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

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.