This is the website for the course M485 and MA805: Partial Differential Equations. I will be maintaining this website regularly during the course.
Prerequisites:
a) Knowing how to multiply.
b) Integration by parts.
Grading: Homework + Quizz = 30%
Mid Term = 30%
Final Exam = 40%
Grading will be absolute.
HW2 is due in class on 6th February by 12:30 pm. No late homework please.
Homework
Quiz
Notes
Notes 1 These notes contain the justification for why the
Laplacian of the Green's function is zero and also the
claim made about the gradient (both, away from the origin).
Notes 2 These notes contain a proof of the fact that if f belongs to S(R)
(the Schwarz space) and g belongs to L-infinity of R, then their
convolution is a smooth function. It explains clearly how to use
the Dominated Convergence Theorem (along with the Mean Value Theorem).
DO NOT COPY this solution for your second homeowork. Give me a simpler
proof of this assertion when g is a continuous function with compact support
(although ofcourse you have to use DCT and MVT).
Notes 3 Convolution of Locally Integrable function and C-infinity function with compact support is C-infinity.
Notes 4 Interchange of time derivative and integral is permitted while convolving ann L-infinity function with Heat Kernel.
Again, this is an application of DCT. The content of Notes 2 combined with Notes 4, shows that space and time derivatives
can be pushed inside the integral (which is the convolution of g and the Heat Kernel).
Mid Term Exam
Mid Term Scanned Solutions to Mid Term
Final Exam
Final Exam Scanned Solutions to Final Exam