Suspension Acoustics: An Introduction to the Physics of Suspensions

Appendix B: Useful Formulas from Vector Analysis

In the following formulas, A, B, C, and D represent vector functions; and ? represent scalar functions.

General Relations


Special Relations

If x= i x+ j y+ k z in the position vector of a point (x, y, z) and r= x, then:


Integral Relations

In the following formulas, V is a volume bounded by a closed surface S, having a unit normal vector n directed outward from V:


Let S be an open surface with unit normal n, bounded by the closed contour C having a line element d I. Then,


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