In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property that its line integral is path independent; the choice of any path between two points does not change the value of the line integral. Path independence of the line integral is equivalent to the vector field under the line integral being conservative. A conservative vector field is also irrotational; in three dimensions, this means that it has vanishing curl. An irrotational vector field is necessarily conservative provided that the domain is simply connected. Conservative vector fields appear naturally in mechanics: They are vector fields representing forces of physical systems in which energy is conserved. For a conservative system, the work done in moving along a path in a configuration space depends on only the endpoints of the path, so it is possible to define potential energy that is independent of the actual path taken. (Wikipedia).
This video explains how to determine if a vector field is conservative. http://mathispower4u.yolasite.com/
From playlist Line Integrals
Worldwide Calculus: Conservative Vector Fields
Lecture on 'Conservative Vector Fields' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
11_9_2 Conservative Vector Fields
The prerequisites to call a vector field conservative.
From playlist Advanced Calculus / Multivariable Calculus
Conservative Vector Fields - The Definition and a Few Remarks
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Conservative Vector Fields - The Definition and a Few Remarks. In this video, I give the definition of a conservative vector field and the potential function.
From playlist All Videos - Part 7
How to Determine if a Vector Field is Conservative
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Determine if a Vector Field is Conservative. A really simple example.
From playlist Calculus
Conservative Vector Fields | Calculus 3 -- Vector Calculus
In this video, we discuss conservative vector fields. This is a topic that many students find difficult when studying vector calculus. In the video, we recall the definition, state the relevant theorems concerning conservative vector fields, and work through some examples. Line Integral E
From playlist All Videos
Calculus 3: Line Integrals (39 of 44) Why is a Gravitational Field Conservative?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain why is a gravitational field conservative. Next video in the series can be seen at: https://youtu.be/u49h994rDdc
From playlist CALCULUS 3 CH 6 LINE INTEGRALS
Introduction to Vector Fields This video discusses, 1) The definition of a vector field. 2) Examples of vector fields including the gradient, and various velocity fields. 3) The definition of a conservative vector field. 4) The definition of a potential function. 5) Test for conservative
From playlist Calculus 3
Finding a Potential for a Conservative Vector Field
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Finding a Potential for a Conservative Vector Field. In this video, I find the potential for a conservative vector field.
From playlist All Videos - Part 7
INTRODUCTION to VECTOR CALCULUS calculus 3
This video is the first in a series of videos which serve as an introduction to vector calculus and calculus 3. These videos are intended as supplemental material for the course MATH2021 which I am presently teaching at the University of Sydney. 0:00 Introduction and chit chat 2:48 Main
From playlist All Videos
Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative)
Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative): What Vector Fields are, and what they look like. We discuss graphing Vector Fields in 2-D and 3-D and talk about what a Conservative Vector Field means.
From playlist Calculus 3 (Full Length Videos)
ME564 Lecture 25: Stokes' theorem and conservative vector fields
ME564 Lecture 25 Engineering Mathematics at the University of Washington Stokes' theorem and conservative vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http://faculty.washington.edu/sbrunton/
From playlist Engineering Mathematics (UW ME564 and ME565)
ME564 Lecture 24: Directional derivative, continuity equation, and examples of vector fields
ME564 Lecture 24 Engineering Mathematics at the University of Washington Directional derivative, continuity equation, and examples of vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L24.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http://facult
From playlist Engineering Mathematics (UW ME564 and ME565)
Are all vector fields the gradient of a potential? ... and the Helmholtz Decomposition
This video asks a classic question: are all vector fields the gradient of a potential field? The answer is no, but by understanding why, we prepare ourselves for potential flows in the next videos. @eigensteve on Twitter eigensteve.com databookuw.com %%% CHAPTERS %%% 0:00 Introducti
From playlist Engineering Math: Vector Calculus and Partial Differential Equations
Math 032 Multivariable Calculus 21 111414: Conservative Vector Fields
Fundamental theorem of Calculus (conservative vector fields); path independent integrals; closed loop condition; checking if a field is conservative
From playlist Course 4: Multivariable Calculus (Fall 2014)
In this video, I give a broad overview of vector calculus, focusing more on the main concepts rather than explicit calculations. I try to emphasize how the concepts relate, and that they should correspond to what we intuitively think they are. More precisely, I'm covering the following t
From playlist Multivariable Calculus