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Ordinary Differential Equations (Dover Books on
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Ordinary Differential Equations (Dover Books on
Mathematics)
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business account Series: Dover Books on Mathematics Paperback: 832 pages Publisher: Dover Publications;
Revised ed. edition (October 1, 1985) Language: English ISBN-10: 9780486649405 ISBN-13: 978-
0486649405 ASIN: 0486649407
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Book Description
This unusually well-written, skillfully organized introductory text provides an exhaustive survey
of ordinary differential equations — equations which express the relationship between variables
and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices
mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of
Purdue University — introduce and explain complex, critically-important concepts to
undergraduate students of mathematics, engineering and the sciences. The book begins with a
section that examines the origin of differential equations, defines basic terms and outlines the
general solution of a differential equation-the solution that actually contains every solution of
such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and
accretion problems; the algebra of complex numbers; the linearization of first order systems;
Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive
Approximations. The book contains two exceptional chapters: one on series methods of solving
differential equations, the second on numerical methods of solving differential equations. The first
includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre
Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation.
Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly
analyzed, and there is an admirable balance between the theory of differential equations and their
application. An abundance of solved problems and practice exercises enhances the value of
Ordinary Differential Equations as a classroom text for undergraduate students and teaching
professionals. The book concludes with an in-depth examination of existence and uniqueness
theorems about a variety of differential equations, as well as an introduction to the theory of
determinants and theorems about Wronskians.

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