APM346-2012 > Home Assignment Y

HAY--as preparation for TT2

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Victor Ivrii:
http://www.math.toronto.edu/courses/apm346h1/20129/HAY.html
http://www.math.toronto.edu/courses/apm346h1/20129/HAY.pdf

You may post solutions immediately

Vitaly Shemet:
In last year TT2 #2 Solution. I can't understand the following reasons. Why do we need to say that tanh(beta l) intersects -1/
alpha?
 

Zarak Mahmud:
The only way we can have a negative eigenvalue is if the line $y=-\frac{1}{\alpha}$ intersects $\tanh \beta l$. This can't happen if $\alpha$ is positive. Have you tried drawing the graph?

By the way, for negative eigenvalues the convention is to use $\gamma$ instead of $\beta$.

 

Vitaly Shemet:
Where this reasoning came from? (I mean what is connection between sign of eigenvalues and intersection of these two graphs, and why do we take specifically 1/alpha or -1/alpha)

Zarak Mahmud:
It is discussed in lecture 13. If you have the Strauss textbook, it is discussed in quite a bit of detail in chapter 4.3

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