Deriving the 3D Wave Equation: A Comprehensive Explanation

Tuneman
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I would like to know how to derive the wave equation for a 3 dimensional case, I was looking it up on wikipedia, and their explination wasn't very comprehensive, I was wondering if anyone knew of any other website that would be able to let me fullly understand it.

Edit: not the shrodinger wave equation, but general case of a wave.
 
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Not sure what you mean by 3 dimensional case but I think it is just a definition. If you see an equation of the form U_tt = U_xx + U_yy + U_zz we choose to call it the wave equation in three dimensions.
 

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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