MATHS 475: Topics in Partial Differential Equations (3)

Syllabus

 

1. Prerequisite:  MATHS 374, MATHS 267; or permission of the department chairperson.
2. Catalog Description:  Classical solution techniques for linear PDEs. Topics include first- and second-order equations, method of characteristics, special functions, orthogonal polynomials, transforms, Green’s functions, and fundamental solutions. A computer algebra system is utilized.
3. Course Objectives:  The primary objective of this course is to introduce the student to the standard ideas necessary to study and solve real-world problems involving partial differential equations. In addition, the student will learn how to utilize a computer algebra package such as Mathematica in problem solving—a crucial skill for today’s applied mathematician.  This course is designed to complement the department’s course on Boundary Value Problems (MATHS 473).
4. Course Rationale:  Many real-world problems found in areas such as financial mathematics and mathematical physics can be modeled with partial differential equations, so any student who wishes to work as an applied mathematician must be familiar with standard equations and solution techniques for partial differential equations.  Many of these problems can be investigated with computer algebra package such as Mathematica, so it is expected that any applied mathematician will have a working knowledge of such software.
5. Course Content:  The topics to be covered are listed in the course description.  They constitute those found in a standard course on partial differential equations at nearly every college and university. 
6. Course Format:  It is expected that the student will master and utilize a computer algebra package such as Mathematica, which is available in the departmental computer laboratories.  Standard modes of instruction will include individual or group projects that involve partial differential equations and available technology.
7. Methods of Evaluating Student Performance:  Course grades are determined primarily by student performance on tests, quizzes, and projects, as well as possibly homework, student presentations, and class participation. The evaluation and weight of these various components are at the discretion of the individual instructor.
8. Evaluation of the Course:  The department Undergraduate Programs Committee will periodically evaluate the MATHS 475 course.  Assessment techniques used in evaluating the teaching of this course may include student evaluations or peer evaluations

 

M. Karls, M. Toda, December 1, 2000

 

M. Karls, A. Mohammed, J.P. Liamba 4/2004, Ahmed Mohammed, Fall 2005