Math 656, Partial Differential Equations II
Spring
2006@ISU
-
Instructor: Hailiang
Liu
-
Lectures: TR 12:40PM -2:00PM, Carver 0068, 01/09/06--05/05/06
- Course Description: This course is intended to give
the student a basic and classical introduction to the subject,
first order equations and systems,
conservation laws, general theory of linear partial differential
equations of elliptic, parabolic and hyperbolic types, maximum
principles, fundamental solutions, Sobolev spaces, variational
and Hilbert space methods.
- Topics to be covered in Math 655 & 656
- Four important linear PDE --- transport equation, Laplace's
equation, heat equation and wave equation ...
- Nonlinear first-order PDE --- characteristic method,
hyperbolic conservation laws, Hamilton-Jacobi equations ...
- An account of various ways to represent solutions --- separation of
variables, transform, asymptotic method, power series, ...
- Theory for linear PDE: Sobolev spaces, 2nd order elliptic equations,
linear evolution equations...
- The calculus of variations ---Euler-Lagrangian, minimizer, regularity,
constraints ...
- An account of various non-variational techniques--- fixed point method,
blow up, gradient flows ...
- Hamilton-Jacobi equations --- viscosity solutions, Hopf-Lax formula ...
- Systems of conservation laws --- Riemann's problem, shock waves,
entropy ...
- Official Catalog Entry (Math 655):
(3-0)
Cr. 3. Alt. F., offered 2005. Prereq: 515 or 519.
First semester of full-year course. First order equations and systems,
conservation laws, general theory of linear partial differential equations
of elliptic, parabolic and hyperbolic types, maximum principles, fundamental
solutions, Sobolev spaces, variational and Hilbert space methods.
(Math 656). Partial Differential Equations II. (3-0) Cr. 3.
Alt. S., offered 2006. Prereq: 655. Continuation of 655.-
Text: Lecture notes + Lawrence
C. Evans, Paritial Differential Equations, AMS 2000.
- Other References:
--- Paritla Differential Equations, Springer-Verlag
1982 (fourth edition).
by Fritz John
--- Paritla Differential Equations --Methods and Applications,
Prentice Hall (1996).
by Robert McOwen
Assignments will be made by topic;
Click here
to get an up-to-date list of homework assignments.
Prior announcement will be made if certain assignment needs to be
collected for grading.
Homework assignments consist of theoretical, and
sometimes computational, work.
Examinations: There will be an
in-class midterm and
one take-home final project. Exam problems will be
similar to homework assignments.
I will clarify a few days ahead of time what topics will be covered on each
exam.
Grading Policy: Homework: 30% + Midterm:
30% + Final: 40%.
An appropriate scaling may be applied at the end of the semester to
determine the final grade.
Disability Resources
Iowa State University complies with the American with Disabilities Act and
Section 504 of the Rehabilitation Act. If you have a disability and require
accommodations, please contact the instructor early in the semester so that your
learning needs may be appropriately met. You should contact the Disability
Resources office for information on appropriate policies and procedures. The
Disability Resources office is located on the main floor of the Student Services
Building, Room 1076; their phone is 515-294-6624.