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Instructor:
Malgorzata Peszynska
Class:
MWF 13:00-13:50 STAG 132
Course information:
CRN 32406 ( MTH 623 )
CRN 52340 ( MTH 657 ).
Credits: 3.00.
Student preparation: the students should have a solid
background in differential equations, senior level/ advanced calculus
and linear algebra. Most students will have taken 621-2 or a similar
course but it is possible for a student to enter 623 without 621-2
(please contact me in such a case or with any other questions).
Syllabus:
This class is the second one in a year-long sequence
MTH 621
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MTH 622
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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 (use MTH 657).
We will discuss the following topics:
- Introduction to hyperbolic conservation laws and applications. Weak solutions,
shocks and entropy conditions.
- Overview of hyperbolic systems: acoustics, crowd modeling, and gas dynamics.
- Wave equation in 2D/3D revisited.
- Special methods for PDEs: similarity
methods, (Cole-Hopf) transformation, asymptotic analysis and more.
- Models of physical phenomena beyond elementary diffusions and vibrations.
- (Time permitting:) Integral equations and integro-differential equations.
Viscoelasticity.
Textbook:
I will use material from the following textbook as well as
some downloadable notes TBA.
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R. Guenther and J. Lee, Partial Differential Equations of Mathematical Physics and Integral Equations, Dover, 1996
- Background and extensive examples on hyperbolic systems:
Leveque (Cambridge, 2002), Godlewski-Raviart (Springer, 1996)
- Fluid mechanics books: Rutherford Aris (Dover, 1989), Chorin,
Marsden (Springer, 2000)
Grading: project based.
Course Outcomes: A successful student will be able to
- Provide qualitiative analysis for solutions of
conservation laws and systems
- Derive various models important in mathematical physics
including those of fluid and solid mechanics
Special arrangements for students with disabilities,
make-up exams etc.: please contact the instructor and Services for Students with
Disabilities, if relevant, and provide appropriate
documentation.
Course drop/add information is at
http://oregonstate.edu/registrar/.
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