For example, in fluid dynamics, take the case that the velocity field under consideration is the flow velocity itself, and the quantity of interest is the temperature of the fluid. Then the material derivative describes the temperature evolution of a certain fluid parcel in time, as it is being moved along its pathline (trajectory) while following the fluid flow.
Names
There are many other names for the material derivative, including:
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as .
Notation
A variety of notations are used to denote the time derivative. In addition to the normal (Leibniz's) notation,
A very common short-hand notation used, especially in physics, is the 'over-dot'. I.E.
Higher time derivatives are also used: the second derivative with respect to time is written as
with the corresponding shorthand of .
As a generalization, the time derivative of a vector, say:
is defined as the vector whose components are the derivatives of the components of the original vector. That is,
Use in physics
Time derivatives are a key concept in physics. For example, for a changing position , its time derivative is its velocity, and its second derivative with respect to time, , is its acceleration. Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk. See motion graphs and derivatives.
How to Solve Time Derivatives (Chain Rule, Implicit Differentiation, dr/dθ)
In this video, you can learn how to solve for time derivatives. You can use the chain rule from calculus to find the time derivative of a composite function. This is incredibly important when you do derivatives of polar coordinates and such.
Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.
published: 10 Jan 2020
Time Differentiation & Integration Property
Time Differentiation & Integration Property
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Ms. Gowthami Swarna, Tutorials Point India Private Limited.
published: 27 Jan 2018
Derivative as a concept | Derivatives introduction | AP Calculus AB | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/derivative-as-a-concept
Why we study differential calculus. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-derivative-intuition/v/derivative-as-a-concept?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-limits-opt-vids/v/proving-a-limit-using-epsilon-delta-definition?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massa...
published: 19 Jul 2017
The paradox of the derivative | Chapter 2, Essence of calculus
What is an "instantaneous rate of change" when change happens across time?
Help fund future projects: https://www.patreon.com/3blue1brown
This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks
Home page: https://www.3blue1brown.com/
Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.
Thanks to these viewe...
published: 29 Apr 2017
Introductory Fluid Mechanics L1 p6: Acceleration - Material Derivative
published: 01 Jul 2015
Material time derivative
Full course at: http://johnfoster.pge.utexas.edu/PGE323M-ResEngineeringIII/course-mat
published: 15 May 2017
03 Vector time derivatives
This project was created with Explain Everything™ Interactive Whiteboard for iPad.
published: 08 Apr 2021
Total Time Derivative Intuition
The total time derivative will appear frequently throughout this Transport Phenomena Course. This total time derivative is a method by which we examine some quantity changing with respect to time and spatial coordinates in our multivariable function.
This timeline is meant to help you better understand what the partial time derivative is:
0:00 Introduction.
0:12 Setup to understanding the total time derivative.
0:44 What is a total derivative?
2:55 Outro
Follow & Support StudySession:
https://www.patreon.com/studysessionyt
http://www.studysession.ca
Email Us: [email protected]
https://teespring.com/stores/studysession
https://twitter.com/StudySessionYT
https://instagram.com/StudySessionyt/
This video is part of our Transport Phenomena course. Transport phenomena is a...
In this video, you can learn how to solve for time derivatives. You can use the chain rule from calculus to find the time derivative of a composite function. Th...
In this video, you can learn how to solve for time derivatives. You can use the chain rule from calculus to find the time derivative of a composite function. This is incredibly important when you do derivatives of polar coordinates and such.
Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.
In this video, you can learn how to solve for time derivatives. You can use the chain rule from calculus to find the time derivative of a composite function. This is incredibly important when you do derivatives of polar coordinates and such.
Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.
Time Differentiation & Integration Property
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Ms. Gowthami Swarna, Tutori...
Time Differentiation & Integration Property
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Ms. Gowthami Swarna, Tutorials Point India Private Limited.
Time Differentiation & Integration Property
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Ms. Gowthami Swarna, Tutorials Point India Private Limited.
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation...
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/derivative-as-a-concept
Why we study differential calculus. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-derivative-intuition/v/derivative-as-a-concept?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-limits-opt-vids/v/proving-a-limit-using-epsilon-delta-definition?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/derivative-as-a-concept
Why we study differential calculus. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-derivative-intuition/v/derivative-as-a-concept?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-limits-opt-vids/v/proving-a-limit-using-epsilon-delta-definition?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
What is an "instantaneous rate of change" when change happens across time?
Help fund future projects: https://www.patreon.com/3blue1brown
This video was support...
What is an "instantaneous rate of change" when change happens across time?
Help fund future projects: https://www.patreon.com/3blue1brown
This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks
Home page: https://www.3blue1brown.com/
Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.
Thanks to these viewers for their contributions to translations
Dutch: @LFWarsen
Hebrew: Omer Tuchfeld
Italian: mulstato
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
What is an "instantaneous rate of change" when change happens across time?
Help fund future projects: https://www.patreon.com/3blue1brown
This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks
Home page: https://www.3blue1brown.com/
Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.
