TEXT: D. G. Zill, M. R. Cullen, Differential Equations with Boundary Value Problems, 6th Ed., Thomson

COURSE DESCRIPTION:

Many problems in science and engineering can be formulated as boundary value problems, i.e., differential equations with boundary conditions. For example, heat conduction in a wall, with prescribed temperatures on both surfaces of the wall, is a boundary value problem. So is vibration of a guitar string. Techniques for solving boundary value problems involve infinite series and Fourier transforms.

PREREQUISITES: Differential Equations (MAT 330 or equivalent).

TOPICS:

1. Infinite Series
   • convergence of series: the ratio test
   • power series
2. Ordinary Differential Equations with Variable Coefficients (Ch. 4.7, 6)
   • Cauchy-Euler equations
   • method of Frobenius
   • Bessel functions and Legendre polynomials
3. Orthogonal Functions and Fourier Series (Ch. 11)
   • Trigonometric Series
   • Sturm-Liouville problem
   • Bessel and Legendre series
4. Boundary Value Problems (Ch. 12)
   • heat equation
   • wave equation
   • Laplace's equation
5. The Fourier Transform (Ch. 14)
   • solving partial differential equations using the Fourier transform

OFFICE HOURS:

T, 9 -10 AM, 5 - 6 PM R, 9 -10 AM, 5 - 6 PM

DON 2275 Applied Math Linux Lab (DON 2110)

GRADES:

Test (Feb. 24) Test (March 17) Test (April 21) Final (cumulative)

30 points 30 points 30 points 40 points

A+ >= 97 pts A = 93,...,96 pts A- = 90,...,92 pts etc.

The lowest test score will be dropped.
Working on projects, i.e., problems which are somewhat tougher than homework assignments, is an excellent way to learn. Projects are optional. However, projects which are successfully completed, documented, and presented in class, can play the same role as the final exam. Project titles and abstracts are due March 15.