Computational
Mathematics,
Department of Mathematical Sciences
Chalmers University of Technology
and
Göteborg University
Partial Differential Equations, 5 credit points
Graduate Course, period 3-4, 2005-06
Teacher:
Stig Larsson
Literature:
L. C. Evans,
Partial Differential Equations,
Graduate Studies in Mathematics 19, American Mathematical Society, 1998.
It can also be ordered from, for example,
Bokus or
Adlibris.
The purpose of the course is to introduce the student to the state of
the art of the modern theory of partial differential equations.
We will study chapters 1-7 (with some omissions), and some selected
topics from chapters 8-11.
Examination:
To pass the course you need x points earned on the following activities:
-
each good solution of a homework problem gives 1 point;
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written theory exam, max 10 points;
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student lecture, 5 points (more details will be given later).
More details will follow here later on.
Check your points
here.
Schedule: (with exceptions indicated in the plan below)
Lectures: Tuesday 13.15-15, room MV:L15
Exercises: Thursday 8.15-10, room MV:L14
Plan of the teaching: (to be completed as we go along)
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week 6 Feb 6-12
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Introductory meeting: Thursday February 9, 11.00, in my office MV:L2078.
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week 7 Feb 13-19
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Read: Ch 1, 2.1, 2.2. Take a quick look at Appendices A - E.
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Lecture: Ch 2.2 (Thursday 16/2 8.15-10, room MV:L14)
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week 8 Feb 20-26
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Read:
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Lecture: Ch 2.2 continued. (Tuesday 21/2 13-15, room MV:F32)
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Exercises: 1.3, 1.4, 2.2, 2.3.
[We did: 1.3 (Aron), 1.4 (Fardin), 2.2 (Mikael), 2.3 (Stig)]
Hand in: 2.4 (Thursday 23/2 8.15-10, room MV:L14)
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week 9 Feb 27-Mar 5
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No teaching. [ Going to the Univ of Florida, Tallahassee, :-) ]
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Read: Ch 2.3
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Exercises:
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week 10
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Read: Ch 2.3, 2.4.
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Tuesday March 7. Lecture cancelled.
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Thursday March 9. Lecture: Ch 2.3.
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week 11
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Tuesday March 14. Lecture: Ch 2.4 (2.4.1 a,b,c n=3 with proofs, the rest without proofs, 2.4.2 without proofs, 2.4.3 with proofs.)
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Thursday March 16. Exercises, we did: 2.5 (Fardin), 2.6 (Aron), 2.7 (Fardin),
2.8 (Marcus). Hand in: 2.13, 2.16
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week 12
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Tuesday lecture: 3.1, 3.2.
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Thursday exercises, we did: 2.9 (Mikael), 3.2 (Aron), 3.3a (Aron).
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week 13
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Skip 3.4. Read 3.4, Theorems 1,2,3 without proof, Theorem 4 with proof.
Skip 3.4.5.
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Tuesday lecture: 3.4, 5.1, 5.2
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Thursday exercises:
we did 3.13 (Mikael), 5.1 (Fardin), 5.2 (Aron),
5.4 (Mikael). Hand in: 5.3.
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week 14
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Read ch 5.
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Tuesday lecture: 5.3, 5.4, 5.6
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Thursday lecture: 5.6-5.7
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week 15
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No teaching this week.
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week 16
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Tuesday lecture: 6.1, 6.2
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Thursday exercises: we did 5.5 (Aron), 5.6 (Fardin), 5.7, 5.8 (Fredrik), 5.9. Hand in: 5.10
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week 17
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Tuesday lecture: 6.3
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Thursday exercises: hand in: 5.17
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week 18
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Tuesday lecture: 6.4
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Exercises, we did: 5.11, 5.12 (Mikael), 6.1 (Fredrik)
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week 19
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Tuesday lecture: 6.5
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Exercises, we did: 6.4, 6.6, 6.7, 6.8
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week 20
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Student lecture, Monday 8.30-10: Semigroups (Mikael).
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Tuesday lecture: Semigroups, continued (Mikael). 7.1
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Exercises:
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week 21
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Tuesday lecture: 7.1
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Thursday: holiday.
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week 22 May 29-June 3
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Tuesday lecture: 7.1 (skip proofs of Harnack and strong max principle)
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Thursday lecture: 7.2
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week 23
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Thursday June 8, 9-10, student lecture: Fredrik, 4.3 Transform methods
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Thursday June 8, 10-11, student lecture: Aron,
Sobolev spaces based on F-transform
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Thursday June 8, 11-12, student lecture: Fardin, 3.3 Hamilton-Jacobi
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Thursday June 8, 13-15, student lecture: Marcus,
7.3 First order hyperbolic systems
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Friday June 9, 8-10, oral exams Mikael, Aron
Introductory meeting:
Thursday February 9, 11.00, in my office MV:L2078.
Welcome!
/stig