Let 5 (x² + y²)³ be a one-form on U = R² \ {(0,0)}, and : V → U be the smooth function (r, t) = (r cost, r sin t) with V = {(r, t) = R² | r ± 0}. # Find d(p*w). d(p*w) = @= -(y dx - x dy) dr ^ dt
Let 5 (x² + y²)³ be a one-form on U = R² \ {(0,0)}, and : V → U be the smooth function (r, t) = (r cost, r sin t) with V = {(r, t) = R² | r ± 0}. # Find d(p*w). d(p*w) = @= -(y dx - x dy) dr ^ dt
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Let
5
(x² + y²)³
be a one-form on U = R² \ {(0,0)), and : V → U be the smooth function
p(r, t) = (r cost, r sin t)
with V = {(r,t) ER ² | r #0}.
Find d(p*w).
d($*w) =
@=
(y dx - x dy)
dr^ dt
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