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 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|