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AMATH 353 A: Partial Differential Equations And Waves

Meeting Time: 
MWF 10:30am - 11:20am
Location: 
MEB 246
SLN: 
10239
Instructor:
Saumya Sinha
Saumya Sinha

Syllabus Description:

Lectures: MWF 10:30-11:20 am, MEB 246

Instructor: Saumya Sinha

Email: saumya@uw.edu

Office Hours: MF 2-3pm, LEW 128

Teaching Assistant: Weston Barger 

Email: wdbarger@uw.edu 

Office Hours: T 11:30-12:30, Th 2-3, LEW 129

Prerequisites: Any one of AMATH 351, MATH 136, MATH 307.

Course 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.

Course Materials: The textbook for this course is Roger Knobel’s ‘An introduction to the mathematical theory of waves’ (American Mathematical Society 2000, Student Mathematical Library Vol 3). We will be following this book closely, and while it is not required, it is highly recommended.

Additionally, lecture notes by Dr. Bernard Deconinck will be provided on Canvas. Dr. Deconick’s notes are not meant as a replacement for the textbook, but will serve as a nice supplement with helpful examples.

Grading: Your course grade will be a weighted sum of your score in the homeworks, midterm and final, added in the proportions 50%, 20% and 30% respectively.

Homework: There will be a total of eight homeworks carrying equal weight, and due at the beginning of class on the due date. I urge you to type up the homework using LaTeX or another typesetting software, but neatly handwritten homework will also be accepted. Typed homeworks may be submitted through Canvas, while handwritten copies must be submitted in person. Upto 5% of the grade on any homework may be penalized for illegible or unclear submissions, at the sole discretion of the Teaching Assistant.

Late policy: You may submit at most one homework up to a week late without any penalty.

You are encouraged to discuss and collaborate with your peers on the homework, but submitted solutions must be written up individually and not shared with others. Questions may be brought to class, office hours and the Canvas discussion board.

Exams: The midterm will be in class on Wednesday, May 3rd.

The final exam will be on June 5th, 8:30-10:20am, in MEB 246.

Reading: The table below outlines the portion of the text we (intend to) cover in each lecture. 'Text' refers to the textbook prescribed for the class, and 'Notes' refers to the lecture notes by Dr. Bernard Deconinck uploaded under the 'Files' tab. There is significant overlap between the text and the notes, and I will only refer to material outside the textbook if it is not contained therein.  

Lecture  Date   Reading 
Lecture 1 03/27/17 Text, Chapters 1 & 2
Lecture 2 03/29/17 Text, Chapters 2.2 & 3
Lecture 3 03/31/17 Text, Chapters 4.1, 6.3
Lecture 4 04/03/17 Text, Chapter 5
Lecture 5 04/05/17 Text, Chapter 4.2-4.3; Notes, sections 2.4-2.6
Lecture 6 04/07/17 Notes, sections 2.7-2.8 (Refer to notes on Wave Fronts and Dispersion)
Lecture 7 04/10/17 Text, Chapter 7
Lecture 8 04/12/17 Text, Chapter 8
Lecture 9 04/14/17 Text, Chapters 10.1-10.2
Lecture 10 04/17/17 Text, Chapters 9.1, 10.3 (Refer to notes on Wave equation on semi-infinite domain.)
Lecture 11 04/19/17 Text, Chapters 9.2, 10.2
Lecture 12 04/21/17 Text, Chapter 11
Lecture 13 04/24/17 Text, Chapter 13; Notes, Sections 3.1 and 3.2
Lecture 14 04/26/17 Notes, Section 3.2
Lecture 15 04/28/17 Notes, Section 3.3
Lecture 16 05/01/17 Review - HW2, #2, and Practice Midterm #2.
Midterm 05/03/17 Covers everything up to Lecture 14.
Lecture 17 05/05/17 Notes, Section 3.3
Lecture 18 05/08/17 Notes, Section 3.4 and 3.5
Lecture 19 05/10/17 Text, Chapters 15-16
Lecture 20 05/12/17 Text, Chapter 17.1-17.2
Lecture 21 05/15/17 Text, Chapter 17.3-17.4, 18.1
Lecture 22 05/17/17 Text, Chapter 18
Lecture 23 05/19/17 Text, Chapter 19
Lecture 24 05/22/17 Text, Chapter 20
Lecture 25 05/24/17 Text, Chapter 21
Lecture 26 05/26/17 Text, Chapter 22
No class 05/29/17 Memorial Day holiday
Lecture 27 05/31/17 Text, Chapter 23, 24.1
Lecture 28 06/02/17 Text, Chapter 24.2, 25, wrapping up
Final Exam 06/05/17 8:30-10:20 am, MEB 246
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 10, 2018 - 9:01pm
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