This 17-minute video lesson shows how to use line integrals to find the work done on a particle moving through a vector field.
This 13-minute video looks at approximating a function at 0 using a polynomial.
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).
This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]
This 17-minute video lesson looks at the iIntuition behind the Mean Value Theorem. [Calculus playlist: Lesson 55 of 156]
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.
This video looks at minimizing combined area.
Using calculus to solve optimization problems.
This video looks at minimizing the cost of a storage container.
This 10-minute video lesson provides more examples of taking derivatives.
This 13-minute video example provides more limit examples.
This video looks at more limits at infinity.
This 9-minute video lesson introduces the calculus series and discusses why we study differential calculus.
This video looks at Optimizing box volume analytically.
This video looks at Optimizing box volume graphically.
This video looks at Optimizing profit at a shoe factory.
This video looks at determining the proper orientation of a boundary given the orientation of the normal vector.
This video looks at determining the proper orientation of the boundary given the orientation of the surface.
This 8-minute video lesson provides understanding for how to parametrize a reverse path for the same curve.
This video looks at Parameterizing the surface.