This 9-minute video lesson looks at 2A of the 2008 Calculus BC exam (free response).
This 11-minute video lesson looks at parts 2B and 2C of the 2008 BC exam (free response).
This 5-minute video lesson looks at part 2D of the 2008 Calculus BC exam free-response section.
This 25-minute video lesson looks at using the first and second derivatives to identify critical points and inflection points and to graph the function.
This video looks at the chain rule definition and example.
This 9-minute video lesson provides examples using the Chain Rule.
This video provides a chain rule introduction.
This video looks at the chain rule for derivative of 2^x.
This video looks at the chain rule with triple composition.
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!
This 8-minute video lesson shows that the line integral along closed curves of conservative vector fields is zero.
This video looks at concavity, concave upwards and concave downwards intervals.
This video looks at understanding the line integral as flux through a boundary.
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.
This video looks at understanding when you can use stokes. Piecewise-smooth lines and surfaces.
This video looks at connecting the first and second fundamental theorems of calculus.
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.
This video looks at deriving a unit normal vector from the surface parametrization.
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).
This 10-minute video lesson provides an introduction to the curl of a vector field.