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"An exceptionally complete overview. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here. This reviewer feels that it is a very hard act to follow, and recommends it strongly. [This book] is a jewel." ---Applied Mechanics Review (Review of First Edition) This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Methods and properties of solutions are presented, along with their physical significance, making the book more useful for a diverse readership. Topics and key features: * Thorough coverage of derivation and methods of solutions for all fundamental nonlinear model equations, which include Korteweg--de Vries, Boussinesq, Burgers, Fisher, nonlinear reaction-diffusion, Euler--Lagrange, nonlinear Klein--Gordon, sine-Gordon, nonlinear Schrödinger, Euler, Water Waves, Camassa and Holm, Johnson, Davey-Stewartson, Kolmogorov, Petrovsky and Piscunov, Kadomtsev and Petviashivilli, Benjamin, Bona and Mahony, Harry Dym, Lax, and Whitman equations * Systematic presentation and explanation of conservation laws, weak solutions, and shock waves * Solitons, compactons, intrinsic localized modes, and the Inverse Scattering Transform * Special emphasis on nonlinear instability of dispersive waves with applications to water waves * Over 600 worked examples and end-of-chapter exercises with hints and selected solutions New features of the Second Edition include: * Improved presentation of results, methods of solutions, and proofs * New section on Sturm--Liouville systems and their fundamental properties * Revised examples, exercises, and updated applications and references * Several revised, nonlinear real-world models, including traffic flow, flood waves, chromatographic models, sediment transport in rivers, glacier flow, and roll waves Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition is an exceptionally complete and accessible text/reference for graduate students, researchers, and professionals in mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference.

Mathematics. --- Partial Differential Equations. --- Applications of Mathematics. --- Theoretical, Mathematical and Computational Physics. --- Mathematical Methods in Physics. --- Classical Continuum Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Differential equations, partial. --- Mathematical physics. --- Engineering mathematics. --- Mathématiques --- Physique mathématique --- Mathématiques de l'ingénieur --- Differential equations, Nonlinear. --- Differential equations, Nonlinear --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Nonlinear differential equations --- Mathematical analysis. --- Analysis (Mathematics). --- Partial differential equations. --- Applied mathematics. --- Physics. --- Continuum physics. --- Analysis. --- Nonlinear theories --- Global analysis (Mathematics). --- Classical and Continuum Physics. --- Physical mathematics --- Physics --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Classical field theory --- Continuum physics --- Continuum mechanics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Engineering --- Engineering analysis --- Mathematical analysis --- 517.1 Mathematical analysis

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517.4 --- Functional determinants. Integral transforms. Operational calculus --- Integral transforms. --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Integral transforms --- Transform calculus --- Integral equations --- Transformations (Mathematics)

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This is perhaps the first book containing biographical information of Sir James Lighthill and his major scientific contributions to the different areas of fluid mechanics, applied mathematics, aerodynamics, linear and nonlinear waves in fluids, geophysical fluid dynamics, biofluid dynamics, aeroelasticity, boundary layer theory, generalized functions, and Fourier series and integrals. Special efforts is made to present Lighthill's scientific work in a simple and concise manner, and generally intelligible to readers who have some introduction to fluid mechanics. The book also includes a list of

Fluid mechanics. --- Mathematicians --- Mathematics. --- Wave mechanics. --- Electrodynamics --- Matrix mechanics --- Mechanics --- Molecular dynamics --- Quantum statistics --- Quantum theory --- Waves --- Math --- Science --- Hydromechanics --- Continuum mechanics --- Lighthill, M. J., --- Lighthill, J. --- Lighthill, James, --- Lighthill, Michael James, --- Appreciation.

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Differential equations, Nonlinear.

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Serves as a historical research monograph on the biographical sketch and career of Leonhard Euler and his major contributions to numerous areas in the mathematical and physical sciences. This title contains fourteen chapters describing Euler's works on number theory, algebra, geometry, trigonometry, and differential and integral calculus.

Mathematics --- Mathematicians --- History --- Euler, Leonhard, --- Geschichte 1750-2010