HP 48gII Graphing Calculator Uživatelský manuál stáhnout pdf (Strana 470)

Jacobian of coordinate transformation

Consider the coordinate transformation x = x(u,v), y = y(u,v). The Jacobian of

this transformation is defined as

JJ det)det(||

When calculating an integral using such transformation, the expression to use

||)],(),,([),(

dudvJvuyvuxdydxyx φφ , where R’ is the region R

expressed in (u,v) coordinates.

Double integral in polar coordinates

To transform from polar to Cartesian coordinates we use x(r,θ) = r cos θ, and

y(r, θ) = r sin θ. Thus, the Jacobian of the transformation is

With this result, integrals in polar coordinates are written as

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HP 48gII Graphing Calculator Uživatelský manuál Strana 470