivatives, and the Cayley transform method for abstract differential equations in Hilbert and Banach spaces. Due to their universality and convenient implementation, the algorithms discussed throughout can be used to solve a wide range of actual problems in science and technology. The book is intended for scientists, university teachers, and graduate and postgraduate students who specialize in the field of numerical analysis.

Author : Steeb Willi-hans
Publisher : World Scientific
Page : 736 pages
File Size : 51,8 Mb
Release : 2018-08-23
Category : Science
ISBN : 9789813275393

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Theoretical and Mathematical Physics by Steeb Willi-hans Pdf

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.

Author : A. A. Samarskii,Petr N. Vabishchevich
Publisher : Walter de Gruyter
Page : 453 pages
File Size : 40,8 Mb
Release : 2008-08-27
Category : Mathematics
ISBN : 9783110205794

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Numerical Methods for Solving Inverse Problems of Mathematical Physics by A. A. Samarskii,Petr N. Vabishchevich Pdf

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.

Author : Joshua F Whitney,Heather M Whitney
Publisher : Morgan & Claypool Publishers
Page : 70 pages
File Size : 47,9 Mb
Release : 2016-11-01
Category : Science
ISBN : 9781681742816

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A Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics by Joshua F Whitney,Heather M Whitney Pdf

This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.

Author : Nikolaĭ Nikolaevich I︠A︡nenko,Nikolaĭ Nikolaevich I͡Anenko
Publisher : American Mathematical Soc.
Page : 204 pages
File Size : 42,7 Mb
Release : 1967
Category : Mathematics
ISBN : 0821818740

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Difference Methods for Solutions of Problems of Mathematical Physics. I by Nikolaĭ Nikolaevich I︠A︡nenko,Nikolaĭ Nikolaevich I͡Anenko Pdf

Author : Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov
Publisher : Courier Corporation
Page : 802 pages
File Size : 45,5 Mb
Release : 1964-01-01
Category : Science
ISBN : 9780486658063

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A Collection of Problems in Mathematical Physics by Boris Mikha?lovich Budak,Aleksandr Andreevich Samarski?,Andre? Nikolaevich Tikhonov Pdf

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

Author : Farkhad G. Aliev,Antonio Lara
Publisher : CRC Press
Page : 538 pages
File Size : 46,6 Mb
Release : 2023-08-31
Category : Science
ISBN : 9781000908480

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Mathematical Methods for Physics by Farkhad G. Aliev,Antonio Lara Pdf

This book presents mathematical tools to solve partial differential equations, typical of physical problems. It explains in a detailed manner the process of solving the problems that typically arise in the context of physics. Although there are a large number of textbooks on this topic, few go so deep into the topic. One of the original and unique features of this book is emphasis on the mathematical formulation of the problems, as well as the analysis of several alternative ways to solve them. Importantly, the book provides a graphical analysis of the results when appropriate. It describes a wide scope of the problems, with detailed solutions and the methods involved, ranging from cases in one to three dimensions, from Cartesian to polar, cylindrical, and spherical coordinates and includes properties and applications of the Fourier transform to solve partial differential equations.

Author : Vasilij S. Vladimirov
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 47,5 Mb
Release : 2013-11-09
Category : Science
ISBN : 9783662055588

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A Collection of Problems on the Equations of Mathematical Physics by Vasilij S. Vladimirov Pdf

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.

Author : Boris Mikhaĭlovich Budak
Publisher : Unknown
Page : 792 pages
File Size : 48,8 Mb
Release : 1964
Category : Differential equations, Partial
ISBN : UOM:39015017194955

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A Collection of Problems on Mathematical Physics by Boris Mikhaĭlovich Budak Pdf

Author : Victor P. Pikulin,Stanislav I. Pohozaev
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 44,7 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783034802673

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Equations in Mathematical Physics by Victor P. Pikulin,Stanislav I. Pohozaev Pdf

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.

Author : B. M. Budak,A. A. Samarskii,A. N. Tikhonov
Publisher : Elsevier
Page : 782 pages
File Size : 52,7 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483184869

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A Collection of Problems on Mathematical Physics by B. M. Budak,A. A. Samarskii,A. N. Tikhonov Pdf

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 : R. Shankar
Publisher : Springer
Page : 371 pages
File Size : 55,5 Mb
Release : 2013-12-20
Category : Science
ISBN : 9781489967985

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Basic Training in Mathematics by R. Shankar Pdf

Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.