Abstract:
This edition, like its predecessors, is written from the viewpoint of the applied
mathematician, whose interest in differential equations may be sometimes quite
theoretical, sometimes intensely practical, and often somewhere in between. We
have sought to combine a sound and accurate (but not abstract) exposition of the
elementary theory of differential equations with considerable material on methods
of solution, analysis, and approximation that have proved useful in a wide variety of
applications.
The book is written primarily for undergraduate students of mathematics, science,
or engineering, who typically take a course on differential equations during their
first or second year of study. The main prerequisite for reading the book is a working
knowledge of calculus, gained from a normal two- or three-semester course sequence
or its equivalent. Some familiarity with matrices will also be helpful in the chapters
on systems of differential equations.
To be widely useful, a textbook must be adaptable to a variety of instructional
strategies. This implies at least two things. First, instructors should have maximum
flexibility to choose both the particular topics they wish to cover and the order in
which they want to cover them. Second, the book should be useful to students who
have access to a wide range of technological capability.
With respect to content, we provide this flexibility by making sure that, so far as
possible, individual chapters are independent of each other. Thus, after the basic
parts of the first three chapters are completed (roughly Sections 1.1 through 1.3, 2.1
through 2.5, and 3.1 through 3.5), the selection of additional topics, and the order and
depth in which they are covered, are at the discretion of the instructor. Chapters 4
through 11 are essentially independent of each other, except that Chapter 7 should
precede Chapter 9 and that Chapter 10 should precede Chapter 11. This means that
there are multiple pathways through the book, and many different combinations
have been used effectively with earlier editions.
