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Applied Ordinary Differential Equations

Alfred Clark Jr.
Organization: University of Rochester
Department: Departments of Mechanical Engineering and Mathematics
Education level


The course is aimed at science and engineering students, and provides an introduction to ordinary differential equations with a strong emphasis on applications and the use of Mathematica.

The textbook used this year is Fundamentals of Differential Equations and Boundary Value Problems, Third Edition, by R.K. Nagle, E.B. Saff, and A.D. Snider (Addison-Wesley, 2000). In addition the students were supplied with a Mathematica Tutorial, available on the course web site.

Conventional analytical methods are supplemented by the use of DSolve and NDSolve in Mathematica. Beginning with the third homework assignment, students are asked to carry out Mathematica work as well as analytical work. Mathematica notebooks illustrating applications in engineering and science are (1) handed out to students, (2) demonstrated in class with a laptop and a computer projector, and (3) placed on the web site for the course. In the last two weeks of the course, students are given a computer project with a Star Trek context. Detailed descriptions of the projects for the last few years are available on the course web site. Based on the course evaluations, it is our belief that the many applications in the course provide strong motivation for engineering and science students. In the project at the end of the course, students exhibit both excellence and enthusiasm.

The three major parts of the course are:
  • first order equations
  • linear second order equations
  • systems of first order equations
The applications presented in the course include:
  • population models
  • free fall and the drag law
  • heating and cooling of buildings
  • measuring parameters in vibrating systems
  • switch design
  • automobile suspensions
  • models of epidemics
  • dynamics of disease
  • predator-prey models
  • nonlinear mechanical oscillators

*Mathematics > Calculus and Analysis > Differential Equations