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AMATH 353 A: Partial Differential Equations and Waves

Summer Term: 
Full-term
Meeting Time: 
TTh 1:10pm - 2:40pm
Location: 
DEN 259
SLN: 
10065
Instructor:
Alexander Hornof
Alexander Hornof

Syllabus Description:

AMATH 353: Partial Differential Equations and Waves

Summer 2018

General Information

Time: Tues. & Thurs. 1:10 - 2:40

Location: Denny Hall (DEN) 259

Instructor Information

Name: Alexander Hornof

Email: ahornof@uw.edu

Office Hours

Wed. 10-11 am,

Thurs. 3-4 pm

Location: Lewis Hall (LEW) 128

TA

Name: Ryan Creedon

 

Prerequisites

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. 

 

Course Description

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
  • Stability
  • Superposition and Fourier analysis 
  • d' Alembert solution
  • Standing waves
  • Vibrations and separation of variables
  • Traveling waves of nonlinear equations
  • Conservation laws
  • Characteristics
  • Breaking
  • Shocks
  • Rarefaction

 

Course Materials

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:

353_course_notes.pdf

 

Homework

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.

 

Exams

There will be 2 equally weighted exams.

First Exam on 7/24

Second Exam on 8/16

 

Grading

Homework: 50%

Exams: 50%

 

Discussion Board

Please direct any questions regarding course material or general logistics to the Canvas discussion board which I will be checking regularly.

 

 

 

 

 

Catalog Description: 
Covers traveling waves of linear equations, dispersion relation, stability, superposition and Fourier analysis, d'Alembert solution, standing waves, vibrations and separation of variables, traveling waves of nonlinear equations, conservation laws, characteristics, breaking, shocks, and rarefaction. Prerequisite: either AMATH 351, MATH 136, or MATH 307. Offered: Sp.
GE Requirements: 
Natural World (NW)
Credits: 
3.0
Status: 
Active
Last updated: 
January 5, 2019 - 9:00pm
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