Equations in Mathematical Physics

A practical course

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Author: Victor P. Pikulin,Stanislav I. Pohozaev

Publisher: Springer Science & Business Media

ISBN: 3034802676

Category: Mathematics

Page: 207

View: 8991

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.

A Practical Course in Differential Equations and Mathematical Modelling

Classical and New Methods, Nonlinear Mathematical Models, Symmetry and Invariance Principles

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Author: Nail H. Ibragimov,Nail? Kha?rullovich Ibragimov

Publisher: World Scientific

ISBN: 9814291951

Category: Mathematics

Page: 348

View: 482

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, CollŠge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.

Handbook of Linear Partial Differential Equations for Engineers and Scientists, Second Edition

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Author: Andrei D. Polyanin,Vladimir E. Nazaikinskii

Publisher: CRC Press

ISBN: 1466581492

Category: Mathematics

Page: 1609

View: 7547

Includes nearly 4,000 linear partial differential equations (PDEs) with solutions Presents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fields Outlines basic methods for solving various problems in science and engineering Contains much more linear equations, problems, and solutions than any other book currently available Provides a database of test problems for numerical and approximate analytical methods for solving linear PDEs and systems of coupled PDEs New to the Second Edition More than 700 pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutions Systems of coupled PDEs with solutions Some analytical methods, including decomposition methods and their applications Symbolic and numerical methods for solving linear PDEs with Maple, Mathematica, and MATLAB® Many new problems, illustrative examples, tables, and figures To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the material in increasing order of complexity.

A Collection of Problems on Mathematical Physics

International Series of Monographs in Pure and Applied Mathematics

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Author: B. M. Budak,A. A. Samarskii,A. N. Tikhonov

Publisher: Elsevier

ISBN: 1483184862

Category: Science

Page: 782

View: 5923

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.

Numerical Partial Differential Equations for Environmental Scientists and Engineers

A First Practical Course

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Author: Daniel R. Lynch

Publisher: Springer Science & Business Media

ISBN: 0387236201

Category: Science

Page: 388

View: 2241

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

A First Course in Computational Physics

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Author: Paul L. DeVries,Javier E. Hasbun

Publisher: Jones & Bartlett Publishers

ISBN: 1449636195

Category: Technology & Engineering

Page: 433

View: 2819

Computers and computation are extremely important components of physics and should be integral parts of a physicist s education. Furthermore, computational physics is reshaping the way calculations are made in all areas of physics. Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. Topics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems. A few topics rarely seen at this level such as computerized tomography, are also included. Within each chapter, the student is led from relatively elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods, often culminating in the solution to problems of significant difficulty. The goal is to demonstrate how numerical methods are used to solve the problems that physicists face. Read the review published in Computing in Science & Engineering magazine, March/April 2011 (Vol. 13, No. 2) (c) 2011 IEEE, Published by the IEEE Computer Society"

Thinking About Equations

A Practical Guide for Developing Mathematical Intuition in the Physical Sciences and Engineering

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Author: Matt A. Bernstein,William A. Friedman

