MATH 817     Introduction to Numerical Methods for Partial Differential Equations

Fall 2010

Syllabus


www.math.udel.edu/~fjsayas/math817.html

Lecture times: MW 3:30pm to 4:45pm, at McDowell Hall 101
Instructor: Francisco-Javier Sayas. 532 Ewing Hall. fjsayas (at) math.udel.edu
Office hours: Tuesday from 8am to 11am or By Appointment (e-mail appointment). You are encouraged to use the office hours for personal or group discussion with your instructor. Do not hesitate to ask for appointments for office hours if you cannot make it on Tuesdays or you have an urgent question.
Textbook: Stig Larsson & Vidar Thomee. Partial Differential Equations with Numerical Methods. Springer Texts in Applied Mathematics 45. We will cover most of the book. The problem sections will be used for homework and quizzes.
Course description: Finite difference and finite element methods for elliptic, parabolic and hyperbolic partial differential equations. We will explore basic notions on stability, convergence and accuracy of different numerical discretizations for these three classes of PDEs. We will also discuss implementation aspects of the methods and will deal with practical issues (data structures, modularity) leading to efficient programming of the discrete schemes. In the last two weeks we will discuss other numerical methods.
Evaluation: The final grade will be composed of quizzes, homework assignments (mainly focused in programming) and two longer projects as shown in the following table. For points related to attendance to lectures, see attendance policy below. There will be no makeup quizzes and all assignments have to be delivered on the due date. No late assignments will be accepted. Quizzes will be open book. (You are allowed to bring the book plus a reasonable amount of hand-written materials, but no photocopies from other person's materials.)

In-class quizzes
 200
 Best four grades out of 5 or 6 quizzes (50 points each)
Homework assignments
 200
 Best four grades out of 5 homework assignments (50 points each)
Project #1
 300
 (Due October 29)
Project #2
 300
 (Due December 1)
TOTAL
 1000
                                                                                                             

Check the continuously updated calendar at the main website of the course for concrete dates of quizzes and due dates of assignments.
What will be evaluated: In Mathematically oriented tasks, part of the grade will reflect the quality of the argumentation and the clarity of its exposition. Solutions limited to formulas spread over the page will get less credit than solutions that are explained (use the book as an example of how to write). In programming tasks, you will be asked to render every piece of code that you have produced (even those used to create graphs and tables). Code has to be indented (non-indented code will be considered wrong and not even evaluated). Credit will be given to the adequate use of data structures, functions, to correct prototyping of functions and to good comments. Low level programming (for example, going element by element on a vector when you can use array operations) will be penalized. Part of the emphasis in programming tasks will be that you get to write clear, readable and efficient programs, even for very menial problems.
Attendance policy: Attendance to the lectures is obligatory. Attendance will be checked on random dates. Unexcused absence in two or more of these checked dates will be penalized with -40 points in the final grade.
Academic honesty: As worded by the University of Delaware All students must be honest and forthright in their academic studies. To falsify the results of one's research, to steal the words or ideas of another, to cheat on an assignment, or to allow or assist another to commit these acts corrupts the educational process. Students are expected to do their own work and neither give nor receive unauthorized assistance. Any violation of this standard must be reported to the Office of Student Conduct.  For more details, check http://www.udel.edu/stuguide/09-10/code.html#honesty Unless you are asked to do so in a concrete assignment, you cannot colaborate with your colleagues in assignments and projects. In particular, you cannot pick pieces of code from internet sites or classmates. Cheating of any kind (even if the student does not take any advantage from it) will be grounds for an F grade.