MATH 686 (Section 001)
Spring 2008

Numerical Solution of Differential Equations

| About the Course | Instructor | Learning Outcomes | Lectures | About Matlab | Course Evaluation | Opportunities | Academic Integrity | Disability Accomodation |


Mathematical models describing physical situations are frequently expressed as differential equations. This course will be devoted to the development and analysis of methods for the numerical solution of differential equations. Both the numerical methods and applications will be considered with emphasis on partial differential equations. The course will focus on finite difference methods and finite element methods for elliptic problems but parabolic and hyperbolic problems will also be considered. Graphics, meshing, and simple iterative techniques will also be discussed and implemented as computer codes. The primary reference will be Lecture notes provided by the instructor that will be posted on the course website on a regular basis.


Dr. Padmanabhan Seshaiyer


In this course, the emphasis will be to apply well-know numerical techniques for solving differential equations arising in engineering problems and evaluate the results. The objective will be to train students to develop, analyze and implement the methods. In particular, the students will become proficient in:
  1. Understanding the theoretical and practical aspects of the use of numerical methods for differential equations

  2. Implementing numerical methods for a variety of multidisciplinary applications

  3. Establishing the limitations, advantages, and disadvantages of the numerical methods used in practice
The expected learning outcomes for the course will be assessed through: Exams, homeworks, in-class activities and class discussions. Problem-based learning will be an integral part of the course.


Copyright Statement: The lecture notes below are copyrighted by Dr. Padmanabhan Seshaiyer and contains material from a graduate textbook in preparation. These notes are intended primarily for use by the students enrolled in MATH686 (Spring 2008). Students who are formally enrolled in this class have permission to print copies of the online notes in unaltered form exclusively for personal use. Note however that, personal use does not extend to additional reproduction, alteration, distribution, or resale of these notes in any form to anybody. Educational or non-profit organizations wishing to reproduce or provide links to any part of these pages must contact Dr. Padmanabhan Seshaiyer ( in writing.


The software package MATLAB will be used for scientific computation, analysis and presentation of data. MATLAB is an interactive programming language for general scientific and technical computation with powerful graphics and library functions.


Evaluation for the course will be based on the following criteria:

Homework 60%
Inclass Presentations 10%
Midterm Exam 10%
Final Exam 20%
TOTAL 100%

There will be six homework assignments during the semester each worth 10% assigned every other week, that will include both theoretical and computational problems. The solutions must be neatly written up and handed in on time to receive full credit as they add towards 60% of the total grade. Students must also prepare for inclass presentations based on their homework which will be worth 10%. There will be one midterm exam worth 10% that will be based on the various mathematical techniques presented in the class during the semester. There will be one final exam which will be worth 20% and will be held on Tuesday May 13, 2008 from 7:30 pm - 10:15 pm.



All students will be expected to abide by the Honor Code: Student members of the George Mason University community pledge not to cheat, plagiarize, steal, or lie in matters related to academic work .


Any student who, because of a disability, may require some special arrangements in order to meet course requirements should contact the instructor as soon as possible to make such accommodations as may be necessary.