math.babelslibrary.com

• Surface explorer — type f(x,y), fly around its graph, slide the level set, see the gradient field.
• Prof. Claude (PDF) — lessons from conversations with Claude: convolution, Euler angles and spinors, inequalities, Newton's binomial series, tensors, grad/div/curl. Each chapter ends with exercises.

Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms

• 2.5 Gauss quadrature — n points at the roots of the Legendre polynomial Pₙ integrate every polynomial of degree ≤ 2n − 1 exactly (exercise 2.5.10).
• 3.7 Lagrange multipliers — slide a point along the constraint g = 0; f is extremal where its level set is tangent, ∇f ∥ ∇g.
• 4.5 Cavalieri's principle — same slice at every height, same volume: leaning pyramids, Archimedes' sphere, the napkin ring, the Steinmetz solid.