16.6 Jeopardy!

Jacobian!

100

What a Jacobian is

What is a conversion/scaling factor when mapping a change of variables?

200

Jacobian of G(u,v) = (3u+v,7u+3v)

What is 2?

300

Jacobian of G(r,s) = (rs,r+s)

What is s-r? 

400

Jacobian of G(x,y) = (xe^y,e^x) 

What is -xe^y+x?

500

Jacobian of G(r,θ) = (rcosθ , rsinθ)

What is r?

Mr. Lee!

100

Mr. Lee's first name

What is John?

200

Mr. Lee's favorite volleyball position

What is outside hitter/wing spiker?

300

Mr. Lee's favorite color

What is green?

400

Mr. Lee's favorite instrument

What are drums?

500

Mr. Lee's favorite pokemon

(hint: it's somewhere in the room)

What is dragonite?

Mapping!

100

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)?

200

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)?

300

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)?

400

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)?

500

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)?

Integrals!

100

Find G(u,v)

What is G(u,v)=(4u+3v,u+3v)?

200

Jacobian of G(u,v)

What is 9?

300

Express f(x,y) in terms of the new variables

What is e^15u+9v?

400

Rewrite Integral 

∫₀¹ ∫₀¹ e^15u+9v*9 dudv

500

Solve Integral

What is 1/15(e^15-1)(e^9-1)

Integrals! again..

100

Bounds of the region

What is 1 ≤ u ≤ 3 and 3 ≤ v ≤ 9?

200

Jacobian

What is -1/3u?

300

f(x(u,v), y(u,v))

What is (4(u^2)v)/3?

400

Final setup

What is ∫₁³∫₃⁹ -4uv/9 dvdu?

500

Solve Integral

What is 64?