Math 449: Numerical Analysis for Differential Equations

Spring 2016 Policy Information

Instructor: Dr. Roger Thelwell
Contact: thelwerj@jmu.edu, (540) 568 -5103.
Section 1: Burruss 30 TuTh 3:30-4:45.
Office hours: ROOP 106 M 10-11, T 12:30-1:30, W noon-1 and 5-6, and by appointment
Webpage: http://educ.jmu.edu/~thelwerj/449
Canvas site: https://canvas.jmu.edu

Course Description
MATH 448 and MATH 449 are a pair of courses designed to introduce you to the idea of numerical methods. While 448 focused on the numerical topics you first encountered in MATH 248, the goal of MATH 449 is to derive, develop and analyze numerical methods that can be applied to the appoximate solution of both ordinary and partial differential equations. We will take a constructive approach to the solution of differential equations, and explore the mathematical and numerical issues as they develop.

Prerequisites
MATH 237, MATH 300 and MATH 248. Students are expected to bring modest programming proficiency to the class

Textbooks
Required: Introduction to Numerical Methods for Differential Equations by Mark Holmes. Springer
Optional: Numerical Analysis by Burden & Faires. Cengage

Most importantly, though, just owning a text won't be enough. You've got to read it. And think about it. And work out the details with pencil and paper. And code examples and generate plots. And ask questions. And THEN repeat until it makes sense.

Stucture
This course is going to require a significant investment of your time. Lectures are a great way for you to see and appreciate math, but they don't do such a great job at giving you the mastery of the material. Since mathematics is learned by practice, homework with integral pogramming assignments are really the core of this course. In general, the more work you put in, the better you will do.

Proposed Outline
Ambitious!

Initial Value ODE (2 weeks): finite difference methods; consistency, stability, convergence
Two point Boundary Value Problems (3 weeks): finite difference methods; consistency, stability, convergence
Parabolic PDE (4 weeks): finite difference methods; consistency, stability, convergence; nonlinear problems
Hyperbolic PDE (3 weeks): finite difference methods; consistency, stability, convergence; wave propagation, dispersion relation
Elliptic PDE (2 weeks): higher dimensional; systems

On-line Material
Course material will be posted on Canvas.

Grading
Grades will be assigned on the 10 point scale:
90-100 A- to A range; 80-89: B- to B+ range; 70-79 C- to C+ range; 60-69 D to D+ range; 59 and below: F.

60% Homework
20% Miterm
20% Final

Computing Software
I will be using Matlab, which at the bookstore, or online (student edition) at http://www.mathworks.com/academia/student_version/. Matlab is also available in Burruss 30 & 130, Roop 103, and Miller G080. A flash drive for storing your files is highly recommended. There are a large number of Matlab resources on the web, including the online textbook by Matlab’s author, at http://www.mathworks.com/moler/index_ncm.html

Attendance Show up ready to think, and be on time.

Homework
There will be homework assignments due (roughy) every two weeks. Many problems will be easier if you use a Computer Algebra (CAS) software like Maple or Mathematica. Other problems will require you to code, run, and analyze your numerical results. Your job is to present your work as clearly and coherently as possible. There will be cases where part of your homework grade will be determined based on your oral presentation of specific problem or topic, either in class or during office hours. Late homework will be accepted, but a 10% penalty per day will be assesed.

Collaboration (but not copying!) is encouraged. The time you spend working on the homework will be invaluable.
Your assignments will be posted here.

Need a little extra help?
I enjoy office hours, and you should seriously think about attending them early in the semester. They will help! And don't be afraid to send an email or give me a call, although in person is likely to be most benefical.Help me find your email by using the subject M232_F16.

Honor code
Remember that JMU has a strict honor code. While you are strongly encouraged to work with others in this class, the work you submit must be your own. Copying someone else's work won't help you learn the material and might just get you expelled.

Nature of the Course Content
(from course catalogue)
MATH/CS 449. Numerical Analysis for Differential Equations. 3 credits. Offered every third semester as of fall 2016. Study and analysis of numerical techniques to solve ordinary and partial differential equations, including Euler, Runge-Kutta, Picard, finite-difference and finite-element methods. Programming using a high-level language and/or software packages. Prerequisite: MATH 237, MATH 238 and MATH 248.

Finally, JMU's standard syllabus statement. Please contact me in the first week of the course if you require disability accommodations.