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
Introducing Functions: Inputs and Outputs
Was this section helpful?
- Calculus: Early Transcendentals, James Stewart, 2015 (Cengage Learning) - A standard and widely used textbook that provides fundamental definitions of functions, their notation, types, and properties, essential for calculus beginners.
- Pattern Recognition and Machine Learning, Christopher M. Bishop, 2006 (Springer) DOI: 10.1007/b137979 - A classic textbook that systematically introduces the mathematical foundations of machine learning, including the role of functions as models and objective functions.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Provides a comprehensive overview of the mathematical concepts underlying deep learning, starting with foundational topics like functions and their application in machine learning models and optimization.
- 18.01SC Single Variable Calculus, David Jerison, Arthur Mattuck, Haynes Miller, Benjamin Brubaker, Jeremy Orloff, Heidi Burgiel, Christine Breiner, David Jordan, Joel Lewis, 2010 (MIT OpenCourseWare) - Offers a structured, university-level introduction to single variable calculus, covering the fundamental definitions, types, and behavior of functions in detail.