Thanks to these viewers for their contributions to translations
Dutch: @LFWarsen
Hebrew: Omer Tuchfeld
Italian: mulstato
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
The total time derivative will appear frequently throughout this Transport Phenomena Course. This total time derivative is a method by which we examine some qua...
The total time derivative will appear frequently throughout this Transport Phenomena Course. This total time derivative is a method by which we examine some quantity changing with respect to time and spatial coordinates in our multivariable function.
This timeline is meant to help you better understand what the partial time derivative is:
0:00 Introduction.
0:12 Setup to understanding the total time derivative.
0:44 What is a total derivative?
2:55 Outro
Follow & Support StudySession:
https://www.patreon.com/studysessionyt
http://www.studysession.ca
Email Us: [email protected]
https://teespring.com/stores/studysession
https://twitter.com/StudySessionYT
https://instagram.com/StudySessionyt/
This video is part of our Transport Phenomena course. Transport phenomena is a key engineering science. Within this Transport Phenomena course we will be discussing transport of momentum, mass and energy between various systems.
The total time derivative will appear frequently throughout this Transport Phenomena Course. This total time derivative is a method by which we examine some quantity changing with respect to time and spatial coordinates in our multivariable function.
This timeline is meant to help you better understand what the partial time derivative is:
0:00 Introduction.
0:12 Setup to understanding the total time derivative.
0:44 What is a total derivative?
2:55 Outro
Follow & Support StudySession:
https://www.patreon.com/studysessionyt
http://www.studysession.ca
Email Us: [email protected]
https://teespring.com/stores/studysession
https://twitter.com/StudySessionYT
https://instagram.com/StudySessionyt/
This video is part of our Transport Phenomena course. Transport phenomena is a key engineering science. Within this Transport Phenomena course we will be discussing transport of momentum, mass and energy between various systems.
In this video, you can learn how to solve for time derivatives. You can use the chain rule from calculus to find the time derivative of a composite function. This is incredibly important when you do derivatives of polar coordinates and such.
Book used: R. C. Hibbeler and K. B. Yap, Mechanics for engineers - dynamics. Singapore: Pearson Education, 2013.
Time Differentiation & Integration Property
Watch more videos at https://www.tutorialspoint.com/videotutorials/index.htm
Lecture By: Ms. Gowthami Swarna, Tutorials Point India Private Limited.
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/ap-calculus-ab/ab-differentiation-1-new/ab-2-1/v/derivative-as-a-concept
Why we study differential calculus. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/math/ap-calculus-ab/ab-derivative-intro/ab-derivative-intuition/v/derivative-as-a-concept?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
Missed the previous lesson? https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-continuity/ab-limits-opt-vids/v/proving-a-limit-using-epsilon-delta-definition?utm_source=YT&utm_medium=Desc&utm_campaign=APCalculusAB
AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan AcademyÕs AP Calculus AB channel: https://www.youtube.com/channel/UCyoj0ZF4uw8VTFbmlfOVPuw?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
What is an "instantaneous rate of change" when change happens across time?
Help fund future projects: https://www.patreon.com/3blue1brown
This video was supported in part by Art of Problem Solving: https://aops.com/3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: http://3b1b.co/lessons/derivatives#thanks
Home page: https://www.3blue1brown.com/
Note, to illustrate my point for the target audience of a new calculus student, I discussed a hypothetical speedometer that makes distance measurements over a very small time. Interestingly, most actual speedometers in modern cars work by analyzing the induced current of a spinning magnet, which is in some sense the universe implementing the derivative.
Thanks to these viewers for their contributions to translations
Dutch: @LFWarsen
Hebrew: Omer Tuchfeld
Italian: mulstato
Vietnamese: @ngvutuan2811
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: http://3b1b.co/recommended
Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Reddit: https://www.reddit.com/r/3Blue1Brown
The total time derivative will appear frequently throughout this Transport Phenomena Course. This total time derivative is a method by which we examine some quantity changing with respect to time and spatial coordinates in our multivariable function.
This timeline is meant to help you better understand what the partial time derivative is:
0:00 Introduction.
0:12 Setup to understanding the total time derivative.
0:44 What is a total derivative?
2:55 Outro
Follow & Support StudySession:
https://www.patreon.com/studysessionyt
http://www.studysession.ca
Email Us: [email protected]
https://teespring.com/stores/studysession
https://twitter.com/StudySessionYT
https://instagram.com/StudySessionyt/
This video is part of our Transport Phenomena course. Transport phenomena is a key engineering science. Within this Transport Phenomena course we will be discussing transport of momentum, mass and energy between various systems.
For example, in fluid dynamics, take the case that the velocity field under consideration is the flow velocity itself, and the quantity of interest is the temperature of the fluid. Then the material derivative describes the temperature evolution of a certain fluid parcel in time, as it is being moved along its pathline (trajectory) while following the fluid flow.
Names
There are many other names for the material derivative, including: