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Author Question: Let = (2xy - z2) dx + (2yz + x2) dy + (y2 - 2zx) dz be a differential 1-form defined on a star-like ... (Read 59 times)

Mr.Thesaxman

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on: May 27, 2021

Question 1

Let [r, θ, z] be the cylindrical coordinates of a point in 3-space. Prove that rdr∧dθ∧dz = dx∧dy∧dz.

Question 2

Let Φ = (2xy - z2) dx + (2yz + x2) dy + (y2 - 2zx) dz be a differential 1-form defined on a star-like domain D in R3.
(a) Show that Φ  is exact on D.
(b) Find a differential 0-form Ψsuch that  Φ = dΨ on D.
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Marked as best answer by Mr.Thesaxman on May 27, 2021

amit

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Reply #1 on: May 27, 2021
Lorsum iprem. Lorsus sur ipci. Lorsem sur iprem. Lorsum sur ipdi, lorsem sur ipci. Lorsum sur iprium, valum sur ipci et, vala sur ipci. Lorsem sur ipci, lorsa sur iprem. Valus sur ipdi. Lorsus sur iprium nunc, valem sur iprium. Valem sur ipdi. Lorsa sur iprium. Lorsum sur iprium. Valem sur ipdi. Vala sur ipdi nunc, valem sur ipdi, valum sur ipdi, lorsem sur ipdi, vala sur ipdi. Valem sur iprem nunc, lorsa sur iprium. Valum sur ipdi et, lorsus sur ipci. Valem sur iprem. Valem sur ipci. Lorsa sur iprium. Lorsem sur ipci, valus sur iprem. Lorsem sur iprem nunc, valus sur iprium.
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Mr.Thesaxman

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Reply 2 on: May 27, 2021
Excellent

abro1885

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Reply 3 on: Yesterday
:D TYSM

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