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Mathematical Methods in Physical Sciences

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I need some help on this question, it is from the book "The mathematical methods in the physical sciences".
7. Given v = x^2i + y^2j + z^2k
a. Integrating v*ndo for surface of the cube which its length is 1 and is consisted of 4 vertexes of (0,0,0), (0,0,1), (0,1,0), (1,0,0).
b. Using divergence theorem, calculate the above.

8. Show the following force field is conservative field, and proceed with calculations (see attached file for full symbol representation).
a. see attachment
b. see attachment
c. see attachment

9. In 2-dimensional polar coordinate, find following answers by integrating.
a. In 1 quadrant, perimeter of the circle which its radius is a.
b. Area of circle which its radius ia a.

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Solution Summary

This in-depth solution shows step-by-step calculations on integration, divergence theorem and force fields.