Topics

1

Final Exam / Problem 3

« on: December 20, 2012, 01:32:15 PM »

Use separation of variables to solve the Dirichlet problem for the Laplacian on the unit disk $\mathbb{D} = \{ (x,y) \in \mathbb{R}^2: x^2 + y^2 < 1\}$ with boundary condition $u(1, \theta) = \cos \theta.$
(The boundary condition is described in polar coordinates $(r, \theta) \rightarrow u(r, \theta)$ along $r=1$).


hopeful solution attached! (since djirar is posting all the solutions right away after 13:30..)

2

Misc Math / Lecture 26 Equation 13 Question

« on: November 28, 2012, 12:34:26 AM »

Hi,

It looks like a mysterious 77 slipped its way into Equation 13 of Lecture 26: http://www.math.toronto.edu/courses/apm346h1/20129/L26.html#mjx-eqn-eq-13 .

I assume this is a typo?

Cheers,

Ian

3

Home Assignment 7 / Problem 4

« on: November 19, 2012, 03:29:55 AM »

For Problem 4, it seems the solution can only defined up to a constant - is that alright?

4

Home Assignment 5 / Problem 4

« on: October 31, 2012, 09:32:02 PM »

Hopeful solutions for 4.c)!

edit: Note that sketch is for m=1.

5

Misc Math / Lecture 12 Eqn 9 Question

« on: October 24, 2012, 01:59:26 AM »

Hi all,

Just to clarify - should equation 9 in the notes for lecture 12 (http://www.math.toronto.edu/courses/apm346h1/20129/L12.html#mjx-eqn-eq-9) read

$\lambda_n = - n^2 \pi^2 / l^2$ ?

Cheers,

Ian