A First Course in Differential Equations with Modeling Applications: Twelfth Edition

by Dennis G. Zill

Authors of books live with the hope that someone actually reads  them. Contrary to
what you might believe, almost everything in a typical college-level mathematics text
is written for you and not the instructor. True, the topics covered in the text are chosen
to appeal to instructors because they make the decision on whether to use it in their
classes, but everything written in it is aimed directly at you, the student. So I want
to encourage you—no, actually I want to tell you—to read this textbook! But do not
read this text as you would a novel; you should not read it fast and you should not skip
anything. Think of it as a workbook. By this I mean that mathematics should always
be read with pencil and paper at the ready because, most likely, you will have to work
your way through the examples and the discussion. Before attempting any problems in
the section exercise sets, work through all the examples in that section. The examples
are constructed to illustrate what I consider the most important aspects of the section,
and therefore, reflect the procedures necessary to work most of the problems. When
reading an example, copy it down on a piece of paper and do not look at the solution in
the book. Try working it, then compare your results against the solution given, and, if
necessary resolve any differences. I have tried to include most of the important steps in
each example, but if something is not clear you should always try—and here is where
the pencil and paper come in again—to fill in the details or missing steps. This may
not be easy, but it is part of the learning process. The accumulation of facts followed by
the slow assimilation of understanding simply cannot be achieved without a struggle.