Partial differential equations of applied mathematics
This new edition features the latest tools for modeling, characterizing, and solving partial differential equations
The Third Edition of this classic text offers a comprehensive guide to modeling, characterizing, and solving partial differential equations (PDEs). The author provides all the theory and tools necessary to solve problems via exact, approximate, and numerical methods. The Third Edition retains all the hallmarks of its previous editions, including an emphasis on practical applications, clear writing style and logical organization, and extensive use of real-world examples.
Among the new and revised material, the book features:
* A new section at the end of each original chapter, exhibiting the use of specially constructed Maple procedures that solve PDEs via many of the methods presented in the chapters. The results can be evaluated numerically or displayed graphically.
* Two new chapters that present finite difference and finite element methods for the solution of PDEs. Newly constructed Maple procedures are provided and used to carry out each of these methods. All the numerical results can be displayed graphically.
* A related FTP site that includes all the Maple code used in the text.
* New exercises in each chapter, and answers to many of the exercises are provided via the FTP site. A supplementary Instructor's Solutions Manual is available.
The book begins with a demonstration of how the three basic types of equations-parabolic, hyperbolic, and elliptic-can be derived from random walk models. It then covers an exceptionally broad range of topics, including questions of stability, analysis of singularities, transform methods, Green's functions, and perturbation and asymptotic treatments. Approximation methods for simplifying complicated problems and solutions are described, and linear and nonlinear problems not easily solved by standard methods are examined in depth. Examples from the fields of engineering and physical sciences are used liberally throughout the text to help illustrate how theory and techniques are applied to actual problems.
With its extensive use of examples and exercises, this text is recommended for advanced undergraduates and graduate students in engineering, science, and applied mathematics, as well as professionals in any of these fields. It is possible to use the text, as in the past, without use of the new Maple material.
An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.
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Random Walks and Partial Differential Equations
Envelopes of Curves and Surfaces
Initial and Boundary Value Problems in Bounded Regions
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apply arbitrary argument assume asymptotic basis functions boundary conditions boundary layer boundary value problem bounded Cauchy problem Chapter characteristic curves coefficients consider constant construct convergence corresponding defined delta function derivatives determined difference equation difference scheme Dirichlet discontinuity discussion eigenfunctions eigenvalue problem evaluated exact solution Example Exercise expressed finite element foregoing Fourier transform fundamental solution Green's function Green's function K(x grid points heat equation homogeneous hyperbolic equation initial and boundary initial condition initial data initial value problem integral interval jump Laplace's equation linear Maple procedure matrix method Neumann nonlinear numerical solution obtain one-dimensional output parabolic equation parameter partial differential equations particle PDEs random walk rays region G replaced represents result satisfies Section separation of variables shown singular solution u(x solution values solve specified stability telegrapher's equation theorem triangulation ut(x valid vanishes vector vertex vertices wave equation yields zero