Publisher: John Wiley & Sons

ISBN: 1118210646

Category: Mathematics

Page: 272

View: 1352

An accessible guide to developing intuition and skills forsolving mathematical problems in the physical sciences andengineering Equations play a central role in problem solving across variousfields of study. Understanding what an equation means is anessential step toward forming an effective strategy to solve it,and it also lays the foundation for a more successful andfulfilling work experience. Thinking About Equationsprovides an accessible guide to developing an intuitiveunderstanding of mathematical methods and, at the same time,presents a number of practical mathematical tools for successfullysolving problems that arise in engineering and the physicalsciences. Equations form the basis for nearly all numerical solutions, andthe authors illustrate how a firm understanding of problem solvingcan lead to improved strategies for computational approaches. Eightsuccinct chapters provide thorough topical coverage, including: Approximation and estimation Isolating important variables Generalization and special cases Dimensional analysis and scaling Pictorial methods and graphical solutions Symmetry to simplify equations Each chapter contains a general discussion that is integratedwith worked-out problems from various fields of study, includingphysics, engineering, applied mathematics, and physical chemistry.These examples illustrate the mathematical concepts and techniquesthat are frequently encountered when solving problems. Toaccelerate learning, the worked example problems are grouped by theequation-related concepts that they illustrate as opposed tosubfields within science and mathematics, as in conventionaltreatments. In addition, each problem is accompanied by acomprehensive solution, explanation, and commentary, and numerousexercises at the end of each chapter provide an opportunity to testcomprehension. Requiring only a working knowledge of basic calculus andintroductory physics, Thinking About Equations is anexcellent supplement for courses in engineering and the physicalsciences at the upper-undergraduate and graduate levels. It is alsoa valuable reference for researchers, practitioners, and educatorsin all branches of engineering, physics, chemistry, biophysics, andother related fields who encounter mathematical problems in theirday-to-day work.

Essential AS Physics for OCR

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Author: Jim Breithaupt

Publisher: Nelson Thornes

ISBN: 9780748785070

Category: Juvenile Nonfiction

Page: 192

View: 7281

Essential Physics for OCR is a brand new series providing clear progression with challenging material for in-depth learning and understanding. Written by the best-selling author of New Understanding Physics, this text has been laid out in double page spreads and written in simple, easy-to-understand language. Designed in a contemporary manner, it ensures that students truly understand, engage and reflect upon the topic studied. A fully networkable and editable Teacher Support CD-ROMs is also available for this series. It contains worksheets, marking schemes and practical help.

Mathematics in Physics and Engineering

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Author: J. Irving,N. Mullineux

Publisher: Academic Press

ISBN: 1483276171

Category: Science

Page: 902

View: 6279

Mathematics in Physics and Engineering describes the analytical and numerical (desk-machine) methods that arise in pure and applied science, including wave equations, Bessel and Legendre functions, and matrices. The manuscript first discusses partial differential equations, as well as the method of separation of variables, three-dimensional wave equation, diffusion or heat flow equation, and wave equation in plane and cylindrical polar coordinates. The text also ponders on Frobenius' and other methods of solution. Discussions focus on hypergeometric equation, Bessel's equation, confluent hypergeometric equation, and change of dependent and independent variables. The publication takes a look at Bessel and Legendre functions and Laplace and other transforms, including orthogonal properties, applications from electromagnetism, spherical harmonics, and application to partial differential equations. The book also examines matrices, analytical methods in classical and wave mechanics, calculus of variations, and complex variable theory and conformal transformations. The book is a dependable reference for mathematicians, engineers, and physicists both at undergraduate and postgraduate levels.

A Unified Grand Tour of Theoretical Physics,

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Author: Ian D. Lawrie

Publisher: CRC Press

ISBN: 9780852740156

Category: Science

Page: 392

View: 2686

A conducted grand tour of the fundamental theories which shape our modern understanding of the physical world. This book covers the central themes of spacetime geometry and the general-relativistic account of gravity; quantum mechanics and quantum field theory; gauge theories and the fundamental forces of nature, statistical mechanics and the theory of phase transitions. The basic structure of each theory is explained in explicit mathematical detail with emphasis on conceptual understanding rather than on the technical details of specialized applications. Straightforward accounts are given of the standard models of particle physics and cosmology, and some of the more speculative ideas of modern theoretical physics are examined. This book is unique in bringing together the diverse areas of physics which are usually treated as independent. Designed to be accessible to final year undergraduates in physics and mathematics and to provide first year graduate students with a broad introductory view of theoretical physics, it will also be of interest to scientists and engineers in other disciplines who need an account of the subject at a level intermediate between semi-popular and technical research.

