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Home Assignment 6 / Re: Laplace Fourier Transform S5.3.P Q1
« on: March 17, 2019, 12:27:26 PM »
What condition is given at infinity? I don't see any condition given in the question for the behaviour of $u$ at infinity.
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Home Assignment 2 / Re: problem 5 (23)
« on: January 27, 2019, 08:43:49 PM »
By parameterizing, the professor means to express x and y in terms of some other parameter. Since the integral curves are circles, think about what is normally used to parameterize a circle in a very easy way - it's essentially a change of variable.
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Home Assignment 3 / S2.3 Problem 8
« on: January 27, 2019, 06:42:08 PM »
In this question, the initial conditions are not given for $t = 0$, as we've discussed in class, but instead for $t = \frac{x^{2}}{2}$. I have no idea how to approach this. Could someone please help?
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Home Assignment 2 / Re: problem4 (20)
« on: January 21, 2019, 05:42:29 PM »
Would we be incorrect to define $C = y-3x$ since saying $y = 3x-C$ is essentially equivalent to $y = 3x+C$ for arbitrary $C$? This is what I did in my solution.
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Home Assignment 2 / Home Assignment 2 Problem 2(a)
« on: January 16, 2019, 06:10:30 PM »
For this question (eqn 14) I found the characteristic curve to be $\frac{x}{y} = C$. It asks what the difference is between the cases $(x,y)\neq (0,0)$ and that the solution be continuous at (0,0). From what I understand, in the former case we can simply say the solution is any funtion of one variable, $u(x,y) = \phi (\frac{x}{y})$, on the domain $(x,y)\neq (0,0)$. In the second case, we need to pick some value for $u(0,0)$ to make it continuous, and elsewhere it's the same as the other case. Is this a sufficient explanation? It feels lacking to me. Could someone offer assistance?
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