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Changes in div, grad, curl and all that going from version 3 to version 4.

Here are the changes made in Schey's div, grad, curl and all that,in going from version 3 to version 4. There is a broad change across chapters and problems to represent spherical polar coordinates the "math way" in version 4, rather than the "physics way," as in previous versions. The math way is to use phi for the polar angle and theta for the azimuthal angle. The physics way just exchanges them, with theta for the polar angle and phi for the azimuthal angle. I have no idea how this difference arose.

So, I will indicate places where this matters, as well as other changes in version 4, below.

• Figure II-25 now has angles the math way. Also in equation II-25.
• Problem II-19 is now in math angles.
• Problem II-21 is now in math angles.
• Figure III-7 now uses math angles.
• Figure III-15(a) now uses math angles.
• Un-numbered equations on Pg. 85 of version 3 (and pg. 86 of version 4) use math angles. And there is an example of calculating the curl in spherical coordinates in version 4 which is not present in version 3.
• Problem III-11 uses spherical polar coordinates.
• Figure IV-6 and the following expression for the Laplacian use math angles.
• Problem IV-6 now uses math angles.
• Problem IV-22 now uses math angles.
• The equations on the back inside cover of the book, summarizing results in spherical coordinates, now use math angles.