SYLLABUS

Math 01 -515-01 Engineering Applications of Analysis – Summer I 2015

Dr Abdul Hassen, Robinson 229E, (856) 256-4500 Ext. 3888, hassen@rowan.edu

Office Hours: By appointment

Textbook: Richard Heberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Fifth Edition, ISBN 9780321797056

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.

 

Grading policy: Grading is based on three homework assignments (30%), midterm exam (20%), a final exam (20%) and student expository paper and presentation (30%).

 

Dates of Exam

Midterm Exam: June 11

Final Exam: June 25

Letter Grade: A(-) 90 -100, B(-,+) 80 – 89, C(-,+) 65 – 79, D(-,+) 50- 59, F <50

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.

II.                 CAS Component: You can submit your programs via e-mail as attachment.  

 Deadlines for Homework Submision:

June 4: Homework I
June 11: Homework II  
June 25: Homework III

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.   

Your talk should focus on the following aspects:

• Short explanation of mathematical model used and its validity based on physical/engineering assumptions.
• Short explanation of both numerical and analytical solutions (if available) and their validity/feasibility based on physical/engineering expectations.  This is best achieved by running through an explicit example.
• Current research status of your topic and its applications.

Your paper should focus on the following aspects:

• In-depth explanation and derivation of mathematical model used and its validity based on physical/engineering assumptions.
• In-depth explanation of both numerical and analytical solutions (if available) and their validity/feasibility based on physical/engineering expectations.  This is best achieved by running through an explicit example.
• Current research status of your topic and its applications, including a broad list of current references to peer-reviewed journal articles

Deadlines for Expository Paper and Student Presentation:

June 4: Topic selection due.
June 11: Two-page outline of your topic is due.
June 24 and 25: Student expository paper presentation

June 25: Expository paper due.