Find the Jacobian of the transformation. x=u+4v , y=u^2-2v

he298c 2021-09-19 Answered
Find the Jacobian of the transformation
x=u+4v,y=u22v
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Expert Answer

Brittany Patton
Answered 2021-09-20 Author has 100 answers

Basic information:
given:
x=u+4v
y=u22v
 Jacobian=|xuxvyuyv|
xu=u(u+4v)=u
yu=u(u22v)=2u
we thear v as command.
xv=v(u+4v)=4
yv=v(u22v)=2
we thear u as command.
Calculation of Jacobian
Now, xu=1,xv=4
yu=2u,yv=2
 Jacobian=|142u2|
=(2)(1)(4)(2u)
=8u2
  Jacobian=8u2

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