Professor: Dr. Nathan Louis Gibson
Office: Kidd 312
Office Hours: MWF 1:00-1:50
Course Website:
http://www.math.oregonstate.edu/~gibsonn/Teaching/MTH553-001S10
Text Book |
A derivation of methods appropriate for particular classes of PDEs will be
presented. We will focus on analysis of stability, accuracy, convergence,
and implementation of these methods. Students will get computationalexperience in applying the
algorithms studied using the MATLAB problem-solving environment.
We will also discuss techniques particularly efficient in solving linear
systems arising from implicit discretizations of PDEs, and
contrast finite difference and finite element methods, as time permits.
Prerequisites: Familiarity with basic properties of differential
equations (MTH 256) and matrices (MTH 341 or 306), and some programming
experience (preferably with MATLAB) is required. Familiarity with PDEs is
a plus; however we will develop the basics as necessary. Those who have
taken the equivalent of MTH452/552 would be well-prepared. Students who
are not sure about prerequisites are encouraged to talk to me.
Course Description
This course will explore numerical methods based on finite difference
discretizations for solving partial differential equations
(PDEs), including time dependent. Partial differential equations are used
to describe a large variety
of physical phenomenon, from fluid flow to electromagnetic fields. They
also arise in many diverse applications as ecology,
mechanical systems, earth sciences and mathematical finance.
Matlab
The programming language for this course is MATLAB.
You can obtain access to MATLAB via one of the following:
| Homework | 40% |
| Midterm | 30%* |
| Final | 30% |
| Total | 100% |
*Note: Final exam grade will replace midterm grade if higher.
| A | 93 |
| A- | 90 |
| B+ | 87 |
| B | 83 |
| B- | 80 |
| C+ | 77 |
| C | 73 |
| C- | 70 |
| D+ | 67 |
| D | 63 |
| D- | 60 |
Assignments should be completed individually. You may confer with fellow
students in general terms, but must write code and solutions on your own.
If your homework is late you will receive up
to half credit for the first two days after the due date. Homework
submitted three days or later after the due date will not receive any
credit.
553: denotes a problem that is required only for students enrolled
in MTH 553, but can serve as
extra credit for MTH 453 students.
There will be approximately four assignments to be posted here.
Homework
Homework assignments will be posted here as pdf files. They will be mostly
self-contained, but possibly referencing methods or equations from the
text. Some problems will require programming and/or computational
experimentation. This is not a programming course, thus many algorithms
will be coded for you. However, you will need to know how to fix, modify
and use MATLAB codes.
453: denotes a problem that is optional for MTH 553 students.
MATLAB codes:
MATLAB codes:
Solutions
MATLAB codes:
Solutions
Exams
There will be one midterm exam
and one cummulative final exam.