Partial Differential Equations

This course is designed to provide students in the Space Science Program, the Physics Program, and the Mathematical Sciences Program with a survey of classical partial differential equations and boundary-value problems. The traditional classification schemes involving concepts such as linearity/non-linearity, homogeneity/non-homogeneity, and constant/variable coefficients will be investigated. The emphasis will be on applications of partial differential equations to physics and chemistry. The method of separation of variables will be emphasized and Fourier series will be discussed. Orthogonal function and Green's functions will be presented along with the Fourier integral and double Fourier series. Laplace transform methods will also be examined as will the method of characteristics. Graphical and geometric methods will be presented. Although the emphasis throughout the course will be on closed-form solutions and the physical/geometrical interpretations of the equations and their associated boundary conditions, computers will be used for drill and practice work once the main analytical technique has been thoroughly investigated.

019910