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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 or Instructor constent.
This class (MTH 622, 3 credits) is the second 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:
- Origins and applications of mathematical models of stationary and
equilibrium problems such as Laplace (potential) equation, and
continued study of (selected) transient models. Boundary value (and
initial value) problems for these equations.
- Properties of solutions, analytical expressions whenever
available, (some) separation of variables, Fourier techniques, Green's
functions, maximum principle(s); square-summable functions.
- Variational approaches, generalized functions, and weak
formulation of boundary value problems; distributional and weak
solutions; Euler-Lagrange formulation.
Course Learning Outcomes: A successful student will be able to
- Provide and justify statements on maximum principles, and on
well-posedness of diffusion equations and Laplace equation.
- Find closed-form solutions for selected boundary value problems (BVP)
and initial value problems for such equations.
- Carry out the derivation of weak and variational form of selected
BVP for the linear elliptic equations, and relate these to the
physical minimum principles.
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.
Exams and Grading: HW counts as 40% and Exams as 30%
each. Midterm in weeks four to six TBA, in class. Final Exam: TBA.
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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