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M05 · Multivariable and Matrix Calculus

A free, illustrated L2 course of 10 modules in the Mathematics track. Modules include: Functions of several variables and level sets; Partial derivatives and the gradient; Directional derivatives and steepest ascent.

M05 L2 · Intermediate 10 modules · about 40 lessons Planned · Ring 2

Part of the Mathematics track. Ships in Ring 2 (Spine) of the roadmap.

Modules

1. Functions of several variables and level sets
2. Partial derivatives and the gradient
3. Directional derivatives and steepest ascent
4. Jacobians and the multivariable chain rule
5. Hessians, curvature and second-order Taylor
6. Multiple integrals and change of variables
7. Matrix calculus identities
8. Computational graphs and automatic differentiation
9. Backpropagation as reverse-mode differentiation
10. Vector fields, divergence and curl

Signature illustrations

The pictures a learner should still see in their head a year later:

Contour maps with gradient arrows, the Jacobian as a local grid warp, forward and backward passes on a computational graph, curvature surfaces.

Status

This course is planned, not written yet. It ships with Ring 2 (Spine).

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.