Preface
Ordinary Differential Equations: Applications, Models, and Computing is
an introductory level textbook for undergraduate students majoring in math-
ematics, applied mathematics, computer science, one of the various fields of
engineering, or one of the physical or social sciences. During the past century,
the manner in which solutions to differential equations have been calculated
has changed dramatically. We have advanced from paper and pencil solution,
to calculator and programmable calculator solution, to high speed computer
calculation. Yet, in the past fifty years there has been very little change in
the topics taught in an introductory differential equations course, in the or-
der in which the topics are taught, or in the methods by which the topics
are taught. The "age of computing" is upon us and we need to develop new
courses and new methods for teaching differential equations. This text is an
attempt to facilitate some changes. It is designed for instructors who wish
to bring the computer into the classroom and emphasize and integrate the
use of computers in the teaching of differential equations. In the traditional
curriculum, students study few nonlinear differential equations and almost no
nonlinear systems due to the difficulty or impossibility of computing explicit
solutions manually. The theory associated with nonlinear systems may be
considered advanced, but generating a numerical solution with a computer
and interpreting that solution is fairly elementary. The computer has put the
study of nonlinear systems well within our grasp.
The word "computing" appears in the title of this book because many
examples and exercises require the use of some computer software to solve a
problem. Consequently, the reader needs to have computer software available
which can perform, at least, the following functions:
- Graph a given function on a specified rectangle.
- Graph the direction field of the first-order differential equation y'
f(x, y) in a specified rectangle. - Solve the first-order initial value problem y' = f(x, y); y(c) =don an
interval [a, b] which contains c. - Find all roots of a polynomial with complex coefficients.
- Calculate the eigenvalues and eigenvectors of a real n x n matrix A
where 2 ::::; n ::::; 6.
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