A First Course in Differential Equations, Modeling, and Simulation

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Author: Carlos A. Smith,Scott W. Campbell

Publisher: CRC Press

ISBN: 1439850887

Category: Mathematics

Page: 345

View: 4003

Emphasizing a practical approach for engineers and scientists, A First Course in Differential Equations, Modeling, and Simulation avoids overly theoretical explanations and shows readers how differential equations arise from applying basic physical principles and experimental observations to engineering systems. It also covers classical methods for obtaining the analytical solution of differential equations and Laplace transforms. In addition, the authors discuss how these equations describe mathematical systems and how to use software to solve sets of equations where analytical solutions cannot be obtained. Using simple physics, the book introduces dynamic modeling, the definition of differential equations, two simple methods for obtaining their analytical solution, and a method to follow when modeling. It then presents classical methods for solving differential equations, discusses the engineering importance of the roots of a characteristic equation, and describes the response of first- and second-order differential equations. A study of the Laplace transform method follows with explanations of the transfer function and the power of Laplace transform for obtaining the analytical solution of coupled differential equations. The next several chapters present the modeling of translational and rotational mechanical systems, fluid systems, thermal systems, and electrical systems. The final chapter explores many simulation examples using a typical software package for the solution of the models developed in previous chapters. Providing the necessary tools to apply differential equations in engineering and science, this text helps readers understand differential equations, their meaning, and their analytical and computer solutions. It illustrates how and where differential equations develop, how they describe engineering systems, how to obtain the analytical solution, and how to use software to simulate the systems.

Basic Training in Mathematics

A Fitness Program for Science Students

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Author: R. Shankar

Publisher: Springer

ISBN: 1489967982

Category: Science

Page: 366

View: 8050

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.

Computational Physics, Vol I

A Practical Introduction to Computational Physics and Scientific Computing

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Author: Konstantinos N. Anagnostopoulos

Publisher: Konstantinos Anagnostopoulos

ISBN: 1312464410

Category: Science

Page: 366

View: 9842

This book is an introduction to the computational methods used in physics and other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering. The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions. The book and the accompanying software is available for free in electronic form at http://goo.gl/SGUEkM (www.physics.ntua.gr/%7Ekonstant/ComputationalPhysics) and a printed copy can be purchased from lulu.com at http://goo.gl/Pg1zHc (vol II at http://goo.gl/XsSBdP )

Handbook of Nonlinear Partial Differential Equations

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Author: Andrei D. Polyanin,Valentin F. Zaitsev

Publisher: CRC Press

ISBN: 0203489659

Category: Mathematics

Page: 840

View: 4579

The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:

Ordinary Differential Equations

A Practical Guide

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Author: Bernd J. Schroers

Publisher: Cambridge University Press

ISBN: 1139503723

Category: Mathematics

Page: N.A

View: 6101

Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.

A First Course in the Numerical Analysis of Differential Equations

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Author: A. Iserles

Publisher: Cambridge University Press

ISBN: 0521734908

Category: Mathematics

Page: 459

View: 7976

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

Electromagnetism

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Author: John C. Slater,Nathaniel H. Frank

Publisher: Courier Corporation

ISBN: 0486150402

Category: Science

Page: 256

View: 7863

A basic introduction to electromagnetism, supplying the fundamentals of electrostatics and magnetostatics, in addition to a thorough investigation of electromagnetic theory. Numerous problems and references. Calculus and differential equations required. 1947 edition.

Handbook of Nonlinear Partial Differential Equations, Second Edition

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Author: Andrei D. Polyanin,Valentin F. Zaitsev

Publisher: CRC Press

ISBN: 142008724X

Category: Mathematics

Page: 1912

View: 6822

New to the Second Edition More than 1,000 pages with over 1,500 new first-, second-, third-, fourth-, and higher-order nonlinear equations with solutions Parabolic, hyperbolic, elliptic, and other systems of equations with solutions Some exact methods and transformations Symbolic and numerical methods for solving nonlinear PDEs with MapleTM, Mathematica®, and MATLAB® Many new illustrative examples and tables A large list of references consisting of over 1,300 sources To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology. They outline the methods in a schematic, simplified manner and arrange the material in increasing order of complexity.