Math 01 -515-01 Engineering Applications of Analysis – Summer II
Dr Abdul Hassen, Robinson 229E, (856) 256-4500 Ext. 3888, hassen@rowan.edu
Office Hours: By appointment
Textbook: Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems, Richard Haberman, Prentice-Hall, 2003 (4th Edition). ISBN: 0130652431.
Prerequisites: Ordinary differential equations, vector calculus, linear algebra, Laplace transforms, knowledge of a computer algebra system (either Mathematica or MATLAB)
Course description: Students will learn various techniques for solving linear and nonlinear partial differential equations (PDEs) arising from physical and engineering applications; this includes both analytical and numerical methods. More specifically, students will learn the method of separation of variables for solving multi-dimensional problems, Fourier/Laplace transforms for solving infinite-domain problems, numerical methods (finite-difference, finite-element, Monte-Carlo), Green's functions, method of characteristics. Basic applications include a vibrating membrane (wave equation), heat flow along a metal plate (heat equation), steady-state fluid flow (Laplace's equation), traffic flow (shock waves), and water waves (solitons). Besides in-class work and homework, there will be a final assignment where students write an expository paper and give a seminar talk on an advanced topic related to PDEs.
You can find the lesson plan for the course here
Grading policy: Grading is based on three homework assignments (30%), student lecture (20%), a final exam (30%) and student expository paper and presentation (20%).
Letter Grade: A(-) 85 -100, B(-,+) 70 – 84, C(-,+) 60 – 69, D(-,+) 50- 59, F <49
Homework Policy: There will be three weekly homework assignments (posted on the WebCT course website). Each assignment will have a written component and a CAS component (see details below) and is due on the Thursday following the week that it was assigned. Here are instructions for handing in homework:
I. Written Component: List all exercises assigned on the front cover page of your written solution set. Circle those exercises that you wrote complete solutions for; if you wrote only a partial solution (e.g. you completed 2 out of 4 parts), then circle the exercise number and write the corresponding fraction that you completed next to it.
II. CAS Component: You can submit your programs via e-mail as attachment.
Be sure to properly format your file so that I can easily understand your subroutines, which must be programmed independently of each other for separate exercises. Since I will be running your subroutines in succession please be sure to clear variables between subroutines to avoid errors (I will NOT attempt to debug your subroutines). Also, please delete output images from your file to reduce its size before uploading and include your name and Rowan ID inside your file.
Student Lecture: Students in teams of 2 are required to lecture for half an hour in class period on certain sections of the material from the textbook as described in the student lecture assignment. Here are some guidelines for preparing your lecture:
1. You (as a team) are required to schedule a 20-minute meeting with me at least one day before your lecture to make sure that your group understands the material and to outline the format of your lecture. Please don’t forget to make this appointment.
2. Please divide your lecture into two ten-minute sessions with a 5-minute break in between. There will be a discussion following the lectures. I will let you decide on the format that you think best serves your objectives. However, all team members should participate in lecturing and be prepared to answer questions from the class.
3. Please make sure that you work out examples during your lecture.
4. Try to describe the main mathematical and physical ideas involved in your technique without having to get into technical details. I will be there to guide you through your lecture and to help answer questions so don't worry about the little details. You are encouraged to keep the lecture informal and to provide a written outline of any techniques discussed so that students can follow it when doing the homework.
5. You will receive a score based on the quality of your lecture and on the average class score from homework assigned that week.
Expository Paper and Student Presentation:
Students are required to write an expository paper and to give a 15-minute in-class presentation (e.g. PowerPoint) on an advanced topic involving PDEs. Topics must be pre-approved by the instructor. You are highly encouraged to select a topic stemming from your current research if it involves PDEs. You may also choose from the list of
Your talk should focus on the following aspects:
Your paper should focus on the following aspects:
Deadlines for Expository Paper and Student Presentation:
June 25: Team assignments completed.
July 8: Topic selection due.
July 15: Two-page outline of your topic is due.
July 22 and 23: Student expository paper presentation
July 23: Expository paper due.