Ebook: Differential equations and their applications: an introduction to applied mathematics

There are three major changes in the Third Edition of Differential Equations and Their Applications. First, we have completely rewritten the section on singular solutions of differential equations. A new section, 2.8.1, dealing with Euler equations has been added, and this section is used to motivate a greatly expanded treatment of singular equations in sections 2.8.2 and 2.8.3. Our second major change is the addition of a new section, 4.9, dealing with bifurcation theory, a subject of much current interest. We felt it desirable to give the reader a brief but nontrivial introduction to this important topic. Our third major change is in Section 2.6, where we have switched to the metric system of units. This change was requested by many of our readers. In addition to the above changes, we have updated the material on population models, and have revised the exercises in this section. Minor editorial changes have also been made throughout the text. Preface to the First Edition This textbook is a unique blend of the theory of differential equations and their exciting application to "real world" problems. First, and foremost, it is a rigorous study of ordinary differential equations and can be fully understood by anyone who has completed one year of calculus. However, in addition to the traditional applications, it also contains many exciting "real life" problems. These applications are completely self contained.

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This text is a clearly written and complete introductory study of differential equations and their applications. Suitable for a one- or two-semester course on the subject, the material is fully comprehensible to anyone who has studied college-level calculus. This book distinguishes itslef from other differential equation texts through its application of the subject matter to fascinating events and its incorporation of relatively recent developments in the field. Some applications include:* a proof that the painting, "Disciples of Emmaus," bought by the Rembrandt Society of Belgium was a modern forgery;* a mathematical explanation of the Tacoma Bridge disaster;* a model of the blood glucose regulatory system which leads to a criterion for the diagnosis of diabetes;*an explanation of why the predator portion (sharks, skates, rays, etc. ) of all fish caught in the port of Flume, Italy, rose dramatically during the years of World War I;* a mathematical verification of Darwin's law that "the more similar two species are, the fiercer is the struggle for existence between them. "An introduction to bifurcation theory, computer programs in C, Pascal, and Fortran, and many original and challenging exercises contribute to the quality of this text.