Welcome to the course tma372/MMG800.
Except this introduction all material should be consided as preliminary and subject to some minor alternation.
This is a first course
on partial differential equations PDEs intended for students following
math and computation oriented studies in master
programs at Chalmers and the University of Gothenburg,
the International Mathematics Master Program, students in
"Teknisk Matematik"(=TM),
E3 students
at Chalmers, as well as PhD students in computational/applied math and
applied sciences and engineering.
Students from other disciplines who are not
following these programs are welcome to register for the course
and encouraged to contact the instructor
to get an approproaite follow-up scheme, if necessary.
Contents: The course covers topics as:
Approximating solutions to various PDEs (ODEs)
using the Finite Element Method, Polynomial Interpolation, Quadrature rules,
and the
solution of large, sparse linear system of equations. Stability and
convergence analysis, error estimates
in a priori and a posteriori settings.
Reisz representation and Lax-Milgram theorems,
Application of finite element methods to problems of dynamical systems,
heat conduction, wave
propagation, convection-diffusion-reaction, etc.
Compulsary home assignments contain both analytic approaches as well as
coding aspects, ranging from iterative
algorithms to problems involving complex multiphysics programing.
Following the course, actively,
you should gain some modeling skills relevant to
the PDE of your own field of interest,
knowledge on weak/variational formulation, and a great deal of
finite element analysis consisting of both theoretical aspects as
stability and convergence of approximate solutions, as well as
numerical analysis and implementations.
The course consists of 36 lecture hours,
20 exercise hours and gives 7.5 points.
The course code is for engineering schools (students registered at Chalmers):
tma372, and for students registered in GU: MMG800.
See also course description:
course description/PM.
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For all current and most recent information please check the
The schedule for the course can be found via the link to
webTimeEdit top of the page.
Below is the concise schedule:
You may work in a group of 2 persons but hand in only one report for the group.
Assignment 1:
See the
file.
For this assignment write a short yet detailed report,
not exceeding ten pages, explaning your work and sumbit it by the end of
study week 4 (Deadline: Friday February 14) . Use MATLAB
to do the coding parts.
Hints:
For problem 1 you need to read chapter 5, but not
chapter 4. In problem 2 consider only the case a=4.
A good
starting point for problem 3 might be the
Matlab code,
which solves -u''=f,
u(0)=u(1)=0 using cG(1).
If you don't have access to FEM-LAB, then
you may skip FEM-LAB comparisons.
Assignment 2:
Can be found
here.
You may use, e.g. COMSOL Multiphysics (or other computational code/environment)
instead of PDE TOLBOX. Hand in report of your work beginning of study week 7
(Deadline: Monday March 3).
To pass this course you should pass the written exam and the assignments 1 and 2.
The two compulsory home assignments should be handed in before the final exam generating max 5 (2+3) bonus points.
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- Written examination
- Final exam is compulsory, written, and consists of 5 questions (4 problems + 1 theorm)
with a maximum score of 30 (=6x5) points.
- The theory question is choosen from a list that will appear in
(see sample exam questions in the course diary).
- As for the proof of Lax-Milgram theotrm,
you may use the proof in lecture notes on web-site,
pp 229-231.
- No aids are allowed.
- You should be able to state and explain all definitions and theorems given in the course
and also apply them in problem solving.
- Grades are set according to the table below.
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| Grades Chalmers |
Points |
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Grades GU |
Points |
- |
<15 |
|
- |
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| 3 |
15-20 |
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G |
15-27 |
| 4 |
21-27 |
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VG |
>28 |
| 5 |
>28 |
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The exam takes place at ..
Bring ID and receipt for your student union fee
Solutions to the exam will be published in the course diary.
You will be notified the result of your exam by email from LADOK
(This is done automatically as soon as the exams have been marked an the results
are registered.)
The exams will then be kept at the students' office in the Mathematical
Sciences building.
Check that the number of points and your grade given on the exam and registered in
LADOK coincide.
Complaints of the marking should be written and handed in at the office. There is a
form you can use, ask the person in the office.).
The following link will tell you all about the examination room rules
at Chalmers: Examination room instructions
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In
Chalmers Student Portal you can read about when exams are
given and what rules apply on exams at Chalmers.
At the link
Scedule
you can find when exams are given for courses at University of
Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to
take the examination. If you study at Chalmers, you will do this
by the
Chalmers Student Portal, and if you study at University of
Gothenburg, so sign up via
GU's
Student Portal.
You can see your results in Ladok by logging on to the Student
portal.
At the annual examination:
When it is practical a separate review is arranged. The date of
the review will be announced here on the course website. Anyone
who can not participate in the review may thereafter retrieve and
review their exam on Mathematical sciences study expedition,
Monday through Friday, from 9:00 to 13:00. Check that you have the
right grades and score. Any complaints about the marking must be
submitted in writing at the office, where there is a form to fill
out.
At re-examination:
Exams are reviewed and picked up at the Mathematical sciences
study expedition, Monday through Friday, from 9:00 to 13:00. Any
complaints about the marking must be submitted in writing at the
office, where there is a form to fill out.
Old exams are posted in
the
course diary.