Free online courseCalculus for Machine Learning
Duration of the online course: 7 hours and 33 minutes
New course
Master calculus for machine learning with this comprehensive online course, covering key concepts like derivatives and integral calculus tailored for AI applications.
In this free course, learn about
- Foundations of Calculus for Machine Learning
- Limits and the Definition of the Derivative
- Core Derivative Rules
- Product, Quotient, and Chain Rules
- Automatic Differentiation and Linear Models
- Single-Variable Gradient Descent and Backpropagation
- Partial Derivatives and Multivariate Gradient Descent
- Integral Calculus and Binary Classification Metrics
Course Description
Enhance your understanding of machine learning with this comprehensive online course focusing on calculus concepts tailored for artificial intelligence applications. Explore the foundational topics that underpin modern machine learning techniques, starting with Calculus I, where you'll delve into the key concept of limits, including practical exercises on calculating limits that are crucial for understanding how derivatives arise. The course progresses to Differential Calculus, a core component in machine learning, offering insights into derivative rules, power rules, and differentiation processes that help optimize algorithms.
Expand your knowledge with Automatic Differentiation, a pivotal topic for implementing efficient machine learning models, utilizing PyTorch and TensorFlow to streamline calculations. Transition seamlessly into Calculus II, focusing on partial derivatives. Engage in hands-on exercises designed to solidify your grasp of how partial derivatives function, particularly how they relate to gradient descent and optimizing cost functions such as mean squared error.
Integral calculus rounds out the course, presenting tools to master numeric integration and integral calculus rules, which play a crucial role in evaluating models using techniques like the ROC curve, an essential measure for binary classification tasks. This course offers a robust foundation in calculus tailored specifically for machine learning, equipping you with the skills needed to understand and apply mathematical concepts to real-world AI problems effectively.
Course content
- Video class: Calculus I: Limits 03m
- Exercise: Why are derivatives central to training in machine learning models?
- Video class: Intro to Differential Calculus —Topic 42 of Machine Learning Foundations 13m
- Exercise: On a distance versus time curve for a vehicle, what does the slope of the tangent line at a point represent?
- Video class: Intro to Integral Calculus –Topic 43 of Machine Learning Foundations 02m
- Exercise: Differential vs. Integral Calculus in Motion
- Video class: The Method of Exhaustion – Topic 44 of Machine Learning Foundations 06m
- Exercise: How does the method of exhaustion illustrate the core idea behind integrals used in machine learning?
- Video class: Calculus of the Infinitesimals – Topic 45 of Machine Learning Foundations 10m
- Exercise: When you zoom in on a curve at a point until it looks straight to estimate its slope, which calculus concept are you applying?
- Video class: Calculus Applications – Topic 46 of Machine Learning Foundations 08m
- Exercise: How is differential calculus primarily used when training ML models?
- Video class: Calculating Limits – Topic 47 of Machine Learning Foundations 18m
- Exercise: Evaluate the limit as x approaches 1: (x^2 - 1) / (x - 1)
- Video class: Exercises on Limits – Topic 48 of Machine Learning Foundations 01m
- Exercise: Two sided limit when one sided limits diverge with opposite signs
- Video class: Derivatives and Differentiation — Segment 2 of Subject 3, Limits 01m
- Exercise: Which expression is the differentiation equation linking limits to derivatives
- Video class: The Delta Method – Topic 49 of Machine Learning Foundations 15m
- Exercise: Using the delta method, what is the slope of the tangent to f(x)=x^2+2x+2 at x=2?
- Video class: How Derivatives Arise from Limits – Topic 50 of Machine Learning Foundations 14m
- Exercise: Using the limit definition of the derivative, what is f'(2) for f(x)=x^2+2x+2?
- Video class: Derivative Notation — Topic 51 of Machine Learning Foundations 04m
- Exercise: Which derivative notation most clearly identifies both dependent and independent variables for the first derivative?
- Video class: The Derivative of a Constant –Topic 52 of Machine Learning Foundations 01m
- Exercise: Derivative of a constant in ML calculus
- Video class: The Power Rule for Derivatives – Topic 53 of Machine Learning Foundations 01m
- Exercise: Using the power rule, what is d/dx of x^7?
- Video class: The Constant Multiple Rule for Derivatives — Topic 54 of Machine Learning Foundations 03m
- Exercise: Apply the constant multiple rule: If g(x) = x^4, what is d/dx [3 g(x)]?
