Math 400 Applied Partial Differential Equations Section 201, Spring term 2012

Instructor: Dong Li
Time: 09:30 - 11:00 TTh
Location: Mathematics Annex 1100

Email: dli at math.ubc.ca (Please put MATH 400 in the subject line)

Announcements

Two examples on heat here
Two problems on Burgers here and the solution here
Morgan note Final review

Office Hours

MATH 111
Monday 16:00-17:00 Thursday 17:00-18:00 (Office hours begins on Jan 10th)

Books

R. Haberman. Elementary Applied PDE, Prentice Hall.(OPTIONAL TEXT)
S.J. Farlow. PDE's for Scientists and Engineers, Dover.
E. Zauderer, Partial Differential Equations of Applied Mathematics, Wiley.
J.Kevorkian, Partial Differential Equations, Springer.

Course Notes can be found here

Course Outline

Review of solution by separation of variables
Linear and quasi-linear first order equations
Shocks and applications to traffic flow
Classification and how to nondimensionalize equations
Eigenfunction expansions and Sturm-Liouville theory
Parabolic, elliptic and hyperbolic equations
Solution by integral transforms

Midterms and Final

Midterm 1: Feb. 9 in class
Midterm 2: Mar. 15 in class
Final: TBD

Grading

Homework: 15%
Midterms: 40% (20% each)
Final: 45%

Homework Policies

Homework will generally be due one week after it is assigned. All assignments will be posted on this website and I will let you know in class when a new assignment is posted.
All homework must be turned in by the beginning of class on the due date. NO LATE HW WILL BE ACCEPTED UNDER ANY CIRCUMSTANCES. Homework can be turned in at class or my office hours. Also, scanned and e-mailed homework will not be accepted. For each assignment, selected problems will be graded thoroughly (usually on a 3, 4, or 5 point scale depending on the complexity of the problem) and the rest will be graded as either attempted or not attempted (for 0 or 1 point). Solutions for ALL assigned problems will be posted. In most cases, homework will be returned within 1 week of its due date.

Begin early. The best time may be shortly following the lecture while the material is still fresh in your mind. This is your time to determine if you understand the concepts. If not, look at the course notes. If that does not help, come see me in office hours. It is also useful to work with your classmates in order to share ideas and compare results. The work you submit however should be your own.

Keep your work organized and legible. A correct final answer is NOT sufficient to receive full credit on a graded problem. All work must be shown in a CLEAR and NEAT fashion. Problems which are not legible will NOT be graded!

The following policies must be followed on each and every homework assignment.

Full name written legibly at the top of the first page.
All pages are STAPLED together at the top left corner. A paper clip does not count, they easily come off and can bind your assignment to others in the stack. I will not have a stapler with me in class, so come prepared!
Write only on ONE SIDE of each page turned in. Paper tends to be see through, and writing on both sides makes it harder to read.

Assigned Homework (please alert me if you find any errors or typos)

Assignment 1 (Due Jan 17th in class) can be found: here and solution here
Assignment 2 (Due Jan 24th in class) can be found: here and solution here
Assignment 3 (Due Jan 31th in class) can be found: here and solution here
Assignment 4 (Due Feb 16th in class) can be found: here and solution here

Midterm 1 solution can be found here
Assignment 5 (Due Feb 28th in class) can be found: here and solution here
Assignment 6(Due Mar 6th in class) can be found: here and solution here
Midterm 2 solution can be found here
Assignment 7(Due Mar 29th in class) can be found: here solution here

In-class live notes (Thanks to Morgan McLean for making these wonderful notes):

Jan 17: Summary and Boundary conditions

Jan 19: Separation of variables and Inhomogeneous

Jan 24 (use with Caution! Not proofread yet!) : Inhomogeneous and Wave

Jan 31st (use with Caution! Not proofread yet!): Inhomogeneous wave and Laplace in a disk

Mid-term review here

Feb 7th Sturm Liouville

Feb 14th continued and Finding Lambda and Nonuniform String

Feb 16th the WKB method

Feb 28th Method of Characteristics

Feb 28th Method of Characteristic: Continue and Traffic flow and Burgers equation

Mar 6th Shock dynamics

Mar 8th Rarefaction wave and Two problems on Burgers and the solution here

Mar 13th Fourier Transform, Intro

Mar 22 and 24 part 1 and part 2 and part 3

Mar 27 Applied to PDEs and heat equation

Mar 29 part 1 and part 2

Other Important Notes

There are no make-up midterms but if you miss a midterm for a legitimate reason (e.g. illness, with a doctor's note), allowances will be made.
All marks are subject to scaling. This ensures fairness of the final grades.