Differential operators | Generalizations of the derivative | Differential forms
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior derivative was first described in its current form by รlie Cartan in 1899. The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is thought of as measuring the flux through an infinitesimal k-parallelotope at each point of the manifold, then its exterior derivative can be thought of as measuring the net flux through the boundary of a (k + 1)-parallelotope at each point. (Wikipedia).
What is a Tensor? Lesson 24: The Exterior Derivative - formal introduction
What is a Tensor? Lesson 24: The Exterior Derivative In this lesson we meet the exterior derivative in a formal setting by asserting its properties and proving its existence and uniqueness.
From playlist What is a Tensor?
Derivatives are the main object of study in differential calculus. They describe rates of change of functions. That makes them incredibly useful in all of science, as many models can be expressed by describing the changes over time (e.g. of physical quantities). However, the abstract defin
From playlist Summer of Math Exposition Youtube Videos
definition of derivative for a rational function
Here we will use the definition of derivative to find the derivative of a rational function. This is a slightly harder calculus 1 problem so be sure you practice it a few times and make sure you can do it on your own. Get a derivative t-shirt: ๐ https://bit.ly/derivativetshirt Use "WELCO
From playlist Sect 2.7, Definition of Derivative
What is implicit differentiation?
โบ My Derivatives course: https://www.kristakingmath.com/derivatives-course Most often in calculus, you deal with explicitly defined functions, which are functions that are solved for y in terms of x. In that case, finding the derivative is usually really simple, because you just call the
From playlist Popular Questions
Calculus - What is a Derivative? (1 of 8) Overview
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general overview and the definition of โWhat is a derivative?โ
From playlist CALCULUS 1 CH 2 WHAT IS A DERIVATIVE?
Lecture 6: Exterior Derivative (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
How to use implicit differentiation with trig
๐ Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a function is called differentiation. A function is said to
From playlist Find the Derivative using Implicit Differentiation
Implicit differentiation using power rule
๐ Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a function is called differentiation. A function is said to
From playlist Find the Derivative using Implicit Differentiation
Maxwell's Equations via Differential Forms Part I
This lesson is NOT prerequisite for a course in QED. The lesson does a fast review the elementary processes and notation of differential forms in preparation for a third way to express Maxwell's equations. Viewers are expected to have already been exposed to the topic of differential forms
From playlist QED- Prerequisite Topics
Maxwell's Equations Via Differential Forms 5 (Final)
This is the last lecture regarding the compression of Maxwells' Equations from the classic presentation in standard vector calculus to the language of differential forms. By the end of this lecture we will find Maxwell's equations inside the two elegant equations dF = 0 and *d*F = J. Here
From playlist QED- Prerequisite Topics
Lecture 9: Discrete Exterior Calculus (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Maxwell's Equations via Differential Forms Part 3
In this less we study the link between the curl and divergence of a vector fields and the language of differential forms. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://apps.apple.co
From playlist QED- Prerequisite Topics
Differential Forms | The exterior derivative and vector calculus.
We describe the operators from classical vector calculus in terms of the exterior derivative, the Hodge operator, and differential forms. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespring.com/stores/michael-penn-math Personal Website: h
From playlist Differential Forms
This lecture reviewed the basic properties of the wedge product and extended the discussion concerning gradient fields and the exterior derivative. We make a number of mathematical definitions concerning the wedge product (which appears in geometric algebra), the exterior derivative, gradi
From playlist MATH2305 -- Semester 1 2022
In this video I take a look at the slope of a curve (that is not straight line).
From playlist Biomathematics
Maxwell's Equations From Differential Forms - 4
In this lesson we discuss why we need to understand the divergence and curl of a 2-form. We discuss why the magnetic field is a "pseudovector" and how to model the magnetic field as a 2-form. Finally we demonstrate how the divergence and curl of a pseudovector can be naturally described in
From playlist QED- Prerequisite Topics
Implicit differentiation using the chain and product rule with cosine
๐ Learn how to find the derivative of an implicit function. The derivative of a function, y = f(x), is the measure of the rate of change of the function, y, with respect to the variable x. The process of finding the derivative of a function is called differentiation. A function is said to
From playlist Find the Derivative using Implicit Differentiation
Computing the exterior derivative and the wedge product | Vector Calculus | Geometric Algebra
In this video, we compute the exterior derivative, emphasizing particular properties of the wedge product. This is an example video for vector calculus and is important for studying geometric algebra My textbook on vector calculus is available here: https://github.com/Kylebroder/VectorCal
From playlist MATH2305 -- Semester 1 2022