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Intermediatecalculusgradientsjacobianhessianodes

Calculus for ML

24 problems·~9h·4 stages

Derivatives, gradients, Jacobians, and Hessians, all computed numerically so you can verify any formula by hand. You will build finite differences, Newton and RK methods, Lagrange multipliers, and convolution integrals. Designed for learners who want optimization and backprop to rest on real calculus rather than hand-waving.

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Continue path · Numerical Derivative

What you will learn

  • Approximate derivatives and integrals with finite differences and quadrature
  • Build gradients, partials, Jacobians, and Hessians numerically
  • Apply the chain rule and matrix calculus to ML losses
  • Solve ODEs and take transforms used in signal and generative models

Before you start

1Derivatives and Integrals

0/6

Numerical differentiation and integration: forward differences, trapezoidal and Simpson rules, midpoint quadrature, and directional derivatives.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

2Gradients and Newton's Method

0/6

From one variable to many: numerical gradients, Newton's method in one and several steps, partial derivatives of quadratic forms, and the Hessian of a quadratic.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

3Multivariable Calculus for Backprop

0/6

The tools behind backprop and constrained optimization: mixed partials, gradient-descent steps, softmax gradients, Jacobians, Hessians, and Lagrange multipliers.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

4ODEs and Transforms

0/6

Continuous dynamics and frequency-domain tools: Euler and Runge-Kutta steps, convolution integrals, Fourier coefficients, and inverse Laplace transforms.

Stage checkpoint

0/2 to pass

A checkpoint is a short retrieval test drawn from this stage: solve 2 of 3 from memory to mark the stage complete. The stage stays open either way.

Tried this set and did not pass? Record it — the next set swaps in fresh problems from the same stage.
LabRecommended next stepNoisy QuadraticMedium

Capstone

Pen and paper

Close the path with one real artifact from the catalog.

Limit of (1 - cos x) / x^2 as x goes to 0

A handwritten final check: derive the classic limit with the small-angle approximation or L'Hopital's rule.