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.
