How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives

Introduction By this point in our series on partial derivates, we not only have expanded upon the idea of multivariate equations, but also introduced the taking of partial derivatives and their associated tangent planes/linear approximations. If you have not referenced these items, we highly recommend it, for as we proceed in our application of theseContinue reading “How to Use Directional Derivatives For Machine Learning: Topics of Partial Derivatives”

Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives

Overview Up to this point, we have really highlighted the nuts and bolts of working with partial derivatives. Firstly, it began by elaborating the roles of equations comprised of multiple variables. We extrapolate on those insights in this article. Secondly, we took a brief detour to examine the nuances of limits and continuity in theseContinue reading “Guide to Tangent Planes and Linear Approximation: Topics of Partial Derivatives”

A Guide to Partial Derivatives: Topics of Partial Derivatives

Setting the Ground on Partial Derivatives Our series which elaborates on the topic of partial derivatives began first by introducing functions of multiple variables. An understanding of how these functions operate is integral to executing partial derivatives. If you need a refresher on this subject before embarking further, check out this article. Furthermore, limits areContinue reading “A Guide to Partial Derivatives: Topics of Partial Derivatives”

Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives

Overview of Functions With Multiple Variables If you’ve been following in our blog, you may have found our discussion of vector calculus before arriving here. If not, it may prove useful to start with this topic; you may find it here. Nevertheless, limits and continuity are fundamental to conceptualizing the various aspects of calculus, andContinue reading “Limits and Continuity Multi-Variable Functions: Topics of Partial Derivatives”

Modeling Functions of Multiple Variables: Topics of Partial Derivatives

Introduction to Functions of Multiple Variables Prior to now, we have quite frequently worked with functions that relate a single variable to another variable. These functions tend to take the form: Here, f(x) represents the traditional variable y. However, in this article, we investigate higher functions that rely on relationships between multiple variable inputs. WeContinue reading “Modeling Functions of Multiple Variables: Topics of Partial Derivatives”

Arc Length and Curvature: Computations for Vector Calculus

The Arc Length and Curvature Question Computing the arc length and curvature of various functions is one of the principal applications of the vectorial calculus we have just learned. Our first article provided a broad introduction into the world of calculus. The subsequent article takes time investigating the dot product and cross product in depth.Continue reading “Arc Length and Curvature: Computations for Vector Calculus”

Vector Differentiation and Vector Integration: Vector Calculus

Vector Differentiation and Integration: An Intro Vector functions can be readily subjected to computations of differentiation and integration in order to derive different components of space curves. Our first article on the subject of vector calculus laid out the various aspects of vector calculus. This included a review on vectors, examination of certain types ofContinue reading “Vector Differentiation and Vector Integration: Vector Calculus”

Vector Functions and Their Uses: Graphing and Applications

Vector Functions: The Scoop If you read our previous post on vector calculus, you likely observed an extensive documentation of topics within the subject. And if you arrived here having just explored our post on dot products and cross products, then you are already aware of the useful computations associated with vectors. However, these computationsContinue reading “Vector Functions and Their Uses: Graphing and Applications”

Cross Product and Dot Product Computation : Vector Calculations

Cross Product and Dot Product Our previous article discussing nuances of vector calculus presented features of the dot product and cross product. These vector computations, though not too complex, are nevertheless fundamental to performing higher level methods. This article provides proofs for these functions to foment comprehension of their governing dynamics. Furthermore, we analyze severalContinue reading “Cross Product and Dot Product Computation : Vector Calculations”

Stuck On Vector Calculus? We Got You Covered.

The word ‘calculus’ itself is sufficient to make the average person cower away, let alone attaching obscure adjectives to such a terrifying concept. Nevertheless, vector calculus opens the portal to a much higher of mathematical computation, and for those in specialized fields, has a wide range of applications. This post serves to provide some clarityContinue reading “Stuck On Vector Calculus? We Got You Covered.”