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Calculus for Data Science & AI
Rating: 4.6 out of 5(3 ratings)
316 students

Calculus for Data Science & AI

Master derivatives, gradients, backpropagation, and autodiff for machine learning with PyTorch
Created byTensor Teach
Last updated 3/2026
English

What you'll learn

  • Understand how calculus powers machine learning models, loss functions, and optimization
  • Compute derivatives and gradients by hand for regression and neural network models
  • Apply gradient descent and backpropagation to train models from scratch in Python
  • Use PyTorch autodiff to efficiently train modern deep learning models

Course content

3 sections • 17 lectures • 1h 36m total length

  • Models, Loss, and Learning as Functions2:50

    See how machine learning models are functions that map inputs to outputs, tuned by parameters and architectures, and optimized with gradient descent to improve accuracy.

  • Models, Loss, and Learning as Functions6:30

    Explore how loss functions like mean squared error and cross entropy evaluate model predictions, compute gradients, and update parameters via gradient descent to reduce error across epochs.

  • Derivatives: Introducing the Power Rule and Chain Rule9:06

    Explore derivatives by applying the power rule to x squared and the chain rule to composite functions, with a note on backpropagation and a future loss function.

  • Calculating The Derivative of a Loss Function7:04

    Explore how to compute the derivative of a mean squared error loss with respect to the model weight W using the chain rule, backpropagation, and gradient updates.

  • Introduction to Gradient Descent4:05

    Explore gradient descent, an algorithm that updates model parameters using the loss derivative, negating the gradient with a learning rate to move toward lower loss across billions of parameters.

  • Notebook for Updating Single Parameter Model Using Gradient Descent8:28

    Demonstrates updating a single parameter w with gradient descent to fit synthetic data, using a ground-truth w of 2, a mean squared error loss, and a learning rate to converge.

Requirements

  • Basic algebra and familiarity with Python; prior exposure to machine learning concepts is helpful but not required

Description

Calculus is the foundation of modern machine learning and AI—but most courses either stay too theoretical or skip the math entirely. This course bridges that gap.

Calculus for Data Science & AI is designed to help you truly understand how machine learning models learn, using calculus as a practical tool—not just abstract theory.

Instead of memorizing formulas, you’ll learn how calculus directly powers core concepts like loss functions, gradient descent, and neural networks.

We start by reframing machine learning models as mathematical functions and show how learning is simply the process of minimizing error. From there, you’ll build a strong intuition for derivatives, slopes, and sensitivity—then apply them step-by-step to real models.

As the course progresses, you’ll move into multivariable calculus, gradients, and Jacobians—key tools for understanding how modern AI systems operate under the hood.

You’ll then connect theory to practice by:

  • Deriving backpropagation by hand

  • Training a neural network from scratch using NumPy

  • Understanding how gradients flow through deep networks

Finally, you’ll explore automatic differentiation, the engine behind modern ML frameworks, and see how tools like PyTorch handle gradient computation at scale.

By the end of this course, you won’t just use machine learning—you’ll understand how it works at a fundamental level.

This course is ideal for intermediate learners who want to go beyond high-level intuition and gain a deeper, more technical understanding of AI systems.

Who this course is for:

  • Data scientists, ML engineers, and developers who want to deeply understand calculus behind AI and build models from first principles

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