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Teach yourself ordinary differential equations in a fraction of the
time most courses take
The shortest distance between two points is a straight line (unless
you are on a curved surface). This book is intended to provide the
shortest path to an understanding of introductory ordinary
differential equations (ODE); however, such a shortcut requires
more than the shortest possible book. In recent years the
understanding of how people learn has improved dramatically. Out of
this enhanced understanding, active learning has emerged as a
powerful educational tool. In preparing this book, active learning
principles have been applied so that this book is a short path to a
solid introductory understanding of ODE. My principle introduction
to active learning has been through several seminars by Dr. Barbara
J. Millis, Director for Faculty Development at the U.S. Air Force
Academy.
The active learning features of are book are as follows: The book
consists of twenty short sections, called Articles, each of which
focuses on a single subject. The conceptual integrity this provides
helps the student develop an organizational framework for the
material. Within each Article, the material is illustrated with
salient examples. Several exercises are provided at the end of each
section and all of the answers are provided. This is done to
provide the necessary quick reinforcement of learning and to
motivate the student by early success. Thus, in keeping with active
learning, the student is actively working with the material,
reading short articles, working through short examples and
exercises, obtaining immediate reinforcement, and gaining increased
confidence and mastery. The book is kept short so that the student
can be confident that they can "own the subject" in a reasonable
span of time.
This book is intended for anyone who has had some calculus, at
least to the point of being able to differentiate and integrate,
and who is motivated to work the examples and exercises.
The material covered here grew out of sophomore-level classroom and
hybrid courses in differential equations that the author taught at
Community College of Aurora in Colorado.
The book is divided into three Parts. The first two parts treat
first-order and higher-order differential equations, respectively,
in the context of solution using in situ methods. By in situ, I
mean that the solution is solved in place by some manipulation or
substitution but without a major transformation of the problem into
another domain. The third part of the book deals with the Laplace
transform method of solution of ordinary differential equations.
Here the differential equation is transformed into a realm in which
many functions become rational functions and in which solution is
often easier to accomplish. There are two appendices: The first
appendix presents solutions to all exercises and the second is a
timeline of differential equations.
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