Math 272: Introduction to PDE's
Fall 2015

Instructor 
Gautam Iyer.
WEH 6121.
gi1242+272@cmu.edu.

Lectures 
MWF 2:303:20 in
PH A18A.

Office Hours 
Wed 11:3012:20

HW presentations 
Fridays, 4:30 in WEH 7201 
Midterm 1 
Fri, Oct 2 (in class) 
Midterm 2 
Fri, Nov 6 (in class) 
Final 
Mon, Dec 14, 8:30AM11:30AM (WEH 5302) 
Mailing list 
math272
(for course announcements and discussion.
Please subscribe to this list.)


Course Description
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).
Tentative Syllabus
 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.
Prerequisites
Before taking this course you should have a good knowledge of ODE’s and multivariable calculus.
Few courses that cover these in sufficient detail are:
 ODE’s: 33232, 21260 or 21261.
 Multivariable calculus: 21259, 21268 or 21269.
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.
References
 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.
Class Policies
Lectures
 If you must sleep, don’t snore!
 Be courteous when you use mobile devices.
Homework
 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.
Exams
 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
here.
Be aware of their schedule before making your travel plans.
Grading
 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.)