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
Finding Maximum and Minimum Points
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- Calculus, James Stewart, Daniel K. Clegg, Saleem Watson, 2020 (Cengage Learning) - A standard undergraduate calculus textbook that provides a comprehensive treatment of derivatives and their applications, including finding local and absolute maxima and minima.
- Mathematics for Machine Learning, Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, 2020 (Cambridge University Press) DOI: 10.1017/9781108679901 - Provides a rigorous yet accessible introduction to the mathematical foundations essential for machine learning, including a dedicated chapter on optimization that clearly explains derivatives in the context of finding minima for cost functions.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - Chapter 4, "Numerical Computation," covers optimization algorithms and the role of derivatives in finding minima for cost functions, offering a foundational understanding relevant to machine learning.
- Single Variable Calculus, Prof. Dr. David Jerison, 2010 (MIT OpenCourseWare) - This free online course from MIT provides lectures and materials covering fundamental concepts of single-variable calculus, including finding maxima and minima using derivatives.