This video looks at the chain rule with triple composition.
- Author:
- Khan, Salman
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This 16-minute video lesson looks at 2010 IIT JEE Paper 1 Problem 52: Periodic Definite Integral. The second term at about minute 14 should have a positive sign. Luckily, it doesn't effect the final answer!
- Author:
- Khan, Salman
This 8-minute video lesson shows that the line integral along closed curves of conservative vector fields is zero.
- Author:
- Khan, Salman
This video looks at concavity, concave upwards and concave downwards intervals.
- Author:
- Khan, Salman
This video looks at understanding the line integral as flux through a boundary.
- Author:
- Khan, Salman
Flux can be view as the rate at which "stuff" passes through a surface. Imagine a next placed in a river and imagine the water that is flowing directly across the net in a unit of time--this is flux (and it would depend on the orientation of the net, the shape of the net, and the speed and direction of the current). It is an important idea throughout physics and is key for understanding Stokes' theorem and the divergence theorem.
- Author:
- Khan, Salman
This video looks at understanding when you can use stokes. Piecewise-smooth lines and surfaces.
- Author:
- Khan, Salman
This video looks at connecting the first and second fundamental theorems of calculus.
- Author:
- Khan, Salman
Using Green's theorem (which you should already be familiar with) to establish that the "flux" through the boundary of a region is equal to the double integral of the divergence over the region. We'll also talk about why this makes conceptual sense.
- Author:
- Khan, Salman
This video looks at deriving a unit normal vector from the surface parametrization.
- Author:
- Khan, Salman
This 6-minute video lesson looks at approximating f(x)=cos x using a Maclauren Series (special case of a Taylor series at x=0).
- Author:
- Khan, Salman
This 10-minute video lesson provides an introduction to the curl of a vector field.
- Author:
- Khan, Salman
This 10-minute video lesson examines the mechanics of calculating curl.
- Author:
- Khan, Salman
This 9-minute video lesson looks at how to solve a definite integral with substitution (or the reverse chain rule).
- Author:
- Khan, Salman
This 10-minute video lesson provides more on why the antiderivative and the area under a curve are essentially the same thing.
- Author:
- Khan, Salman
This 10-minute video lesson provides examples of using definite integrals to find the area under a curve.
- Author:
- Khan, Salman
This 10-minute video lesson provides more examples of using definite integrals to calculate the area between curves.
- Author:
- Khan, Salman
This 10-minute video lecture provides more on why the antiderivative and the area under a curve are essentially the same thing.
- Author:
- Khan, Salman
This video looks at definite integrals and negative area.
- Author:
- Khan, Salman