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 amazing tool to describe changes in complex systems with multiple inputs. But to unleash the power of Calculus, we need to describe

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 into higher dimensions. How does the Multivariable Chain Rule Work? Remember that the chain rule helps us differentiate nested

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 the local gradient of a non-linear function. In many applications, we are interested in optimizing a function.

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 first-order partial derivatives of a function. It gives us the slope of the function along multiple dimensions. Previously, we’ve discussed how

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 always differentiated functions with respect to one variable. Many real-life problems in areas such as physics, mechanical engineering, data science, etc., can

In this post, we are going to explain the product rule, the chain rule, and the quotient rule for calculating derivatives. We derive each rule and demonstrate it with an example. The product rule allows us to differentiate a function that includes the multiplication of two or more variables. The quotient rule enables us

In this post, we learn how to find the derivative of a function from first principles and how to apply the power rule, the sum rule, and the difference rule. We previously established that the definition of a derivative equals the following expression. Note that f'(x) is a more compact form to denote the

We introduce the basics of calculus by understanding the concept of rise over run, followed by a more formal definition of derivatives. At the heart of calculus are functions that describe changes in variables. In complex systems, we usually deal with many changing variables that depend on each other. The concept of rise over

In this post, we build an understanding of the singular value decomposition (SVD) to decompose a matrix into constituent parts. What is the Singular Value Decomposition? The singular value decomposition (SVD) is a way to decompose a matrix into constituent parts. It is a more general form of the eigendecomposition. While the eigendecomposition is

This series of blog posts aims to introduce and explain the most important mathematical concepts from linear algebra for machine learning. If you understand the contents of this series, you have all the linear algebra you’ll need to understand deep neural networks and statistical machine learning algorithms on a technical level. Most of my