Items tagged with parabolic

How I can graph parabolic cylinder y=x^2 and elipsoid x^2+4y^2+4z^2=16 on a three-dimensional coordinate system?

Dear all,

I tried to use pdsolve to solve the parabolic pde but get the unexpected answer:

Is it the PDESolStruc or the other structure? Where can I find the description about this kind of structure.



In trying to solve:

 a := diff(u(t), t$2)+(p^2-I+t^2)*u(t) = 0;
I get the following solutions,              
sol1 := u(t) = _C1*WhittakerM(-1/4-(1/4*I)*p^2, 1/4, I*t^2)/sqrt(t)+_C2*WhittakerW(-1/4-(1/4*I)*p^2, 1/4, I*t^2)/sqrt(t)        
It should be possible to expand these into parabolic cylinder functions and but im not sure how, i would appreciate any help.

This excellent application

demonstrates the paths of light rays against various surfaces.  Can the initialization code be made more efficient and faster?  The only thing I could think of was to remove the call to plottools and replace it with just plot and adding an extra...

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