Calculus

Core concepts in calculus with applications to Machine Learning and optimization.

Topics

Core concepts in calculus with applications to Machine Learning and optimization.

Reference: https://www.coursera.org/learn/machine-learning-calculus

Notes

Derivatives and Their Intuition
calculus

Before jumping into the mathematics, let’s understand why calculus is so important in machine learning. The short answer: derivatives are used to…

Jun 8, 2026

Derivatives of Basic Functions
calculus

Like any language, mathematics has its own way of expressing concepts. There are two common notations for the derivative, and we will use whichever is…

Jun 8, 2026

Derivative Rules
calculus

So far, you have learned derivatives of simple functions (constants, lines, polynomials, , , , ). In order to find derivatives of more complicated…

Jun 8, 2026

Optimization
calculus

By now you have lots of tools to work with derivatives. But what are they useful for, beyond calculating rates of change? In machine learning, the main…

Jun 9, 2026

Log Loss
calculus

In the previous page you saw that minimizing the squared error leads to the mean. Now there’s another important loss function in machine learning…

Jun 11, 2026

Gradients
calculus

Now that you know what a partial derivative is, you pretty much know what a gradient is.

Jun 11, 2026

Partial Derivatives
calculus

So far, everything has been about functions of one variable: , with one input and one output. Now we move to functions of two or more variables, like ….

Jun 11, 2026

Gradient Descent
calculus

So far you have learned how to solve optimization problems using derivatives and gradients. For a function of one variable, you take the derivative,…

Jun 12, 2026

Gradient Descent in Multiple Variables
calculus

Now that you have learned gradient descent for one variable, let us extend it to functions of multiple variables.

Jun 12, 2026

Optimization Using Gradient Descent
calculus

You may remember from the Optimization page that we solved a linear regression problem (the power lines example) analytically. We set the gradient to…

Jun 12, 2026

Lab: Linear Regression with Gradient Descent
calculus

In this lab, you will build a linear regression model to predict sales based on TV marketing expenses. You will implement gradient descent from scratch…

Jun 13, 2026

Optimization in Neural Networks
calculus

In this section we will see how the optimization ideas from calculus (derivatives, gradient descent, loss functions) come together in the building…

Jun 14, 2026

Lab: Regression with a Perceptron
calculus

In this lab, we will put the optimization ideas from calculus (derivatives, gradient descent, loss functions) into practice by implementing a neural…

Jun 14, 2026

Classification with a Perceptron
calculus

We have already seen how a perceptron solves regression problems. The output was a continuous number (a price, a sales figure, etc.). But a perceptron…

Jun 15, 2026

Lab: Classification with a Perceptron
calculus

In this lab, we will implement a single-perceptron neural network for binary classification. This is the companion lab to the Classification with a…

Jun 15, 2026
 
Classification with a Neural Network
calculus

Now that you know what a perceptron is, you are just one step away from knowing what a neural network is. A neural network is a collection of…

Jun 15, 2026

Newton’s Method
calculus

So far we have used gradient descent to find the minimum of a function. It works, but it can be slow — you take many small steps, and the learning rate…

Jun 17, 2026
 
Second Derivative
calculus

In the previous page, you saw how the derivative of a derivative appeared naturally in Newton’s method for optimization. This “derivative of a…

Jun 17, 2026
 
Hessian Matrix
calculus

In the previous page, you learned the second derivative and how it helps with optimization in one variable. Now we extend this to functions of multiple…

Jun 18, 2026

Newton’s Method for Multiple Variables
calculus

Now that you know the Hessian matrix, we can extend Newton’s method to optimize functions of many variables. The Hessian plays the role that the second…

Jun 18, 2026

Lab: Neural Network with Two Layers
calculus

In this lab, you will build a neural network with two layers and train it to solve a classification problem that a single perceptron cannot handle. By…

Jun 18, 2026
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