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Calculus - Line Integrals and Green's Theorem: Green's Theorem
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It is sometimes easier to take a double integral (a particular double integral as we'll see) over a region and sometimes easier to take a line integral around the boundary. Green's theorem draws the connection between the two so we can go back and forth. This tutorial proves Green's theorem and then gives a few examples of using it. If you can take line integrals through vector fields, you're ready for Mr. Green.

Subject:
Calculus
Math
Material Type:
Activity/Lab
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
10/10/2018
Calculus - Line Integrals and Green's Theorem: Line Integrals For Scalar Functions
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With traditional integrals, our "path" was straight and linear (most of the time, we traversed the x-axis). Now we can explore taking integrals over any line or curve (called line integrals).

Subject:
Calculus
Math
Material Type:
Activity/Lab
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
10/10/2018
Calculus - Line Integrals and Green's Theorem: Line Integrals In Vector Fields
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You've done some work with line integral with scalar functions and you know something about parameterizing position-vector valued functions. In that case, welcome! You are now ready to explore a core tool math and physics: the line integral for vector fields. Need to know the work done as a mass is moved through a gravitational field. No sweat with line integrals.

Subject:
Calculus
Math
Material Type:
Activity/Lab
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Salman Khan
Date Added:
10/10/2018
Calculus: Mean Value Theorem
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If over the last hour on the highway, you averaged 60 miles per hour, then you must have been going exactly 60 miles per hour at some point. This is the gist of the mean value theorem (which generalizes the idea for any continuous, differentiable function).

Subject:
Calculus
Math
Material Type:
Lesson
Provider:
Khan Academy
Author:
Salman Khan
Date Added:
05/03/2018
Calculus: Mean Value Theorem
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This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]

Subject:
Calculus
Math
Material Type:
Lesson
Provider:
Khan Academy
Author:
Salman Khan
Date Added:
02/20/2011
Calculus: Minima, Maxima and Critical Points
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Can calculus be used to figure out when a function takes on a local or global maximum value? Absolutely. Not only that, but derivatives and second derivatives can also help us understand the shape of the function (whether they are concave upward or downward). If you have a basic conceptual understanding of derivatives, then you can start applying that knowledge here to identify critical points, extrema, inflections points and even to graph functions.

Subject:
Calculus
Math
Material Type:
Lesson
Provider:
Khan Academy
Author:
Salman Khan
Date Added:
05/03/2018