# 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") |