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I'm trying to find the fact that the Jacobi determinant (functional determinant) of the cartesian->spherical coordinate change is $r^2 \sin\theta$ in a mathematical reference book, "Taschenbuch der Mathematik" by Bronstein, Semendjajew, Musiol and Mühlig.

I've searched the index for "curvilinear", "Jacobi determinant" and "functional determinant", but can only find the general formula (determinant of the matrix of all first-order partial derivatives). Shouldn't this information be somewhere in a 1000-page work? Where should I look?

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1 Answer 1

In my 25th German edition from 1991, this is on p. 340 in Section 3.1.11.3, "Variablentransformation in Raumintegralen" (variable transformation in spatial integrals). There's an index entry for that term. There's also an index entry for spherical coordinates ("Kugelkoordinaten"), but the Section 4.2.2.2, "Felder" (fields) that it leads to only defines the coordinates and doesn't give the Jacobi determinant.

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Just what I'm looking for! The sections seem to have been shuffled around for the German 2008 edition. 3.1 is called "Planimetrie" and 3.1.11 doesn't exist. Would it be possible to note what 3, 3.1 and 3.1.11 are called in your edition? –  Andy Aug 1 '11 at 17:53
    
Sure: 3. Analysis, 3.1 Differential- und Integralrechnung von Funktionen einer und mehrerer Variablen, 3.1.11 Integrale über räumliche Bereiche. –  joriki Aug 1 '11 at 18:04

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