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Chapter 10: Q8P (page 517)
Write the transformation equations for to verify the results of Example 3.
This answer proves that is a polar vector.
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Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates .
In equationlet the variables be rectangular coordinates x, y, z, and let , be general curvilinear coordinates, orthogonal or not (see end of Section 8 ). Show that is the matrix in [or in for an orthogonal system]. Thus show that the volume element in a general coordinate system is where , and that for an orthogonal system, this becomes [by or ], . Hint: To evaluate the products of partial derivatives in , observe that the same expressions arise as in finding . In fact, from and , you can show that row i times column j in is just in equations to .
Parabolic.
In the text and problems so far, we have found the e vectors for Question: Using the results of Problem 1, express the vector in Problem 4 in spherical coordinates.
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