Can Anyone Help Solve These Fourier Series and Heat Equation Problems Quickly?

malee006
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Any one Solution will be appreciated , just solve as soon as possible!
1) Fourier Series
2) Heat Equation
 

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If you are waiting for someone to do your homework for you, you have come to the wrong site.

Please show us what you have done, or at least make an effort to show that you have even read the problems.
 
Do you know how to take a Fourier transform?

Do you understand heat equations?

Frankly I don't think anyone can help you until we understand what you're having trouble with.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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