How to solve the wave equation with Dirac delta function initial conditions?

FrattyMathMan
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Homework Statement


Solve the IVP for the wave equation:

Utt-Uxx=0 for t>0
U=0 for t=0
Ut=[dirac(x+1)-dirac(x-1)] for t=0


2. The attempt at a solution

By D' Almbert's solution:

1/2 integral [dirac(x+1)-dirac(x-1)] dx from (x-t) to (x+t)

I apologize for not using Latex- my browser does not seem to agree with the reference.

My issue is what am I to do with the dirac function inside the integral? Can anyone point me in the right direction? I've already read all common literature on the dirac delta function.

Thank you for any help!
 
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Any help? Seriously drawing a blank!

Am I supposed to just use the heavyside function?
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'

Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...
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