Jacobian!
What a Jacobian is
What is a conversion/scaling factor when mapping a change of variables?
Mr. Lee's first name
What is John?
The image of triangle T mapped with vertices (1,2), (2,1), (3,4) under the linear map G(u,v)=(2u-v,u+v)
What is G(1,2)=(0,3) G(2,1)=(3,3) G(3,4)=(2,7)?
Find G(u,v)
What is G(u,v)=(4u+3v,u+3v)?
Bounds of the region
What is 1 ≤ u ≤ 3 and 3 ≤ v ≤ 9?
Jacobian of G(u,v) = (3u+v,7u+3v)
What is 2?
Mr. Lee's favorite volleyball position
What is outside hitter/wing spiker?
The image of triangle T mapped with vertices (0,0), (1,1), (0,4) under the linear map G(u,v)=(u^2,2v+u)
What is G(0,0)=(0,0) G(1,1)=(1,3) G(0,4)=(0,8)?
Jacobian of G(u,v)
What is 9?
Jacobian
What is -1/3u?
Jacobian of G(r,s) = (rs,r+s)
What is s-r?
Mr. Lee's favorite color
What is green?
The image of triangle T mapped with vertices (1,1), (3,3), (5,2) under the linear map G(u,v)=(3u,u)
What is G(1,1)=(3,1) G(3,3)=(9,3) G(5,2)=(15,5)?
Express f(x,y) in terms of the new variables
f(x(u,v), y(u,v))
What is (4(u^2)v)/3?
Jacobian of G(x,y) = (xey,ex)
What is -xey+x?
Mr. Lee's favorite instrument
What are drums?
The image of triangle T mapped with vertices (2,3), (3,2), (0,1) under the linear map G(u,v)=(-v,u+v)
What is G(2,3)=(-3,5) G(3,2)=(-2,5) G(0,1)=(-1,1)?
Rewrite Integral
∫01 ∫01 e15u+9v*9 dudv
Final setup
What is ∫13∫39 -4uv/9 dvdu?
Jacobian of G(r,θ) = (rcosθ , rsinθ)
What is r?
Mr. Lee's favorite pokemon
(hint: it's somewhere in the room)
What is dragonite?
The image of triangle T mapped with vertices (6,7), (2,5), (3,10) under the linear map G(u,v)=(3u+v,v-u)
What is G(6,7)=(25,1) G(2,5)=(11,3) G(3,10)=(19,7)?
Solve Integral
What is 1/15(e^15-1)(e^9-1)
Solve Integral
What is 64?