Separable Boundary Value Problems In Physics
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Separable Boundary Value Problems In Physics
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Author : Morten Willatzen
language : en
Publisher: John Wiley & Sons
Release Date : 2011-05-03
Separable Boundary Value Problems In Physics written by Morten Willatzen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-03 with Science categories.
Innovative developments in science and technology require a thorough knowledge of applied mathematics, particularly in the field of differential equations and special functions. These are relevant in modeling and computing applications of electromagnetic theory and quantum theory, e.g. in photonics and nanotechnology. The problem of solving partial differential equations remains an important topic that is taught at both the undergraduate and graduate level. Separable Boundary-Value Problems in Physics is an accessible and comprehensive treatment of partial differential equations in mathematical physics in a variety of coordinate systems and geometry and their solutions, including a differential geometric formulation, using the method of separation of variables. With problems and modern examples from the fields of nano-technology and other areas of physics. The fluency of the text and the high quality of graphics make the topic easy accessible. The organization of the content by coordinate systems rather than by equation types is unique and offers an easy access. The authors consider recent research results which have led to a much increased pedagogical understanding of not just this topic but of many other related topics in mathematical physics, and which like the explicit discussion on differential geometry shows - yet have not been treated in the older texts. To the benefit of the reader, a summary presents a convenient overview on all special functions covered. Homework problems are included as well as numerical algorithms for computing special functions. Thus this book can serve as a reference text for advanced undergraduate students, as a textbook for graduate level courses, and as a self-study book and reference manual for physicists, theoretically oriented engineers and traditional mathematicians.
Unified Transform For Boundary Value Problems
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Author : Athanasios S. Fokas
language : en
Publisher: SIAM
Release Date : 2014-12-30
Unified Transform For Boundary Value Problems written by Athanasios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-30 with Mathematics categories.
This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.? The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Computational Physics
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Author : Michael Bestehorn
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-04-27
Computational Physics written by Michael Bestehorn and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-27 with Science categories.
The work shows, by means of examples coming from different corners of physics, how physical and mathematical questions can be answered using a computer. Starting with maps and neural networks, applications from Newton's mechanics described by ordinary differential equations come into the focus, like the computation of planetary orbits or classical molecular dynamics. A large part of the textbook is dedicated to deterministic chaos normally encountered in systems with sufficiently many degrees of freedom. Partial differential equations are studied considering (nonlinear) field theories like quantum mechanics, thermodynamics or fluid mechanics. In the second edition, a new chapter gives a detailed survey on delay or memory systems with a direct application to epidemic and road traffic models. Most of the algorithms are realized in FORTRAN, a language most suitable for effectively solving the discussed problems. On the other hand, the codes given and presented on the book’s homepage can be easily translated into other languages. Moreover, several MATLAB examples are presented, mainly for didactic reasons. The book is addressed to advanced Bachelor or Master students of physics, applied mathematics and mechanical engineering.
Boundary Value Problems For Linear Partial Differential Equations
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Author : Manuel Mañas
language : en
Publisher: CRC Press
Release Date : 2024-07-12
Boundary Value Problems For Linear Partial Differential Equations written by Manuel Mañas and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-12 with Mathematics categories.
Boundary value problems play a significant role in modeling systems characterized by established conditions at their boundaries. On the other hand, initial value problems hold paramount importance in comprehending dynamic processes and foreseeing future behaviors. The fusion of these two types of problems yields profound insights into the intricacies of the conduct exhibited by many physical and mathematical systems regulated by linear partial differential equations. Boundary Value Problems for Linear Partial Differential Equations provides students with the opportunity to understand and exercise the benefits of this fusion, equipping them with realistic, practical tools to study solvable linear models of electromagnetism, fluid dynamics, geophysics, optics, thermodynamics and specifically, quantum mechanics. Emphasis is devoted to motivating the use of these methods by means of concrete examples taken from physical models. Features No prerequisites apart from knowledge of differential and integral calculus and ordinary differential equations. Provides students with practical tools and applications Contains numerous examples and exercises to help readers understand the concepts discussed in the book.
Essential Mathematics For The Physical Sciences Volume 1
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Author : Brett Borden
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-10-31
Essential Mathematics For The Physical Sciences Volume 1 written by Brett Borden and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with Science categories.
Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus asound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations (PDEs) and the special functions introduced. Solving PDEs can't be done, however, outside of the context in which they apply to physical systems. The solutions to PDEs must conform to boundary conditions, a set of additional constraints in space or time to be satisfied at the boundaries of the system, that small part of the universe under study. The first volume is devoted to homogeneous boundary-value problems (BVPs), homogeneous implying a system lacking a forcing function, or source function. The second volume takes up (in addition to other topics) inhomogeneous problems where, in addition to the intrinsic PDE governing a physical field, source functions are an essential part of the system. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well. It is based on the assumption that it follows a math review course, and was designed to coincide with the second quarter of student study, which is dominated by BVPs but also requires an understanding of special functions and Fourier analysis.
Partial Differential Equations And Boundary Value Problems With Applications
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Author : Mark A. Pinsky
language : en
Publisher:
Release Date : 2003
Partial Differential Equations And Boundary Value Problems With Applications written by Mark A. Pinsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Boundary value problems categories.
A Unified Approach To Boundary Value Problems
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Author : Athanassios S. Fokas
language : en
Publisher: SIAM
Release Date : 2008-01-01
A Unified Approach To Boundary Value Problems written by Athanassios S. Fokas and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
This text presents a new approach to analysing initial-boundary value problems for integrable partial differential equations.
Mathematical Tools For Physicists
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Author : Michael Grinfeld
language : en
Publisher: John Wiley & Sons
Release Date : 2015-01-12
Mathematical Tools For Physicists written by Michael Grinfeld and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-12 with Science categories.
The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Differential Equations With Boundary Value Problems
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Author : Dennis G. Zill
language : en
Publisher:
Release Date : 2005
Differential Equations With Boundary Value Problems written by Dennis G. Zill and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Boundary value problems categories.
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
Mathematical Methods For Physicists And Engineers
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Author : Royal Eugene Collins
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11
Mathematical Methods For Physicists And Engineers written by Royal Eugene Collins and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Science categories.
Practical text focuses on fundamental applied math needed to deal with physics and engineering problems: elementary vector calculus, special functions of mathematical physics, calculus of variations, much more. 1968 edition.