- Video class: The Sum Rule for Derivatives — Topic 55 of Machine Learning Foundations 02m
- Exercise: Using the sum rule and power rule, what is d/dx of x^4 + x^9
- Video class: Exercises on Derivative Rules — Topic 56 of Machine Learning Foundations 03m
- Exercise: Find the derivative of f(x) = 10x^5 - 6x^3 - x using basic rules
- Video class: The Product Rule for Derivatives — Topic 57 of Machine Learning Foundations 03m
- Exercise: Compute dy/dx using the product rule for y = (6x^3)(7x^4)
- Video class: The Quotient Rule for Derivatives — Topic 58 of Machine Learning Foundations 04m
- Exercise: Select the correct quotient rule form for y equals w over z with w equals 4x^2 and z equals x^3 plus 1
- Video class: The Chain Rule for Derivatives — Topic 59 of Machine Learning Foundations 06m
- Exercise: Using the chain rule, compute dy/dx for y = (2x^2 + 8)^2
- Video class: Advanced Exercises on Derivative Rules — Topic 60 of Machine Learning Foundations 02m
- Exercise: Which rule should you apply first to differentiate f(x) = (3x^2 + 1) sqrt(5x - 2)?
- Video class: The Power Rule on a Function Chain — Topic 61 of Machine Learning Foundations 05m
- Exercise: Find dy dx for y equals left parenthesis 3x plus 1 right parenthesis squared using the power rule on a function chain
- Video class: Automatic Differentiation – Segment 3 of Subject 3, Limits 01m
- Exercise: Which technique enables scalable derivative computation for large machine learning models and is implemented in libraries such as PyTorch and TensorFlow?
- Video class: What Automatic Differentiation Is — Topic 62 of Machine Learning Foundations 04m
- Exercise: What best characterizes reverse mode automatic differentiation in calculus for machine learning
- Video class: Automatic Differentiation with PyTorch — Topic 63 of Machine Learning Foundations 06m
- Exercise: What is dy/dx at x = 5 for y = x^2 computed via automatic differentiation?
- Video class: Automatic Differentiation with TensorFlow — Topic 64 of Machine Learning Foundations 03m
- Exercise: Autodiff in TensorFlow: dy dx for y equals x squared at x equals 5
- Video class: The Line Equation as a Tensor Graph — Topic 65 of Machine Learning Foundations 20m
- Exercise: Which action enables gradient computation for parameters in a PyTorch linear model y=mx+b
- Video class: Machine Learning from First Principles, with PyTorch AutoDiff — Topic 66 of ML Foundations 40m
- Exercise: In a four step learning loop for linear regression with y_hat equals m x plus b, what is the role of step three?
- Video class: Calculus II: Partial Derivatives 22m
- Exercise: In linear regression y = m x + b trained with mean squared error, if ∂C/∂m > 0 and ∂C/∂b > 0 at the current parameters, which update will reduce the cost using gradient descent?
- Video class: What Partial Derivatives Are (Hands-on Introduction) — Topic 67 of Machine Learning Foundations 29m
- Exercise: Compute the slope of z with respect to y at y = -1 for z = x^2 - y^2 (x held constant)
- Video class: Partial Derivative Exercises — Topic 68 of Machine Learning Foundations 03m
- Exercise: For z = x^2 − y^2, at x = 3 and y = 0, what is the partial derivative ∂z/∂x?
- Video class: Calculating Partial Derivatives with PyTorch AutoDiff — Topic 69 of Machine Learning Foundations 05m
- Exercise: Using automatic differentiation for z = x^2 − y^2, what are the partial derivatives at (x, y) = (0, 0)?
- Video class: Advanced Partial Derivatives — Topic 70 of Machine Learning Foundations 14m
- Exercise: Compute ∂V/∂l for a cylinder with r = 3 and l = 5 where V = π r^2 l
- Video class: Advanced Partial-Derivative Exercises — Topic 71 of Machine Learning Foundations 02m
- Exercise: What is ∂A/∂r for A(r,h) = 2πr^2 + 2πrh?
