Theory and Applications of Ordinary Differential Equations

Textbook Media Press presents Theory and Applications of Ordinary Differential Equations, a well-balanced blend of theory, techniques, and applications for the undergraduate differential equations course. The text is written so that instructors can choose to emphasize whichever of these three aspects is appropriate for their course.

In physical systems, and even in systems that are not physical, a change in one quantity often precipitates changes in other quantities. Relationships among the rates at which these changes take place lead to what are called differential equations, and the number of areas of applied mathematics that give rise to them is truly amazing. They serve as mathematical models not only in the physical sciences of engineering, physics, and chemistry, but also in less traditional areas such as economics, medicine, and music.

The author’s writing style will appeal to students. It replaces the stylized language akin to technical papers and more advanced texts with smoothly flowing discussions that students will find easy to follow. The author seems to know when and what questions students will ask, and provides the answer at the appropriate time.

Applications are given their own chapters rather than being confined to end-of-section notes. Chapter 3 works through growth and decay, Newtonian mechanics, population dynamics, mixing problems, pursuit curves, orthogonal trajectories, and electric circuits; Chapter 5 covers vibrating mass-spring systems, LCR circuits, and beam deflections. Exercises range from the routine, to test understanding of basic subject matter, to the challenging, for the enterprising student, and avoid the long and involved applications that few students are likely to investigate.

The last four chapters open onto partial differential equations. Partial differential equations is a vast area of study, and the author gives thorough treatments to the most prominent topics in any introductory course rather than excerpts. Included are separation of variables on homogeneous and nonhomogeneous problems in Cartesian coordinates, regular and singular Sturm-Liouville systems, and separation in polar, cylindrical, and spherical coordinates. There is enough here to support a second course.

A Student Solutions Manual is available as a download or in paperback. The complete solutions manual has been written and prepared by the author, so students can be assured that all exercises can be solved by techniques discussed in the text.