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

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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 2nd-order linear PDEs

-To derive 2nd 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.