- Video class: Partial Derivative Notation — Topic 72 of Machine Learning Foundations 02m
- Exercise: Which notation best emphasizes the operator when taking the partial derivative of f(x, y) with respect to x
- Video class: The Chain Rule for Partial Derivatives — Topic 73 of Machine Learning Foundations 09m
- Exercise: Given y = f(u, v) with u = g(x, z) and v = h(x, z), what is the correct expression for the partial derivative ∂y/∂x?
- Video class: Exercises on the Multivariate Chain Rule — Topic 74 of Machine Learning Foundations 01m
- Exercise: Using the multivariate chain rule for y = f(u, v) with u = g(x1, x2) and v = h(x1, x2), what is ∂y/∂x1?
- Video class: Linear Regression Fit Point by Point — Topic 75 of Machine Learning Foundations 15m
- Exercise: In the four-step loop for single-point linear regression y = m x + b, which step computes the gradient ∂C/∂m and ∂C/∂b?
- Video class: The Gradient of Quadratic Cost — Topic 76 of Machine Learning Foundations 15m
- Exercise: Compute the partial derivative dC/dm for C = (y_hat - y)^2 with y_hat = m x + b
- Video class: Gradient Descent (Hands-on with PyTorch) — Topic 77 of Machine Learning Foundations 12m
- Exercise: Which update direction reduces cost in multivariate gradient descent?
- Video class: The Gradient of Mean Squared Error — Topic 78 of Machine Learning Foundations 24m
- Exercise: Gradient of mean squared error with respect to m in linear regression y_hat = m x + b
- Video class: Backpropagation — Topic 79 of Machine Learning Foundations 06m
- Exercise: Which description best defines backpropagation during neural network training?
- Video class: Higher-Order Partial Derivatives — Topic 80 of Machine Learning Foundations 12m
- Exercise: Compute the mixed second-order partial derivative for z = x^2 + 5xy + 2y^2
- Video class: Exercise on Higher-Order Partial Derivatives — Topic 81 of Machine Learning Foundations 01m
- Exercise: For z = x^3 + 2xy, which set lists (z_xx, z_yy, z_xy) correctly?
- Video class: Integral Calculus — The Final Segment of Calculus Videos in my ML Foundations Series 02m
- Exercise: Which task in binary classification directly applies integral calculus?
- Video class: Binary Classification — Topic 82 of Machine Learning Foundations 09m
- Exercise: Which evaluation metric better captures model performance for binary classification than a single 0.5 threshold when outputs reflect varying confidence levels
- Video class: The Confusion Matrix — Topic 83 of Machine Learning Foundations 02m
- Exercise: Identify the false negative in a binary confusion matrix
- Video class: The ROC Curve (Receiver-Operating Characteristic Curve) — Topic 84 of Machine Learning Foundations 10m
- Exercise: Given a ROC curve that passes through the points FPR,TPR = 0.5,1.0 and 0.5,0.5 and 0,0.5 with the standard endpoints 0,0 and 1,1 added, what is the approximate area under the curve AUC
- Video class: What Integral Calculus Is — Topic 85 of Machine Learning Foundations 06m
- Exercise: What is the primary use of integral calculus in machine learning?
- Video class: The Integral Calculus Rules — Topic 86 of Machine Learning Foundations 05m
- Exercise: Compute the indefinite integral of x^4 + 9x^2 using standard integration rules
- Video class: Indefinite Integral Exercises — Topic 87 of Machine Learning Foundations 01m
- Exercise: Compute the indefinite integral ∫(12x^5 - x) dx
- Video class: Definite Integrals — Topic 88 of Machine Learning Foundations 07m
- Exercise: Evaluate the definite integral of 0.5 x dx from x = 1 to x = 2
- Video class: Numeric Integration with Python — Topic 89 of Machine Learning Foundations 04m
- Exercise: What is the value of the definite integral of x/2 over the interval [1, 2] computed numerically?
- Video class: Definite Integral Exercise — Topic 90 of Machine Learning Foundations 01m
- Exercise: Compute the definite integral of 2x over the interval [3, 4]
- Video class: Finding the Area Under the ROC Curve — Topic 91 of Machine Learning Foundations 03m
- Exercise: Given ROC points (0,0), (0,0.5), (0.5,0.5), (0.5,1), (1,1), what is the AUC computed via the trapezoidal rule?
- Video class: My Favorite Calculus Resources — Topic 92 of Machine Learning Foundations 04m
- Exercise: Best calculus approach to compute AUC from an ROC curve with discrete points
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