Math 511-1 Fall 2001
Numerical Methods for Partial Differential Equations
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News items will be posted here as required. Please check
back frequently.
Files for lab: Galerkin methods: file 1, file
2
Here's Test 2: pdf
, postscript.
High-Order Compact Scheme paper:
(username/password required due to copyrighted content)
Project 3: pdf file
Test 2 will be posted on Wednesday, Nov 7, 2001.
File for lab: explicit convection diffusion equation (maple)
Project 2: pdf file
Files for lab: one way wave (maple)
Test I: pdf
, postscript.
Files for lab: runge example (maple),
1 D heat problem (matlab).
 .
Course Info
 Textbooks
:
- Computational
Differential Equations, K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Cambridge University
Press, 1996.
- Numerical Solution of Partial Differential Equations, K W
Morton and D F Mayers, CUP, 1993.
References:
- Numerical Analysis of Differential Equations, A. Iserles, Cambridge
University Press, 1996.
- Numerical Partial Differential Equations, J.W. Thomas, Springer,1995.
Pre-requisite:
Pre-requisite: Math 311
(Introduction to Numerical Methods),
Math 343 (Elementary
Linear Algebra), Math 213
(Advanced Engineering
Mathematics) or Math
347 (Introduction to Partial Differential Equations); or equivalent. Computer literacy is
expected. Good programming skill desired. Strong undergraduate
linear algebra background preferred.
Course Objective:
To familiarize the students with the fundamental concepts in numerical solution
of partial differential equations and to enable them to apply materials learned in the course to compute
the solutions related to application problems efficiently and to assess the quality of
the solutions.
Syllabus:
Finite element and finite difference methods for elliptic problems, parabolic and
hyperbolic problems. Stability, consistency, and convergence theory.
Convection dominated flows and finite volume method will only be discussed briefly.
Covering chapters 5, 6-9, 12, 14-16, 21 of Computational Differential
Equations and topics from finite difference method.
Fall 2001
Syllabus
Homework:
Homework will not be collected. Students are expected to work on all the
homework problems. Occasionally, students will be asked to present
homework solutions in class.
Reminder: assigned homework is representative of the minimal
set of problems that you should attempt. In general you should also
work on as many unassigned problems as possible.
Collaborative discussion is encouraged when completing homework
and project assignments. However, plagiarism is not acceptable
(see Honor
Code.)
Tests:
Two mid-term tests are currently scheduled. Made up test may not be arranged except in case of emergency
or absence due to official university business. If you want to attend
special events, e.g., your sister's wedding or your nephew's baptism, you
may arrange to take the test up to a week prior
to but not after the set test date.
Projects:
Five class projects, including a final project, will be assigned. Projects
that are submitted a week beyond the due date will not accepted. Further information will be provided
in class.
- One dimensional reaction-diffusion equation: explicit method. Due Sept 21,
2001.
- Reaction-diffusion equation: implicit methods and linear solvers.
Due Oct 10, 2001
- ADI methods on L-shaped domain. Due Oct 24, 2001.
- Steady and unsteady Burgers' equation. Due Nov 14, 2001.
- (Final project) Topic will be selected by students with consent of
instructor. Topic proposal submission by Nov 12, 2001. Project
report due Dec 12, 2001.
Final:
The final is scheduled on Wednesday, December 19, 2001, 2:30 p.m. to
5:30 p.m.
Course Grade:
Course grade will be calculated from the following distribution
| Class Projects (4)
|
30 % |
| Final Project |
20 % |
| Test (2) |
30% |
| Final |
20% |
| Total score (max 100) |
95-100 |
90-94 |
87-89 |
83-86 |
80-82 |
77-79 |
73-76 |
70-72 |
67-69 |
63-66 |
60-62 |
<60 |
| Course Grade |
A |
A- |
B+ |
B |
B- |
C+ |
C |
C- |
D+ |
D |
D- |
E |
Please keep track of your homework, quizzes, and examination scores
so that you will be able to determine your grade during the course. Grades
will not be posted at the end
of the semester.
Resources
Numerical Analysis
Resources (under construction)
Related links
Math Archives: Partial
Differential Equations, Numerical
Analysis, Linear
and Matrix Algebra.
The Mathematical Atlas: Partial
Differential Equations, Numerical
Linear Algebra
Computational Science Education Project:
Differential
Equations (e-Lecture). Postscripts files of webpages are also available.
(Some of the links seem to be broken, please contact me if you want more
details.) Conjugate
gradient Note (in pdf): An Introduction to the Conjugate Gradient
Method Without the Agonizing Pain by J. R. Shewchuk
Miscellaneous
Preventing Sexual Harassment
Title IX of the Education Amendments of 1972 prohibits
sex discrimination against any participant in an education program or activity
that receives federal funds. The act is intended
to eliminate sex discrimination in education. Title IX covers discrimination
in programs, admissions, activities, and student-to-student sexual harassment.
BYU's policy against sexual harassment extends not only to employees of
the university but to students as well. If you encounter unlawful sexual
harassment or gender based discrimination, please talk to your professor;
contact the campus Equal Employment Office
at 378-5895 or 367-5689 (24-hours); or contact the Honor Code
Office at 378-2847.
Students with Disabilities
Brigham Young University is committed to
providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. If you have any disability, which may impair your ability
to complete this course successfully, please contact the Services
for Students with Disabilities (SSD) Office at 378-2767. Please
also inform the instructor about your situation during
the first week of class. Reasonable academic accommodations are reviewed for all
students who have qualified documented disabilities. Services are coordinated
with the students and the instructor in consultation by the SSD Office.
If you need assistance or if you feel you have been unlawfully discriminated
against on the basis of disability, you may seek resolution through established
grievance policy and procedures. You should contact the Equal
Employment Office at 378-5895, D-282 ASB.
Dress and Grooming Standards
The dress and grooming of both men and women should
always be modest, neat, and clean, consistent with the dignity adherent
to representing The Church of Jesus Christ of Latter-day Saints and
any of its institutions of higher learning. Modesty and cleanliness are
important values that reflect personal dignity and integrity, through which
students, staff, and faculty of BYU represent the principles and standards
of the Church.
Honor Code
As a reminder, students are expect to adhere to the Honor
Code. In particular, academic dishonesty will not be tolerated. |
