Calculus Fundamentals for Machine Learning
Chapter 1: Why Calculus for Machine Learning?
The Role of Math in Machine Learning
Introducing Functions: Inputs and Outputs
Visualizing Functions: Graphs
What is a Limit?
Intuition Behind Limits
Connecting Functions and Limits to ML
Quiz for Chapter 1
Chapter 2: Derivatives: Measuring Change
Rate of Change: Average vs Instantaneous
The Derivative: Slope of a Tangent Line
Derivative Notation (Leibniz and Lagrange)
Calculating Derivatives: The Power Rule
Calculating Derivatives: Constants and Sums
Introduction to Higher-Order Derivatives
Practice: Calculating Simple Derivatives
Quiz for Chapter 2
Chapter 3: Optimization with Derivatives
Finding Maximum and Minimum Points
Optimization: Why Minimize or Maximize?
Cost Functions in Machine Learning
Goal: Minimizing the Cost Function
Introduction to Gradient Descent
How Derivatives Guide Gradient Descent
Visualizing Gradient Descent
Quiz for Chapter 3
Chapter 4: Handling Multiple Inputs: Partial Derivatives
Functions of Multiple Variables
Partial Derivatives: The Concept
Calculating Partial Derivatives
Partial Derivative Notation
The Gradient Vector
Geometric Meaning of the Gradient
Practice: Calculating Partial Derivatives and Gradients
Quiz for Chapter 4
Chapter 5: Calculus in Action: Simple Optimization
Recap: Optimization Goal and Gradient Descent
Example: Simple Linear Regression Model
Defining a Cost Function for Linear Regression
Calculating Gradients for the Cost Function
Performing a Gradient Descent Step
The Learning Rate Parameter
Putting It All Together: The Optimization Process
Hands-on Practical: Manual Gradient Calculation
Quiz for Chapter 5
Example: Simple Linear Regression Model
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- An Introduction to Statistical Learning: With Applications in R, Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani, 2013 (Springer) DOI: 10.1007/978-1-4614-7137-0 - A foundational textbook offering a clear introduction to simple linear regression, its principles, and interpretation, serving as an excellent entry point for machine learning concepts.
- Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, 2020 (Cambridge University Press) - Provides the mathematical rigor behind machine learning algorithms, including detailed explanations of derivatives, gradients, and optimization techniques essential for understanding linear regression training.
- Machine Learning, Andrew Ng, 2012 Coursera (DeepLearning.AI and Stanford Online) - A widely acclaimed online course that clearly demonstrates how simple linear regression is formulated and optimized using gradient descent, providing practical examples and intuition.