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Instructor:
Malgorzata Peszynska
(Contact information including office hours on webpage)
Class:
MWF 13:00-13:50 STAG 111
Prerequisites: MTH 621-2 or Instructor constent.
This class (MTH 623, 3 credits) is the third one
in a year-long sequence
MTH 621 -
MTH 622
-
MTH 623. In principle, each of these classes can be taken
separately but it is best if they are taken in order. May be repeated
for credit (you can also use MTH 657). The students should have a
solid background in differential equations and real variables. (Please
contact the instructor with questions.)
Course content: In the course we will cover the following topics organized in modules:
- I: Introduction to nonlinear hyperbolic conservation laws. Weak solutions, shocks and entropy
conditions.
- II: Solving systems of hyperobilc conservation laws arising in important physical models.
- III: Deriving and simplifying models of physical phenomena beyond
elementary diffusions and vibrations. Fluids, gas
dynamics, acoustics, traffic and crowd modeling,
phase transitions, and more.
- IV: Special methods for PDEs: asymptotic and
multiscale analysis, homogenization, similarity
methods, variational techniques.
- V: Integral and integro-differential equations, and
applications.
Course Learning Outcomes: A successful student will be able to
- Follow the principles for finding physically meaningful weak
solutions to selected nonlinear conservation laws and construct the
shock or rarefaction solutions to the associated Riemann problems
- Construct solutions for model examples of quasilinear hyperbolic systems
- Outline the physical principles behind general models for fluids
and solids and the rationale behind simplifications leading to the
Navier-Stokes, Bernoulli, Euler, Stefan, Darcy, Richards, Buckley-Leverett, and Langmuir equations.
- Construct solutions to problems requirung special techniques such as homogenization
- Analyze solvability of selected integral equations in the framework of linear operators
Textbook:
R. Guenther and J. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations, Dover, 1996.
We will also use additional notes and materials.
Grading: will be based on HW assignments and class worksheets assigned for each module.
Special arrangements for students with disabilities: please contact the instructor and Services for Students with
Disabilities prior to or during the first week of the term to discuss
accommodations. Students who believe they are eligible for
accommodations but who have not yet obtained approval through DAS
should contact DAS immediately at 737-4098.
Course drop/add information is at
http://oregonstate.edu/registrar/.
Student Conduct: All students are expected to obey to OSU's student
conduct regulations, see
OSU's Statement of Expectations for Student Conduct
at this link
http://studentlife.oregonstate.edu/sites/studentlife.oregonstate.edu/files/student_conduct_code_1.pdf,
and specifically the information about Academic or Scholarly
Dishonesty beginning on p.2. In particular, please consult the
definitions of (A) CHEATING, (C) ASSISTING, and (E) PLAGIARISM, as
well as recommended handling.
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