SYLLABUS

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.

Grading policy: Grading is based on three homework assignments (40%), midterm and final exams (30%) and student expository paper and presentation (30%).

Letter Grade: A(-) 90 -100, B(-,+) 80 – 89, C(-,+) 70 – 79, D(-,+) 60- 69, F <60

Homework Policy: There will be three homework assignments (posted on the  course website).

Expository Paper and 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:

• 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 5: Topic selection due.

·       June 14: Two-page outline of your topic is due. You cannot present your work unless you submit the outline.

·       June 19 to 20: Student expository paper presentation

·       June 20: Expository paper due.