Bearded-android-docs

Created Monday 06 January 2014

• http://tutorial.math.lamar.edu/Classes/CalcIII/ChangeOfVariables.aspx#MultInt_Change_Ex1a

The Jacobian of the transformation `x=g(u,v)`, `y=h(u,v)` is

`\ \ (del(x,y))/(del(u,v)) = |( (del(x))/(del(u)), (del(x))/(del(v)) ), ( (del(y))/(del(u)), (del(y))/(del(v)) ) |`

`\ \ = (del(x))/(del(u)) (del(y))/(del(v)) - (del(x))/(del(v)) (del(y))/(del(u))`

Jacobian Matrix

• http://www.math.vt.edu/people/dlr/m2k_svb15_jacobn.pdf

Let `F` is a vector function from `bb R^n` to `bb R^m` with outputs `f_1,...f_m`.
Let `F` be continously differentiable at a point `X=(x_1,...x_n)`.

Then the Jacobian matrix of F at X is defined as an `m xx n` matrix

`\ grad F(X) = ( (grad f_1(X)), (vdots), (grad f_m(X)) ) = ( ((del f_1)/(del x_1)(X), ..., (del f_1)/(del x_n)(X)), (vdots, vdots, vdots), ((del f_m)/(del x_1)(X),...,(del f_m)/(del x_n)(X)) )`

where `grad f` is the gradient.