Jacobian

Purpose - Understand Jacobian
I stumbled on to Jacobian and then realized that it is used in quite a lot of places - Change of variable in integral calculus - Density of the transformed random variables

This This wiki link gives info about Jacobian

Also I happenend to watch a video( here ) on Jacobian

In this example there was a mention of a transformation x = u2 - v2 y = u2 - v2 Jacobian = 8 uv

Wanted to look at this in 3d and see how it looks

> set.seed(1977)
> u <- runif(5000, -5, 5)
> v <- runif(5000, -5, 5)
> x <- u^2 - v^2
> y <- u^2 + v^2
> par(mfrow = c(2, 2))
> plot(u, v, pch = 19, col = "blue", main = "Original Var")
> plot(u, x, pch = 19, col = "blue", main = (expression(x == u^2 -
+     v^2)))
> plot(v, y, pch = 19, col = "blue", main = (expression(y == u^2 +
+     v^2)))
> plot(x, y, pch = 19, col = "blue", main = "Transformed Var")