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How to Take Partial Derivatives
We learn how to take partial derivatives and develop an intuitive understanding of them by calculating the change in volume of a cylinder. Lastly, we explore total derivatives. Up until now, we’ve...
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The Jacobian Matrix: Introducing Vector Calculus
We learn how to construct and apply a matrix of partial derivatives known as the Jacobian matrix. In the process, we also introduce vector calculus. The Jacobian matrix is a matrix containing the...
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The Hessian Matrix: Finding Minima and Maxima
In this post, we learn how to construct the Hessian matrix of a function and find out how the Hessian helps us determine minima and maxima. What is a Hessian Matrix? The Jacobian matrix helps us find...
View ArticleThe Multivariable Chain Rule
In this post we learn how to apply the chain rule to vector-valued functions with multiple variables. We’ve seen how to apply the chain rule to real number functions. Now we can extend this concept...
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Power Series: Understand the Taylor and MacLaurin Series
In this post, we introduce power series as a method to approximate unknown functions. We derive the Maclaurin series and the Taylor series in simple and intuitive terms. Differential calculus is an...
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Linearization of Differential Equations for Approximation
In this post we learn how to build linear approximations to non-linear functions and how to measure the error between our approximation and the desired function. Given a well-behaved higher-order...
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Understanding The Gradient Descent Algorithm
In this post, we introduce the intuition as well as the math behind gradient descent, one of the foundational algorithms in modern artificial intelligence. Motivation for Gradient Descent In many...
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Lagrange Multipliers: An Introduction to Constrained Optimization
In this post we explain constrained optimization using LaGrange multipliers and illustrate it with a simple example. Lagrange multipliers enable us to maximize or minimize a multivariable function...
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The Fundamental Theorem of Calculus and Integration
In this post, we introduce and develop an intuitive understanding of integral calculus. We learn how the fundamental theorem of calculus relates integral calculus to differential calculus. Integration...
View ArticleCalculus For Machine Learning and Data Science
This series of blog posts introduces multivariate calculus for machine learning. While the first few posts should be accessible to anyone with a high-school math background, the articles covering...
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