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 **Blackboard
** 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.