AMATH 353
SLN 10199, MWF 2:30-3:20, Loew Hall 106
Syllabus
- (1) Introduction and Classification:
Overview of the major PDE's of Mathematical and
Theoretical Physics: Navier-Stokes equations,
Schroedinger equation, Maxwell's equations.
Classification of second order PDE's. Solving PDE's with
methods arising in ODE's
- (2) Parabolic Equations: Overview of general methods for solving PDE's applied to the simple case of diffusion/heat and related equations: Separation of variables, Eigenfunction Expansions, Fourier Transforms and some special methods such as similarity. Mainly 1-D.
- (3) Hyperbolic Equations: D'Alembert solution, for the 1-D wave equation. Higher order equations, separation of variables, characteristics.
- (4) Elliptic Equations: Laplace, Poisson equations. Mainly 1-D separation of variables.
- (5) PDEs in several variables: Diffusion, Wave, Laplace, Helmholtz equations. Separation of variables and Fourier Transforms.
- (6) PDE's in curvilinear coordinates: Separation of variables in plane polar, Cylindrical, Spherical coordinates. Legendre and Bessel Functions.
- (7) Non-homogeneous PDE's: Method of Eigenfunction expansions. Method of Green's functions.
- (8) First Order PDE's: Linear and Quasi-linear. The method of characteristics. Shocks, fans. Systems of 1st order PDE's. Euler equations of compressible flow and other models of wave propagation.
- (9) Advanced methods: The Legendre transformation, Charpit and others (Courant and Hilbert Vol II)
- (2) Parabolic Equations: Overview of general methods for solving PDE's applied to the simple case of diffusion/heat and related equations: Separation of variables, Eigenfunction Expansions, Fourier Transforms and some special methods such as similarity. Mainly 1-D.
Learning Objectives and Instructor Expectations
Become familiar with basic methods for solving linear pde's. Understand the geometrical meaning of the solutions.
Schedule and Homework
Homework Format There will be approximately 10 homework assignments. Some but not all problems will be graded. You may discuss and compare your results with other students in the class but you should provide your own answers. Effective Oct 26, no late homeworks will be accepted .
Follow links in the table below to obtain a copy of the homework in
PostScript (.ps) or 
Adobe
Acrobat (.pdf) format. You may also obtain here solutions to some of the
homework and exam problems. An item shown below in plain text is not yet
available. For additional information regarding viewing and printing the
homework and solution sets,
click here.
| Homework and Exams | Homework Due Date | Homework Problem Sets | Homework Solutions | |
| First day of classes | Wednesday, September 26 | |||
| Thursday, September 27 | Exta lecture | 16:00-18:00 | Lowe 102 | |
| Homework#1 | due Friday, 9/28 | Homework #1 (.pdf) | HW #1 Solutions ( .pdf) | |
| Homework#2 | due Friday, 10/5 | Homework #2 (.pdf) | HW #2 Solutions ( .pdf) | |
| Homework#3 | due Friday, 10/12 | Homework #3 (.pdf) | HW #3 Solutions (.pdf) | |
| Homework#4 | due Friday, 10/19 | Homework #4 (.pdf) | HW #4 Solutions ( .pdf) | |
| Homework#5 | due Friday, 10/26 | Homework #5 (.pdf) | HW #5 Solutions ( .pdf) | |
| Homework#6 | due Friday, 11/2 | Homework #6 (.pdf) | HW #6 Solutions ( .pdf) | |
| Mid-term | Monday, November 5 | in class |
Midterm info/review sample questions |
|
| Veteran's Day | Monday, November 12 | No class | ||
| Homework#7 | due Friday, 11/16 | Homework #7 (.pdf) | HW #7 Solutions ( .pdf) | |
| Thanksgiving | Thursday, November 22 | No class | ||
| Thanksgiving | Friday, November 23 | No class | ||
| Homework#8 | due Friday, 11/30 | Homework #8 (.pdf) | HW #8 Solutions ( .pdf) | |
| Homework#9 | due Friday, 12/7 | Homework #9 (.pdf) | HW #9 Solutions ( .pdf) | |
| Last day of classes | Friday, December 7 | |||
| Final Exam | Tuesday, 12/11 | Lowe 106 2:30-3:30 |
Final review Sample final |
Grading, Exams and Office Hours
Your course grade will be calculated by weighing your Homework, Midterm Exam and Final Exam grades in the proportions 30%, 30% and 40% respectively. However, depending on your level of preparation, you might need to complete a paper on special functions. This will count towards 15% of your grade, with a corresponding reduction of the above three percentages. Homework problem sets will be assigned weekly, normally due on Friday.Mid-term exam: Monday November 5
This is a 50-minute written examination that will cover material as described in the corresponding paragraphs from the Syllabus. Bring a one-sided sheet of notes
Final Exam: December 11
The final exam will last 60-minutes, testing your understanding of the material not covered in the mid-term and will emphasize basic techniques as applied to simple, fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity. Bring a two-sided sheet of notes. More info on this later in the quarter
Important Note on Office hours
Office hours are hours during which I am guaranteed to be in my office, answering your questions and dealing with problems you may have in this course. Office hours are not time during which you do your homework in my office. Rather, you should use this time to ask questions about problems which you have tried to work out, but got stuck at some point. In other words, you should come to office hours prepared, just like you should come to class prepared.
Extra credit
(1) I will frequently assign some homework problems of extra difficulty for those
wishing to
explore the techniques further and test their understanding.
(2)
Since most of you come from diverse areas of science and engineering, economics etc.
where numerical methods are frequently used, in every homework,
you are strongly encouraged to explore your area further
and find one (1) problem that uses the
techniques of this week's homework (which I will be describing each week). You will
get extra credit for a sound explanation of the origins of the problem and a
full solution.
What to do next
You may view your homework and exam grades on-line.
| <kirkinis@amath.washington.edu> | Thu Sep 19 16:31:00 PDT 2007 |