|Lecture Room:||1333 Sterling|
|Lecture Time:||12:05–12:55 MWF|
|Office:||503 Van Vleck|
|Office Hours:||Wed 13:00–14:00, Thu 13:15–14:15|
Here are the solutions to the take-home final, which contain other approaches to solving the problem.
See the official syllabus.
The required textbook for the class is Introduction to Partial Differential Equations by Peter Olver. Homework problems will mostly be assigned from this book, so it's important to have access to it.
A good optional textbook for conformal mappings is Complex Variables: Introduction and Applications by M. J. Ablowitz & A. S. Fokas. [erratum]
If you're interested in learning more about the rigorous theory of homogenization of PDEs, there are a few textbooks available, such as Homogenization of partial differential equations by V. A. Marchenko & E. Y. Khruslov.
An undergraduate course in ODEs (on the level of Math 319); an undergraduate course in Linear Algebra (on the level of Math 340); an undergraduate course on PDEs (on the level of Math 322).
Every two weeks or so I will assign homework from the textbook (or other sources) and post it here. The homework will be due in class about two weeks later.
|1||02/06||2.1: 8,10; 2.2: 1,6,11,13,21,26,29; 2.3:3,7,13,20,21 [partial solutions]|
|2||02/20||2.4: 5,12–15; 3.2: 17,22,24,30,40,42,43,59,60,61; 3.3: 2,10; 3.5: 5,6,20,22|
|3||03/06||4.1: 1,4,8,13,14,16,17 4.2: 8,11,22,28 4.3: 1,18,30,31,43,49,50|
|4||03/27||6.1: 9,20,41 6.2: 2,4,12 6.3: 4,5,6,17,18,31 Additional questions on conformal mappings|
|5||04/12||8.1: 1,17,18 8.2: 7,8,10,16 8.4: 2,8,11 8.5: 3,4,14,18|
There will be a midterm exam and a cumulative final exam. The final grade will be computed according to:
The midterm exam will be given in the evening on the date below.
|Midterm exam||Monday March 6, 2017 at 17:30–19:00, room Van Hise 114||[solutions]||(average 87.6%, standard dev 10.6%)|
|Final exam||TBD (possibly take-home)|
We'll use Piazza Q&A for discussions about the class and related topics. Feel free to post questions and answers there about homeworks and exams, logistics, or relevant interesting things you found on the web. Note that we will only use Piazza for the Q&A feature, not for posting the actual homeworks.
Note: there is not necessarily a one-to-one correspondence between lectures numbers and dates.
|3||01/23||2.2||Transport equation (examples)|
|9||02/06||3.2–3.5||Convergence of Fourier series|
|11||02/10, 02/13||4.1||More on heat equation|
|12||02/13||4.2||Separation of wave equation|
|13||02/15, 02/17||4.3||Laplace equation|
|14||02/17||4.3||More on Laplace|
|16||02/22||6.2||Green('s) functions ["The Green of Green functions"]|
|17||02/24||6.3||2D Green's functions|
|18||02/27||–||Complex variable methods|
|20||03/03||–||Conformal mappings (cont'd)|
|–||03/06||–||Discussion of homework|
|22||03/10, 03/13||–||Janus particles [Legendre's equation (supplement)]|
|23||03/15||8.2||Symmetry and similarity|
|29||04/10–14||–||The exit time equation [extra notes]|
|30||04/17||–||Optimization of exit times|
|33||04/24–26||–||Winding around a point|
|35||05/01||–||Applications of Laplace transforms|
|36||05/03||–||Singular perturbation theory|