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Ordinary Differential Equations

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By George F. Carrier and Carl Pearson


1991 / x + 220 pages / Softcover / ISBN: 978-0-898712-65-0 / List Price $67.50 / SIAM Member Price $47.25 / Order Code CL06

"This volume is a new edition of the original text, published in 1968. In these days of drearily identical textbooks, it is good to see one that is unique; its reappearance is welcome. . . .The range of topics considered is extensive. In just over 200 pages, you will meet first- and second-order differential and difference equations, power and asymptotic series, eigenvalue expansions, special functions, (error, gamma, Bessel, Airy, and Legendre), the Laplace transform, variational calculus, solution of partial differential equations using separation of variables, nonlinear differential equations, numerical methods, and singular perturbation methods. . . . In summary, this is a nice book, moderately priced and well worth owning. . . . The publishers have done us a service in reissuing it." – J. M. Anthony Danby, SIAM Review, Vol. 35, No. 4, December, 1993

"A refreshing change from the omnipresent "cookbook" approach; heuristic arguments and beautiful, open-ended problems drive the discussion. Most problems end with a question forcing the solver to think about what he or she just did. Covers all the usual topics; great source of challenging problems for standard course." – American Mathematical Monthly, January 1992.

Offers an alternative to the "rote" approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume.

Introduction; First-Order Linear Differential Equations; Second-Order Differential Equations; Power- Series Descriptions; The Wronskian; Eigenvalue Problems; The Second-Order Linear Nonhomogeneous Equation; Expansions in Eigenfunctions; The Perturbation Expansion; Asymptotic Series; Special Functions; The Laplace Transform; Rudiments of the Variational Calculus; Separation of Variables and Product Series Solutions of Partial Differential Equations; Nonlinear Differential Equations; More on Difference Equations; Numerical Methods; Singular Perturbation Methods.

ISBN: 9780898712650

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