Author Question: You probably know by now that a differential k-form k 1 on a domain D Rn is very similar to a ... (Read 31 times)

eruditmonkey@yahoo.com · **on:** May 27, 2021

You probably know by now that a differential k-form k ≥ 1 on a domain D ⊂ Rⁿ is very similar to a vector field on D, and hence a correspondence between the two may be established.
For instance, we may set a correspondence between the 1-form F₁ dx + F₂ dy + F₃ dz and the vector field F = F₁ i + F₂ j + F₃ k. Using this setup, find the vector differential identity corresponding to the fact

for any differential 0-form g on a domain D in R³.
◦ ∇²(g) = 0
◦ ∇ ∙ (∇g) = 0
◦ ∇g = 0
◦ ∇ × (∇g) = 0
◦ (∇g)∙ ∇) = 0

brittrenee · **Reply #1 on:** May 27, 2021

A FREE account is required to view all solutions!

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.

Answer Preview

Only 55% of students answer this correctly