Math 7760 – Mathematical Foundations of Finite Element Method, Fall 2005

Jan Mandel

Department of Mathematics
University of Colorado at Denver

This web page http://www-math.cudenver.edu/~jmandel/classes/7760f05 serves as the class syllabus and source of further information. Homeworks, material covered, and handouts are in the class notes file. Photographs and scans will be in the photos directory.


  Please contact me if you are interested in this class and have any questions. Thanks for considering my class!

Important announcements will be put here during the semester. It is a good idea to check this space regularly before the class or before you want to come to my office.


Textbooks:

  1. William McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000 (The first few chapters about Sobolev spaces and PDEs will form the bulk of this course. We will not do anything about integral equations.)
  2. Claes Johnson, Numerical Solutions of Partial Differential Equations by the Finite Element Method, Cambridge University Press, 1988 (for applications to Finite Elements; out of print, the bookstore will make copies)
  3. A. N. Kolmogorov and S.V. Fomin: Elements of the Theory of Functions and Functional Analysis,  Dover 1999 (optional, for prerequisites)

Time and location:  Tuesday and Thursday 1-2:15 location UCD Building Room 641
Office hours: Tuesday 12-12:45 and Thursday 11-11:30 UCD building 640 
Contact: Phone 303-556-4475; email jmandel@math.cudenver.edu. I am usually pretty good at answering email even at strange hours.


Class objective

Gain understanding of the basic contemporary tools in the theory of partial differential equations, as they are needed in the mathematical analysis of the Finite Element methods, Multigrid methods, and Domain Decomposition methods.

Class approach

Theoretical, no programming.  Homeworks with hard problem solving and assigned independent reading. A good level of mathematical writing will be required. Some complicated proofs will be skipped, but students will need be able to expand arguments into tiny details on demand. Discussions with student participation.

Prerequisites

Material to be covered

See the class notes file for details. The file will be updated during the semester and contain also the material actually covered and homeworks.


Office Hours Policy

I enjoy discussing technical topics related to the class with my students during my office hours or any other time you walk in. However: Please do your homeworks ahead of time, and try not to come to my office on the day a long homework is due and expect me to do it for you.   Please do not try to negotiate grades (except in the case of clear error on my part) or partial credit.  I usually need few minutes before the class to get organized, so please respect  the end of the office hours and do not show up right before the class.

Assignments, Tests, and Grading

There will be some homeworks and in-class midterm and final. The homeworks will consist of more challenging problems that will require some independent work. The in-class exams will be concerned with the very basics. The midtem will be on October 20. The final will be on December 13. The final score will be determined by the sum of the best 2 out out of the following, each scaled separately from 0 to 50: 1. homeworks 2. midterm 3. final. The letter grades will be A >= 90,  A- >= 85, B+ >= 80, B >= 75, B- >=70,  C+ >= 65, C >= 60, C- >= 55, D+ >= 50, D >= 45, D- >= 40.

Fall 2005 Registration and Academic Deadlines

 

Consult the Academic Calendar for details on registration/payment deadlines at http://www.cudenver.edu/registrar.

Drops and incompletes: You have until October 31 to drop the course with only the instructor's (but not a Dean's) signature.

      The incomplete policy of the department and college is strictly enforced. Incompletes are given only in situations in which a student has: (1) Successfully completed 75 percent of the course (i.e is passing the course)(2) Special circumstances (verification may be required) that preclude the student from attending class and completing graded assignments, and (3) Made arrangements to complete missing assignments with the original instructor. A CLAS Course Completion agreement is required.

Responsibilities for CLAS Students


CLAS students must always have an accurate mailing and e-mail address. Please go to http://www.cudenver.edu/registrar to update.
Students are responsible for completing financial arrangements with financial aid, family, scholarships, etc.

 Fall 2005 Registration and Academic Deadlines

 
Important Dates:

Last updated 8/23/05