Domain of Influence: PDEs Info

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Homework Statement



I don't have a real question, i was looking for where i could find info on the domain of influence, regarding pdes

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The Attempt at a Solution

 
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Most books on PDEs will have a section in it. For example the book, An introduction to partial differntial equations with MATLAB by Matthew Coleman
 
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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