**Fall Semester
2006-2007**

**MATH 3353: Methods
of Applied Mathematics**

**Instructor: **Dr. Vu
Kim Tuan** **

**Time & Location: **TR,
11:00 AM-12:15 PM, Boyd Building 304

**Office: **Boyd
Building 325

Office Hours: Wednesdays: 10:00 AM-12:00
PM, Tuesdays + Thursdays, 10:00 AM-11:00 AM, 12:15 PM-1:15 PM, or by
appointment. Please contact me
only through campus MyUWG e-mail or in person.

**Phone: **678-839-4135** **

**E-mail: **vu@westga.edu

**Hours Credit: **3
hours** **

**Prerequisites: **MATH
3303** **

**Textbook: ***A Very
Applied First Course in Partial Differential Equations***, **by Michael K. Keane, Prentice Hall, Inc. 2002, ISBN 0-13-030417-4

.

**Course Description: **A
first** **course in Partial
Differential Equations (PDEs). The student is assumed to know some basic facts
in Ordinary Differential Equations. We will cover Chapters 2-5, 7-8, 10-11 with
emphasis on Problem Solving. The student will learn how to solve PDE's using
orthogonal function systems, studies classical boundary-value problems,
including the heat equation, wave equation, and potential, Fourier series,
Fourier transform and numerical methods of solutions.

**Topics: **Derivation
of heat conduction and boundary conditions for a one-dimensional rod. The
maximum principle and uniqueness. Derivation of the one-dimensional wave
equation and boundary conditions. Conservation of energy. Method of
characteristics and DÕAlambertÕs solution. Fourier series. Separation of
variables for homogeneous and nonhomogeneous problems. Sturm-Liouville
eigenvalue problem and Rayleigh quotient. Classical PDE problems. Fourier
integral. Finite Difference Numerical Methods.

**Learning
Outcomes: **the student will be able:

-To classify 2^{nd}-order linear PDEs

-To derive 2^{nd} order PDEs from physical problems.

-To discuss and solve the heat equation in some cases.

-To discuss and solve the wave equation in some cases.

-To discuss and solve the Laplace equation in some cases.

-To understand Fourier series and Fourier transform and apply them to solve PDEs.

-To apply finite differences for numerical solutions of PDEs.

-To find engenvalues of Sturm-Liouville boundary value problems.

**Tests and Final Exam: **There
will be two in-class tests and two take-home tests worth 100 points each. Take-home
tests are supposed to be completed *individually*. The lowest of
these test scores will be dropped. You can miss at most one test, and that test
will be considered to be the test with the lowest score to be dropped. The
final counts 200 points. No make-up for missing tests and final exam.

**Extra Credits: **The Department**
**runs an applied mathematics seminar on
Mondays 4:30 PM-5:30 PM. You are encouraged to attend these seminars, and up to
25 bonus points will be given for the attendance (5 bonus points for every
seminar attendance).

** **

**Important Dates: **9/12
: Test 1 (In-class)

9/28 : Test 2 (Take-home) Due 10/3

10/26 : Test 3 (Take-home) Due 10/31;

11/16 : Test 4 (In-class)

12/5 : Final, 11 AM Ð 1 PM

Grading: The final letter grade
will be determined by the following scale:

A = 450-525, B = 400-<450, C
= 350-<400,
D = 300-<350, F =
below 300

**W Deadline: **October
6th is the last day to withdraw with grade W

** **

**Homework**: This is an
important part of the course. At the end of most classes you will be given a
list of problems Ð these are the minimum that you should work on. These
problems will not be graded. Some of these problems will be gone over in the
next class session and some will be included into the in-class tests. Practice
is important. I encourage you to use my office hours if you have any questions
about them. You should make sure to set aside some time every class day to work
problems.

**Disabilities:** Students with
documented disabilities (through West GeorgiaÕs Disability Services) will be
given all reasonable accommodations. Students must take the
responsibility to make their disability known and request academic adjustments
or auxiliary aids. Adjustments needed in relation to test-taking must be
brought to the instructor's attention well in advance of the test (at least one
week prior).

Attendance Policy: You are expected to attend every class. Although absences
are not penalized, if a class is missed, you are responsible for all material
and assignments.

Academic Honesty: You are
expected to achieve and maintain the highest standards of academic honesty and
excellence as described in the Undergraduate Catalog. In short, be responsible
and do your own work.

** **