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.
This video provides Part 2 of shell method with 2 functions of y.
This video covers doing some hairy algebra and arithmetic to evaluate the definite integral from the last video.
This 11-minute video lesson provides an introduction to partial derivatives.
This 10-minute video lesson provides more explanation of partial derivatives.
Let's jump out of that boring (okay, it wasn't THAT boring) 2-D world into the exciting 3-D world that we all live and breath in. Instead of functions of x that can be visualized as lines, we can have functions of x and y that can be visualized as surfaces. But does the idea of a derivative still make sense? Of course it does! As long as you specify what direction you're going in. Welcome to the world of partial derivatives!
This 10-minute video lesson looks at Partial Derivatives of Vector-Valued Functions.
This 17-minute video lesson shows that if a vector field is the gradient of a scalar field, then its line integral is path independent.
This 10-minute video lesson shows how to use a polynomial to approximate a function at f(0).
This 10-minute video lesson looks at how to approximate a function with a polynomial by making the derivatives equal at f(0) (Maclauren Series).
This 10-minute video lesson show how to approximate cos x with a Maclaurin series.
In this 10-minute video lesson (part 6 of the Polynomial approximation of functions series) a pattern emerges!
This 10-minute video lesson examines the most amazing conclusion in mathematics!