Methods for Solving Mathematical Physics Problems

Methods for Solving Mathematical Physics Problems
Author: Valeriĭ Ivanovich Agoshkov
Publisher: Cambridge Int Science Publishing
Total Pages: 335
Release: 2006
Genre: Science
ISBN: 1904602053
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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.

Methods for Solving Inverse Problems in Mathematical Physics

Methods for Solving Inverse Problems in Mathematical Physics
Author: Global Express Ltd. Co.
Publisher: CRC Press
Total Pages: 736
Release: 2000-03-21
Genre: Mathematics
ISBN: 9780824719876
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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.

Numerical Methods for Solving Inverse Problems of Mathematical Physics

Numerical Methods for Solving Inverse Problems of Mathematical Physics
Author: A. A. Samarskii
Publisher: Walter de Gruyter
Total Pages: 453
Release: 2008-08-27
Genre: Mathematics
ISBN: 3110205793
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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.

Basic Training in Mathematics

Basic Training in Mathematics
Author: R. Shankar
Publisher: Springer
Total Pages: 371
Release: 2013-12-20
Genre: Science
ISBN: 1489967982
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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.

A Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics

A Handbook of Mathematical Methods and Problem-Solving Tools for Introductory Physics
Author: Joshua F Whitney
Publisher: Morgan & Claypool Publishers
Total Pages: 70
Release: 2016-11-01
Genre: Science
ISBN: 1681742810
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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.

Traditional Functional-Discrete Methods for the Problems of Mathematical Physics

Traditional Functional-Discrete Methods for the Problems of Mathematical Physics
Author: Volodymyr Makarov
Publisher: John Wiley & Sons
Total Pages: 356
Release: 2024-02-23
Genre: Science
ISBN: 1394276656
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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.

Theoretical And Mathematical Physics: Problems And Solutions

Theoretical And Mathematical Physics: Problems And Solutions
Author: Willi-hans Steeb
Publisher: World Scientific
Total Pages: 734
Release: 2018-08-23
Genre: Science
ISBN: 9813275391
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'This is an excellent, well-written and very comprehensive book covering many topics of mathematics and physics. An exhaustive collection of problems with detailed solutions that may be valuable to students and young researchers in several fields, ranging from Mathematics to Quantum Physics is presented … I found the book helpful in regards to several subjects that are not covered in other mathematical physics introductory textbooks.'Contemporary PhysicsThis 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.