Lilly Tech Systems
Calculus for Machine Learning
Understand the mathematics behind model training. From derivatives and gradients to the chain rule and optimization, learn how calculus enables neural networks to learn from data through backpropagation and gradient descent.
What You'll Learn
By the end of this course, you'll understand the calculus that drives every ML training loop.
Derivatives
Understand rates of change, partial derivatives, and how they measure the sensitivity of loss functions to model parameters.
Gradients
Master gradient vectors, directional derivatives, and the gradient descent algorithm that trains neural networks.
Chain Rule
Learn the chain rule — the mathematical foundation of backpropagation and automatic differentiation.
Optimization
Apply calculus to find optimal model parameters through gradient-based optimization methods.
Course Lessons
Follow the lessons in order or jump to any topic you need.
1. Introduction
Why calculus is essential for ML. Overview of how derivatives and integrals connect to model training and loss minimization.
2. Derivatives
Derivatives, partial derivatives, and their interpretation in the context of loss functions and model parameters.
3. Gradients
Gradient vectors, directional derivatives, the Jacobian, and the Hessian matrix in machine learning.
4. Chain Rule
The chain rule for composite functions, computational graphs, backpropagation, and automatic differentiation.
5. Optimization
Gradient descent variants, learning rates, convergence, local minima, saddle points, and second-order methods.
6. Best Practices
Gradient checking, numerical differentiation tips, autograd libraries, and common calculus pitfalls in ML.
Prerequisites
What you need before starting this course.
- Basic understanding of algebra and functions
- Familiarity with vectors and matrices (see our Linear Algebra course)
- Python with NumPy installed
- No prior calculus experience required — we start from the basics