Let be a one-form on

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=(x+y) dx+(x−y) dy\alpha = (x+y)\,\mathrm{d}x + (x-y)\,\mathrm{d}y be a one-form on R2\mathbb{R}^2. Let γ\gamma be the straight-line path from (0,0)(0,0) to (2,3)(2,3). ((a)) Write a parameterisation x(t),y(t)x(t), y(t) for t∈[0,1]t \in [0,1] that traces γ\gamma. ((b)) Compute ∫γα\int_\gamma \alpha.

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