# Calculus

> ML Prep practice set.

- Stable ID: `calculus`
- Area: mathematics
- Timebox: 120 minutes

Cover single-variable foundations, multivariable differentiation, approximation, and optimization.

## Instructions

1. State dimensions for vector and matrix derivatives.
2. Separate method-selection errors from algebra errors.

## Ordered items

1. [Single-variable calculus foundation check](https://mlprep.iwase.dev/item/mit-18-01sc-f2010-final-foundations/?set=calculus) — `mit-18-01sc-f2010-final-foundations` (easy, 24 min)
2. [Gradient, tangent plane, linearization, and directional derivative](https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q1/?set=calculus) — `mit-18-02sc-f2010-exam2-q1` (easy, 12 min)
3. [Jacobian and chain rule](https://mlprep.iwase.dev/item/original-calc-jacobian/?set=calculus) — `original-calc-jacobian` (medium, 10 min)
4. [Critical points and constrained domain boundaries](https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q3/?set=calculus) — `mit-18-02sc-f2010-exam2-q3` (medium, 14 min)
5. [Multivariable chain rule under a change of variables](https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q4/?set=calculus) — `mit-18-02sc-f2010-exam2-q4` (medium, 10 min)
6. [Lagrange multiplier equations and tangent geometry](https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q5/?set=calculus) — `mit-18-02sc-f2010-exam2-q5` (medium, 10 min)
7. [Total differentials and implicit differentiation](https://mlprep.iwase.dev/item/mit-18-02sc-f2010-exam2-q6/?set=calculus) — `mit-18-02sc-f2010-exam2-q6` (medium, 10 min)
8. [Matrix gradient and Hessian](https://mlprep.iwase.dev/item/original-calc-matrix/?set=calculus) — `original-calc-matrix` (medium, 10 min)

## Completion

Derive gradients, Jacobians, Hessians, and constrained first-order conditions without relying on source notation.

## Next recommended practice

- [Probability](https://mlprep.iwase.dev/set/probability.md)