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Inhomogenous Boundary Conditions for Eigenvalue Problem

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Andrew Hardy:
Chapter 4.2 gives the solutions to several different boundary conditions for an eigenvalue problem. All of the solutions provided are for inhomogeneous BC's though.  Would the exam cover homogeneous BC? What would be the method in that case?

Also, point of clarification for the solution  to previous TT2 #3
http://forum.math.toronto.edu/index.php?topic=841.0

$ Y_m $ should depend upon the variable $ y $ correct?  So the correct solution to Laplacian in the rectangle
 ${0<x<a,0<y<b} $ with Neumann boundary conditions should be?:
$$ u_{n,m}(x,y) = \cos(\frac{n\pi x}{a})\cos(\frac{m\pi y}{b}) $$

Victor Ivrii:

--- Quote from: Andrew Hardy on March 17, 2018, 10:39:32 AM ---Chapter 4.2 gives the solutions to several different boundary conditions for an eigenvalue problem. All of the solutions provided are for inhomogeneous BC's though.  Would the exam cover homogeneous BC? What would be the method in that case?
--- End quote ---
? 4.2. Eigenvalue problem only homogeneous b.c. are considered here, because only in this case we have eigenvalue problem.



--- Quote ---Also, point of clarification for the solution  to previous TT2 #3
http://forum.math.toronto.edu/index.php?topic=841.0

$ Y_m $ should depend upon the variable $ y $ correct?  So the correct solution to Laplacian in the rectangle
 ${0<x<a,0<y<b} $ with Neumann boundary conditions should be?:
$$ u_{n,m}(x,y) = \cos(\frac{n\pi x}{a})\cos(\frac{m\pi y}{b}) $$

--- End quote ---
Indeed. I waited someone to correct it ... and forgot then...

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