Let . Let be the quarter circle of radius centred at the origin, traversed from to…

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

Let α=y dx−x dy\alpha = y\,\mathrm{d}x - x\,\mathrm{d}y. Let γ\gamma be the quarter circle of radius 33 centred at the origin, traversed from (3,0)(3,0) to (0,3)(0,3) (anticlockwise). ((a)) Parameterise γ\gamma by the polar angle θ∈[0,π/2]\theta \in [0, \pi/2]. ((b)) Compute ∫γα\int_\gamma \alpha.

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