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Eigenvalues, Heat Equations and Parseval's Identity

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You can solve problems except matlab problems(1.(c),3(c),6(d,e)).
But I still hope you would solve all problems including matlab problems.
And you can send me solutions separating into two parts regardless of problem's order.

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Eigenvalues, Heat Equations and Parseval's Identity are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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