Transform Methods For Solving Partial Differential Equations
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Transform Methods For Solving Partial Differential Equations
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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 2004-07-15
Transform Methods For Solving Partial Differential Equations written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-15 with Mathematics categories.
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana
Transform Methods For Solving Partial Differential Equations
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Author : Dean G. Duffy
language : en
Publisher: CRC Press
Release Date : 1994-02-16
Transform Methods For Solving Partial Differential Equations written by Dean G. Duffy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-16 with Mathematics categories.
For most scientists and engineers, the only analytic technique for solving linear partial differential equations is separation of variables. In Transform Methods for Solving Partial Differential Equations, the author uses the power of complex variables to demonstrate how Laplace and Fourier transforms can be harnessed to solve many practical, everyday problems experienced by scientists and engineers. Unlike many mathematics texts, this book provides a step-by-step analysis of problems taken from scientific and engineering literature. Detailed solutions are given in the back of the book. This essential text/reference draws from the latest literature on transform methods to provide in-depth discussions on the joint transform problem, the Cagniard-de Hoop method, and the Wiener-Hopf technique. Some 1,500 references are included as well.
Transform Methods For Solving Partial Differential Equations Second Edition
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Author : Dean G. Duffy
language : en
Publisher: Chapman and Hall/CRC
Release Date : 2004-07-15
Transform Methods For Solving Partial Differential Equations Second Edition written by Dean G. Duffy and has been published by Chapman and Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-15 with Mathematics categories.
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found analytically, numeric and asymptotic techniques now exist for their inversion, and because the problem retains some of its analytic aspect, one can gain greater physical insight than typically obtained from a purely numerical approach. Transform Methods for Solving Partial Differential Equations, Second Edition illustrates the use of Laplace, Fourier, and Hankel transforms to solve partial differential equations encountered in science and engineering. The author has expanded the second edition to provide a broader perspective on the applicability and use of transform methods and incorporated a number of significant refinements: New in the Second Edition: · Expanded scope that includes numerical methods and asymptotic techniques for inverting particularly complicated transforms · Discussions throughout the book that compare and contrast transform methods with separation of variables, asymptotic methods, and numerical techniques · Many added examples and exercises taken from a wide variety of scientific and engineering sources · Nearly 300 illustrations--many added to the problem sections to help readers visualize the physical problems · A revised format that makes the book easier to use as a reference: problems are classified according to type of region, type of coordinate system, and type of partial differential equation · Updated references, now arranged by subject instead of listed all together As reflected by the book's organization, content, and many examples, the author's focus remains firmly on applications. While the subject matter is classical, this book gives it a fresh, modern treatment that is exceptionally practical, eminently readable, and especially valuable to anyone solving problems in engineering and the applied sciences.
Transformation Methods For Nonlinear Partial Differential Equations
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Author : Dominic G B Edelen
language : en
Publisher: World Scientific
Release Date : 1992-06-09
Transformation Methods For Nonlinear Partial Differential Equations written by Dominic G B Edelen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-09 with Science categories.
The purpose of the book is to provide research workers in applied mathematics, physics, and engineering with practical geometric methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of contact manifolds rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent publications of the authors'. The text contains numerous fully worked examples so that the reader can fully appreciate the power and scope of the new methods. In effect, the problem of solving systems of nonlinear partial differential equations is reduced to the problem of solving families of autonomous ordinary differential equations. This allows the graphs of solutions of the system of partial differential equations to be realized as certain leaves of a foliation of an appropriately defined contact manifold. In fact, it is often possible to obtain families of solutions whose graphs foliate an open subset of the contact manifold. These ideas are extended in the final chapter by developing the theory of transformations that map a foliation of a contact manifold onto a foliation. This analysis gives rise to results of surprising depth and practical significance. In particular, an extended Hamilton-Jacobi method for solving systems of partial differential equations is obtained.
A First Course In Partial Differential Equations
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Author : H. F. Weinberger
language : en
Publisher: Courier Corporation
Release Date : 2012-04-20
A First Course In Partial Differential Equations written by H. F. Weinberger and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-20 with Mathematics categories.
Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.
Transforms And Partial Differential Equations Combo
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Author : P. Sivaramakrishna Das
language : en
Publisher: Pearson Education India
Release Date :
Transforms And Partial Differential Equations Combo written by P. Sivaramakrishna Das and has been published by Pearson Education India this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Transforms and Partial Differential Equations, 6e is designed to provide a firm foundation on the basic concepts of partial differential equations, Fourier series analysis, Fourier series techniques in solving heat flow problems, Fourier transform techniques and Z-transforms. In their trademark student-friendly style, the authors have endeavored to provide an in-depth understanding of the important principles, methods and processes of obtaining results in a systematic way with emphasis on clarity and academic rigor. Features: • More than 320 solved examples • More than 250 exercises with answers • More than 150 Part A questions with answers • Plenty of hints for problems • Includes a free book containing FAQs Table of Contents: Preface Acknowledgements About the Authors 1. Partial Differential Equations 2. Fourier Series 3. Application of Partial Differential Equations 4. Fourier Transforms 5. Z-transforms and Difference Equations Formulae To Remember
Partial Differential Equations
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Author : Victor Henner
language : en
Publisher: CRC Press
Release Date : 2019-11-20
Partial Differential Equations written by Victor Henner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-20 with Mathematics categories.
Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses. Highlights: Offers a complete first course on PDEs The text’s flexible structure promotes varied syllabi for courses Written with a teach-by-example approach which offers numerous examples and applications Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions The text’s graphical material makes excellent use of modern software packages Features numerous examples and applications which are suitable for readers studying the subject remotely or independently
An Introduction To Partial Differential Equations
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Author : Daniel J. Arrigo
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-12-18
An Introduction To Partial Differential Equations written by Daniel J. Arrigo 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 2017-12-18 with Mathematics categories.
This book is an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject. The chapters include the following topics: First-order PDEs, Second-order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform. The reader is guided through these chapters where techniques for solving first- and second-order PDEs are introduced. Each chapter ends with a series of exercises illustrating the material presented in each chapter. The book can be used as a textbook for any introductory course in PDEs typically found in both science and engineering programs and has been used at the University of Central Arkansas for over ten years.
Applied Partial Differential Equations
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Author : Donald W. Trim
language : en
Publisher: PWS Publishing Company
Release Date : 1990
Applied Partial Differential Equations written by Donald W. Trim and has been published by PWS Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
The emphasis in this book is placed on techniques for solving partial differential equations found in physics and engineering but discussions on existence and uniqueness of solutions are included. Several different methods of solution are presented, with the primary emphasis on the classical method of separation of variables. Secondary emphasis is placed on transform solutions, as well as on the method of Green's functions.
Applied Partial Differential Equations
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Author : Paul DuChateau
language : en
Publisher: Courier Corporation
Release Date : 2012-10-30
Applied Partial Differential Equations written by Paul DuChateau and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
Superb introduction devotes almost half its pages to numerical methods for solving partial differential equations, while the heart of the book focuses on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included, with solutions for many at end of book. For students with little background in linear algebra, a useful appendix covers that subject briefly.