A linear change of coordinates is given by , .

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry

Invariance, Ch Differential forms and the exterior derivative

Problem

A linear change of coordinates is given by

x = 3u + 2v

y = u + 4v

. ((a)) Compute

\mathrm{d}x \wedge \mathrm{d}y

in terms of

\mathrm{d}u \wedge \mathrm{d}v

using the wedge product algebra directly (do not quote a determinant formula, derive it). ((b)) Hence find the area of the image, under this map, of the unit square

0 \le u \le 1

0 \le v \le 1

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