AMATH 353: Partial Differential Equations and Waves
Time: Tues. & Thurs. 1:10 - 2:40
Location: Denny Hall (DEN) 259
Name: Alexander Hornof
Wed. 10-11 am,
Thurs. 3-4 pm
Location: Lewis Hall (LEW) 128
Name: Ryan Creedon
Either AMATH 351, MATH 136, or MATH 307. Beyond the mathematical skills implied by the prerequisite classes, you should be comfortable using scientific computing software (i.e. MATLAB, python, Mathematica, Octave, Maple, etc.) to plot and preform simple computations.
This course will provide an introduction to partial differential equations (PDE), cover some methods for solving PDEs, and study how to interpret these solutions. There will be a particular focus on those concepts which utilized in the mathematical study of waves. Topics covered will include (time permitting):
- Traveling waves of linear equations
- Dispersion relations
- Superposition and Fourier analysis
- d' Alembert solution
- Standing waves
- Vibrations and separation of variables
- Traveling waves of nonlinear equations
- Conservation laws
The required textbook for this course is Roger Knobel's "An introduction to the mathematical theory of waves", American Mathematical Society 1999, Student Mathematical Library Vol 3. We will cover all the material in this text, and supplementary resources will be provided as needed.
Much of the course material is also covered in Professor Bernard Deconinck's detailed course notes:
Homework will be assigned roughly once a week, for a total of approximately 9 assignments. Homework will be assigned on and submitted to Canvas. I will not be collecting physical copies in class. For each assignment, 2-3 problems will be randomly selected for grading. Points will be deducted for illegibility, and typesetting your homework is appreciated. Your lowest assignment will be dropped.
There will be 2 equally weighted exams.
First Exam on 7/24
Second Exam on 8/16
Please direct any questions regarding course material or general logistics to the Canvas discussion board which I will be checking regularly.