*Linear, Nonlinear, Ordinary, Partial*

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

**Publisher:**Cambridge University Press

**ISBN:**9780521016872

**Category:**Mathematics

**Page:**541

**View:**3811

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# Search Results for: differential-equations-linear-nonlinear-ordinary-partial

*Linear, Nonlinear, Ordinary, Partial*

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

**Publisher:** Cambridge University Press

**ISBN:** 9780521016872

**Category:** Mathematics

**Page:** 541

**View:** 3811

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

**Author**: Lokenath Debnath

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817644185

**Category:** Mathematics

**Page:** 738

**View:** 8827

This expanded, revised edition is a thorough and systematic treatment of linear and nonlinear partial differential equations and their varied applications. It contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, make the book useful for a diverse readership including graduates, researchers, and professionals in mathematics, physics and engineering.
*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:** 5464

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, Collge 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.

**Author**: W. F. Ames

**Publisher:** Academic Press

**ISBN:** 008095524X

**Category:** Mathematics

**Page:** 510

**View:** 8885

Nonlinear Partial Differential Equations in Engineering

**Author**: Tyn Myint-U,Lokenath Debnath

**Publisher:** Springer Science & Business Media

**ISBN:** 9780817645601

**Category:** Mathematics

**Page:** 778

**View:** 1076

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.

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

**Publisher:** Oxford University Press on Demand

**ISBN:** 9780198527718

**Category:** Mathematics

**Page:** 449

**View:** 1429

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.

**Author**: Peter J. Olver

**Publisher:** Springer Science & Business Media

**ISBN:** 3319020994

**Category:** Mathematics

**Page:** 636

**View:** 4483

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.

**Author**: Zegarelli

**Publisher:** John Wiley & Sons

**ISBN:** 3527657983

**Category:** Mathematics

**Page:** 358

**View:** 9614

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

**Author**: Andrei D. Polyanin,Valentin F. Zaitsev

**Publisher:** CRC Press

**ISBN:** 1135440816

**Category:** Mathematics

**Page:** 840

**View:** 5095

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:
*Mathematischer Begleiter zur Experimentalphysik*

**Author**: May-Britt Kallenrode

**Publisher:** Springer-Verlag

**ISBN:** 3540274820

**Category:** Science

**Page:** 386

**View:** 1547

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.

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

**Publisher:** CRC Press

**ISBN:** 9780415272674

**Category:** Mathematics

**Page:** 520

**View:** 3093

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.

**Author**: Lamberto Cesari,Rangachary Kannan,Jerry D. Schuur

**Publisher:** CRC Press

**ISBN:** 9780824764524

**Category:** Mathematics

**Page:** 368

**View:** 4467

**Author**: Giampiero Esposito

**Publisher:** Springer

**ISBN:** 3319575449

**Category:** Mathematics

**Page:** 432

**View:** 2194

This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

**Author**: Fritz John

**Publisher:** Springer Science & Business Media

**ISBN:** 9780387906096

**Category:** Mathematics

**Page:** 252

**View:** 1123

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.

**Author**: Tomas B. Co

**Publisher:** Cambridge University Press

**ISBN:** 1107004128

**Category:** Mathematics

**Page:** 559

**View:** 2682

This engineering mathematics textbook is rich with examples, applications and exercises, and emphasises applying matrices.
*Classical, Quantum, and Computational Methods*

**Author**: Vasudevan Lakshminarayanan,María L. Calvo,Tatiana Alieva

**Publisher:** CRC Press

**ISBN:** 1351832859

**Category:** Science

**Page:** 630

**View:** 2569

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical waveguides. Part II explores solutions to paraxial, linear, and nonlinear wave equations. Part III discusses cutting-edge areas in transformation optics (such as invisibility cloaks) and computational plasmonics. Part IV uses Lorentz groups, dihedral group symmetry, Lie algebras, and Liouville space to analyze problems in polarization, ray optics, visual optics, and quantum optics. Part V examines the role of coherence functions in modern laser physics and explains how to apply quantum memory channel models in quantum computers. Part VI introduces super-resolution imaging and differential geometric methods in image processing. As numerical/symbolic computation is an important tool for solving numerous real-life problems in optical science, many chapters include Mathematica® code in their appendices. The software codes and notebooks as well as color versions of the book’s figures are available at www.crcpress.com.

**Author**: John David Logan

**Publisher:** Wiley-Interscience

**ISBN:** N.A

**Category:** Mathematics

**Page:** 400

**View:** 2063

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.

**Author**: Jeffrey Rauch

**Publisher:** American Mathematical Soc.

**ISBN:** 0821872915

**Category:** Mathematics

**Page:** 363

**View:** 6836

This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.

**Author**: Gustavo L¢pez

**Publisher:** World Scientific

**ISBN:** 9789810237462

**Category:** Science

**Page:** 116

**View:** 2177

This book is about the theory and applications of Partial Differential Equations of First Order (PDEFO). Many interesting topics in physics such as constant motion of dynamical systems, renormalization theory, Lagrange transformation, ray trajectories, and Hamilton-Jacobi theory are or can be formulated in terms of partial differential equations of first order. In this book, the author illustrates the utility of the powerful method of PDEFO in physics, and also shows how PDEFO are useful for solving practical problems in different branches of science. The book focuses mainly on the applications of PDEFO, and the mathematical formalism is treated carefully but without diverging from the main objective of the book.

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