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: 4479

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For students taking second courses; the subject is central and required at second year and above.

A Practical Course in Differential Equations and Mathematical Modelling

Classical and New Methods, Nonlinear Mathematical Models, Symmetry and Invariance Principles
Author: Nail H. Ibragimov,Nail? Kha?rullovich Ibragimov
Publisher: World Scientific
ISBN: 9814291951
Category: Mathematics
Page: 348
View: 1717

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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.

Nonlinear Partial Differential Equations for Scientists and Engineers


Author: Lokenath Debnath
Publisher: Springer Science & Business Media
ISBN: 9780817682651
Category: Mathematics
Page: 860
View: 9727

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The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.

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: 4070

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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.

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: 8887

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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.

ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS

THEORY AND APPLICATIONS
Author: NITA H. SHAH
Publisher: PHI Learning Pvt. Ltd.
ISBN: 8120350871
Category: Mathematics
Page: 528
View: 3820

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This revised and updated text, now in its second edition, continues to present the theoretical concepts of methods of solutions of ordinary and partial differential equations. It equips students with the various tools and techniques to model different physical problems using such equations. The book discusses the basic concepts of ordinary and partial differential equations. It contains different methods of solving ordinary differential equations of first order and higher degree. It gives the solution methodology for linear differential equations with constant and variable coefficients and linear differential equations of second order. The text elaborates simultaneous linear differential equations, total differential equations, and partial differential equations along with the series solution of second order linear differential equations. It also covers Bessel’s and Legendre’s equations and functions, and the Laplace transform. Finally, the book revisits partial differential equations to solve the Laplace equation, wave equation and diffusion equation, and discusses the methods to solve partial differential equations using the Fourier transform. A large number of solved examples as well as exercises at the end of chapters help the students comprehend and strengthen the underlying concepts. The book is intended for undergraduate and postgraduate students of Mathematics (B.A./B.Sc., M.A./M.Sc.), and undergraduate students of all branches of engineering (B.E./B.Tech.), as part of their course in Engineering Mathematics. New to the SECOND Edition • Includes new sections and subsections such as applications of differential equations, special substitution (Lagrange and Riccati), solutions of non-linear equations which are exact, method of variation of parameters for linear equations of order higher than two, and method of undetermined coefficients • Incorporates several worked-out examples and exercises with their answers • Contains a new Chapter 19 on ‘Z-Transforms and its Applications’.

Contact Geometry and Nonlinear Differential Equations


Author: Alexei Kushner,Valentin Lychagin,Vladimir Rubtsov
Publisher: Cambridge University Press
ISBN: 0521824761
Category: Mathematics
Page: 496
View: 7968

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Shows novel and modern ways of solving differential equations using methods from contact and symplectic geometry.

Analysis II für Dummies


Author: Mark Zegarelli
Publisher: John Wiley & Sons
ISBN: 3527657983
Category: Mathematics
Page: 358
View: 5682

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Nach der Analysis ist vor der Analysis. Dies ist das richtige Buch f?r Sie, wenn es in der Analysis ein wenig mehr sein soll oder auch muss. Mark Zegarelli erkl?rt Ihnen, was Sie zur infiniten Integration und zu differential- und multivariablen Gleichungen wissen m?ssen. Er f?hrt mit Taylorreihe und Substitutionen fort und f?hrt Sie auch in die Dritte Dimension der Analysis; und das ist lange noch nicht alles! Im Ton verbindlich, in der Sache kompetent f?hrt er Ihre Analysiskenntnisse auf eine neue Stufe.

Introduction to Partial Differential Equations


Author: Peter J. Olver
Publisher: Springer Science & Business Media
ISBN: 3319020994
Category: Mathematics
Page: 636
View: 6197

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This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

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: 5044

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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.

Rechenmethoden der Physik

Mathematischer Begleiter zur Experimentalphysik
Author: May-Britt Kallenrode
Publisher: Springer-Verlag
ISBN: 3540274820
Category: Science
Page: 386
View: 6436

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Die vollständig überarbeitete zweite Auflage der Rechenmethoden der Physik führt beispiel- und praxisorientiert in mathematische Handwerkszeuge wie Differentialgleichungen ein. Methoden der Fehlerrechnung, wie im Praktikum benötigt, werden unter konsequenter Verwendung von Verteilungsfunktionen behandelt. Durch die enge Anbindung an das Themenspektrum der Experimentalphysik werden die Rechenmethoden in der Reihenfolge bereitgestellt, wie sie in der Experimentalphysik benötigt werden. Zahlreiche Aufgaben und Lösungen vervollständigen das Buch. In der neuen Auflage werden zudem Optimierungsprobleme, statistische Verfahren im Praktikum und numerische Verfahren ausführlich beschrieben.

Partial Differential Equations


Author: Fritz John
Publisher: Springer Science & Business Media
ISBN: 9780387906096
Category: Mathematics
Page: 252
View: 6714

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This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions.

An Introduction to Nonlinear Partial Differential Equations


Author: J. David Logan
Publisher: John Wiley & Sons
ISBN: 0470225955
Category: Mathematics
Page: 397
View: 8464

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An Introduction to Nonlinear Partial Differential Equations is a textbook on nonlinear partial differential equations. It is technique oriented with an emphasis on applications and is designed to build a foundation for studying advanced treatises in the field. The Second Edition features an updated bibliography as well as an increase in the number of exercises. All software references have been updated with the latest version of [email protected], the corresponding graphics have also been updated using [email protected] An increased focus on hydrogeology...

An introduction to nonlinear partial differential equations


Author: John David Logan
Publisher: Wiley-Interscience
ISBN: N.A
Category: Mathematics
Page: 400
View: 4708

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Uses an analytical and techniques-oriented approach to present a concise introduction to the subject focusing on time-evolution problems. Emphasizes hyperbolic and parabolic problems and includes a range of applications--chemistry, porous media, biological problems, traffic flow, reactors, heat transfer and detonation. Packed with exercises, examples and illustrations.

Handbook of Nonlinear Partial Differential Equations, Second Edition


Author: Andrei D. Polyanin,Valentin F. Zaitsev
Publisher: CRC Press
ISBN: 142008724X
Category: Mathematics
Page: 1912
View: 9760

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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.