Chapter 1. calc_tutorial_15_6_013

1.1 Problem Statement

{3,5,7}
{2,4,6}
{3,4,5}
$a*(-$c)-$b

Compute the Jacobian.

G(u, v) = ($au + $bv, u − $cv)

1.2 Step 1

Question Sequence

Question 1.1

Recall the definition of the Jacobian.

The Jacobian of a map G(u, v) = (x(u, v), y(u, v)) is the following determinant.

Jac(G) = ∂(x, y) / ∂(u, v) = the determinant of the following table interpreted as a matrix.

(∂x / ∂u) (∂x / ∂v)
(∂y / ∂u) (∂y / ∂v)
Table : Matrix A

Jac(G) = ∂(x, y) / ∂(u, v) = det(Matrix A) = (∂x / ∂u)(∂y / ∂v) - (∂x / ∂v)(∂y / ∂u)

For x(u, v) = $au + $bv, and y(u, v) = u − $cv, calculate the partial derivatives in the Jacobian.

(∂x / ∂u) = nc1ItEz0kR4=

(∂x / ∂v) = iSba6t70dtA=

(∂y / ∂u) = 0VV1JcqyBrI=

(∂y / ∂v) = YWSdEbNFjeo=

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Compute the Jacobian.

∂(x, y) / ∂(u, v) = (∂x / ∂u)(∂y / ∂v) - (∂x / ∂v)(∂y / ∂u) = U2GIbglD1oM=

Correct.
Incorrect.