Gradient

calculus in \(\mathbb{R}^n\): functions of several variables, the surfaces they define, and the fields that flow over them. the programme is the same as one variable — linearise locally, integrate globally — but the derivative becomes a matrix, the chain rule becomes matrix multiplication, and the fundamental theorem splits into three named theorems (green, stokes, gauss) that are secretly one (Courant, Richard, 1996). this page is also the mathematical spine of machine learning: gradients, hessians, jacobians and constrained optima are chapter 5 of (Deisenroth, Marc Peter and Faisal, A. Aldo and Ong, Cheng Soon, 2020).