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: 4959

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For students taking second courses; the subject is central and required at second year and above.
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Nonlinear Partial Differential Equations for Scientists and Engineers

Author: Lokenath Debnath

Publisher: Springer Science & Business Media

ISBN: 9780817644185

Category: Mathematics

Page: 738

View: 2772

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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.
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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: 4005

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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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Mathematical Optics

Classical, Quantum, and Computational Methods

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

Publisher: CRC Press

ISBN: 1351832859

Category: Science

Page: 630

View: 3165

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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.
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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: 6515

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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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Ordinary Differential Equations

Author: Vladimir I. Arnold

Publisher: Springer Science & Business Media

ISBN: 9783540548133

Category: Mathematics

Page: 338

View: 3691

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Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW
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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: 324

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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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