Math 272: Introduction to PDE's
MWF 2:30-3:20 in
||Fridays, 4:30 in WEH 7201
||Fri, Oct 2 (in class)
||Fri, Nov 6 (in class)
||Mon, Dec 14, 8:30AM-11:30AM (WEH 5302)
(for course announcements and discussion.
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A Partial Differential Equation (PDE for short), is a differential equation
involving derivatives with respect to more than one variable. These arise in
numerous applications from various disciplines. A prototypical example is the
heat equation, governing the evolution of temperature in a conductor.
This course will serve as a first introduction to PDE’s, and will focus on the
simplest model equations that arise in real life. It will study both
analytical methods (e.g. separation of variables, Greens functions), numerical
methods (e.g. finite elements) and the use of a computer to compute and
visualize solutions. Time permitting, it will touch upon the mathematical
ideas behind phenomenon observed in real life (e.g. speed of wave propagation,
and or shocks in traffic flow).
- Physical motivation of PDE’s
- Transport, heat, wave and Laplace equations.
- Initial data, boundary conditions and classification of PDE’s.
- Separation of variables and Fourier series.
- Heat, wave and Laplace equations.
- Numerics and computation.
- Ideas behind finite differences and finite elements.
- Using software to compute (e.g. MATLAB)
- Newton potentials and Greens functions.
- Computation in standard domains.
- Harmonic functions: Maximum principle and mean value property.
- Heat kernel.
- Wave equation and finite speed of propagation.
- Burgers equation, characteristics and traffic flow.
Before taking this course you should have a good knowledge of ODE’s and multi-variable calculus.
Few courses that cover these in sufficient detail are:
- ODE’s: 33-232, 21-260 or 21-261.
- Multi-variable calculus: 21-259, 21-268 or 21-269.
It isn’t imperative you have taken these courses; but it is imperative that you have a good understanding of the material in these courses.
- 372 Lecture Notes Wiki
- Introduction to Partial Differential Equations with MATLAB Corrected Edition
by Jeffery M. Cooper.
- Numerical Analysis of Partial Differential Equations by Charles A. Hall and Thomas A. Porsching.
- An Introduction to Partial Differential Equations 1st Edition
by Yehuda Pinchover, Jacob Rubinstein.
- Introduction to PDE by Walter Strauss.
- If you must sleep, don’t snore!
- Be courteous when you use mobile devices.
- Homework solutions will be presented by students every week.
- You may work together on the homework, and coordinate amongst yourselves regarding who presents what solution. The presentation itself will not count towards your grade.
- 50% of your exams will consist of homework questions, so it is in your best interest to understand solutions to all questions.
- All exams are closed book, in class.
- No calculators, computational aids, or internet enabled devices are allowed.
- The final time will be announced by the registrar
Be aware of their schedule before making your travel plans.
- Between 25% and 50% of your exams will consist of homework questions.
- Your better midterm will count as 30% of your grade.
(Your worse midterm will not count at all.)
- Your final will count as 50% of your grade.
- Projects will count as 20% of your grade. (If, we do not cover enough
material in time to successfully complete projects, then your midterm and
final percentages will be scaled up appropriately.)