Differential Equations

Linear, Nonlinear, Ordinary, Partial

Author: A. C. King,J. Billingham,S. R. Otto

Publisher: Cambridge University Press

ISBN: 9780521016872

Category: Mathematics

Page: 541

View: 5426

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For students taking second courses; the subject is central and required at second year and above.
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Applications of Lie's Theory of Ordinary and Partial Differential Equations

Author: L Dresner

Publisher: CRC Press

ISBN: 9781420050783

Category: Science

Page: 225

View: 8859

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Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
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Linear Partial Differential Equations for Scientists and Engineers

Author: Tyn Myint-U,Lokenath Debnath

Publisher: Springer Science & Business Media

ISBN: 9780817645601

Category: Mathematics

Page: 778

View: 1858

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This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books. It also contains a large number of worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry; solutions are provided.
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Applied Partial Differential Equations

Author: J. R. Ockendon,Sam Howison,Andrew Lacey,Alexander Movchan

Publisher: Oxford University Press on Demand

ISBN: 9780198527718

Category: Mathematics

Page: 449

View: 2753

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Partial differential equations are used in mathematical models of a huge range of real-world phenomena, from electromagnetism to financial markets. This revised edition of Applied Partial Differential Equations contains many new sections and exercises including transform methods, free surface flows, linear elasticity and complex characteristics.
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Handbook of Nonlinear Partial Differential Equations

Author: Andrei D. Polyanin,Valentin F. Zaitsev

Publisher: CRC Press

ISBN: 1135440816

Category: Mathematics

Page: 840

View: 5340

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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:
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Handbook of First-Order Partial Differential Equations

Author: Andrei D. Polyanin,Valentin F. Zaitsev,Alain Moussiaux

Publisher: CRC Press

ISBN: 9780415272674

Category: Mathematics

Page: 520

View: 6942

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This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding types of differential equations are outlined and specific examples are considered. It presents equations and their applications, including differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. This handbook is an essential reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences.
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A First Course in Partial Differential Equations

Author: J Robert Buchanan,Zhoude Shao

Publisher: World Scientific Publishing Company

ISBN: 9813226455

Category: Mathematics

Page: 624

View: 648

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Resources for instructors who adopt this textbook:Lecture SlidesInstructors' Manual (complete solutions and supporting work)Students' Manual (final answers to computational exercises) Kindly send your requests to [email protected] This textbook gives an introduction to Partial Differential Equations (PDEs), for any reader wishing to learn and understand the basic concepts, theory, and solution techniques of elementary PDEs. The only prerequisite is an undergraduate course in Ordinary Differential Equations. This work contains a comprehensive treatment of the standard second-order linear PDEs, the heat equation, wave equation, and Laplace's equation. First-order and some common nonlinear PDEs arising in the physical and life sciences, with their solutions, are also covered. This textbook includes an introduction to Fourier series and their properties, an introduction to regular Sturm–Liouville boundary value problems, special functions of mathematical physics, a treatment of nonhomogeneous equations and boundary conditions using methods such as Duhamel's principle, and an introduction to the finite difference technique for the numerical approximation of solutions. All results have been rigorously justified or precise references to justifications in more advanced sources have been cited. Appendices providing a background in complex analysis and linear algebra are also included for readers with limited prior exposure to those subjects. The textbook includes material from which instructors could create a one- or two-semester course in PDEs. Students may also study this material in preparation for a graduate school (masters or doctoral) course in PDEs. The lecture slides, instructors' manual and students' manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected]
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