This web page serves as the class syllabus and source of further information.

Instructor: Dr. Son-Young Yi

Office: Bell Hall 218

Email:syi@utep.edu

Phone: 915-747-6864

Time and Place: MW 15:00 ~16:20 LART 210

Textbook: Computational Partial Differential Equations Using MATLAB® , by Jichun Li and Yi-Tung Chen

Office hours: MW 13:30 ~ 14:20 or by appointments

Syllabus: For a printable syllabus, click here.

Other references:

• "Finite Difference Methods for Ordinary and Partial Differential Equations-Steady State and Time Dependent Problems", SIAM 2007, by Randall J. LeVeque.

• "Partial Differential Equations with Numerical Methods" by Stig Larsson and Vidar Thomee

Course description: Many important problems arising in science or engineering are described by partial differential equations. In most cases, these PDEs cannot be solved analytically and one must resort to approximating the solution numerically. In this course, we will focus on the most important and widely used numerical methods, namely finite difference methods and finite element methods. We will discuss the issues such as convergence, stability and error analysis. We will also discuss how to implement and test the methods.

Homework: Homework assignments will be collected approximately every three weeks. Assignments will be posted on this website and announced in class as well. Homework problems will be both theoretical and programming problems. No late homework will be accepted. Computer programming problems must be done in MATLAB. You should turn in a complete printout of the program and of the output along with detailed explanation of solutions.

• HW1:

  • M-files needed for HW1: example1.m, fdcoeffF.m, fdstencil.m, bvp_2.m, bvp_4.m, xgrid.m, error_loglog.m, ,error_table.m

• HW2: Homework is due on Monday, March 8.

All problems are from the text book.

• 4.7 excercises: #2, 3, 8

• 2.7 excercises: #3, 4, 8

• HW3: due on Monday, April 26.

• 7.8 exercises:#1, 2, 6, 8

 

Final Project: In addition to the homework assignments, students will work on a final project on a topic of their own choice, preferably related to their research.

• Project proposal: Submit a written project proposal electronically to the instructor at syi@utep.edu by Monday, Feb. 8 with the following information:

  • Project title, background, mathematical description of your problem (equations, domain), and your goal.

• Final report: Submit your final project report electronically to the instructor by Friday, April 30. Your report should be written in a format of a journal article. Choose a journal in your research area and download their latex template. You should include the following sections:

  • Introduction: background on the problem and relevance with respect to previous work done on the subject.

  • Govering Equations

  • Numerical Discretization

  • Results: stability, convergence study, figures/tables, etc.

  • Conclusion

• Presentation: Give a short presentation on your project during the last week of the semester (week of May 3).

Exams: There will be no exam.

Grading: Homework(50%), Final Project(50%)

MATLAB: MATLAB is an interactive environment for numerically manipulating arrays and matrices, as well as providing tools for visualizing data. The following are online resources for learning MATLAB.

1. MATLAB Tutorial from the MathWorks

2. An Introductory Guide to MATLAB, by Ian Cavers

3. MATLAB Basics from MIT

4. Tutorial from Boston University

You can access MATLAB in any of the following ways

1. ACES Academic Centers for Engineer and Scientists: Bell Hall 130, Physics 2nd floor lobby

2. ETC: Engineering Technology Center: Classroom building 401/402

3. Use Remote Desktop Connection (server: utepsoftware.utep.edu).

 

Lecture materials:

• Jan. 25: example1.m, fdcoeffF.m

Help: If you need any help, seek it sooner rather than later!