SOLVED:Let f: ℝ^2-{0} →ℝ^2-{0}, f(r, θ)=(r cosθ, r sinθ), be the polar coordinate map on the "punctured" plane. Prove: a) The winding form satisfies f^*((x d y-y d x)/(x^2 y^2))=d θ; b) the radial form x d x y d y satisfies f^*(x d x y d y)=r d r.
SOLVED:Let f: ℝ^2-{0} →ℝ^2-{0}, f(r, θ)=(r cosθ, r sinθ), be the polar coordinate map o…
Nov 11, 2023
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