In this tutorial, we'll think about how we can find the area under a curve. We'll first approximate this with rectangles (and trapezoids)--generally called Riemann sums. We'll then think about find the exact area by having the number of rectangles approach infinity (they'll have infinitesimal widths) which we'll use the definite integral to denote.

This 16-minute video lesson covers the Calculus-Derivative: Understanding that the derivative is just the slope of a curve at a point (or the slope of the tangent line).

This series of videos focusing on calculus covers using definite integrals with the shell and disc methods to find volumes of solids of revolution.

This 8-minute video lesson presents an intuition (but not a proof) of the Squeeze Theorem. [Calculus playlist: Lesson 7 of 156]

If a function is always smaller than one function and always greater than another (i.e. it is always between them), then if the upper and lower function converge to a limit at a point, then so does the one in between. Not only is this useful for proving certain tricky limits (we use it to prove lim (x Œ_ 0) of (sin x)/x, but it is a useful metaphor to use in life (seriously). :) This tutorial is useful but optional. It is covered in most calculus courses, but it is not necessary to progress on to the "Introduction to derivatives" tutorial.

This video looks at starting to apply stokes theorem to solve a line integral.

This video looks at Finding the curl of the vector field and then evaluating the double integral in the parameter domain.

Stokes' theorem relates the line integral around a surface to the curl on the surface. This tutorial explores the intuition behind Stokes' theorem, how it is an extension of Green's theorem to surfaces (as opposed to just regions) and gives some examples using it. We prove Stokes' theorem in another tutorial. Good to come to this tutorial having experienced the tutorial on "flux in 3D".

This video covers The beginning of a proof of stokes' theorem for a special class of surfaces. Finding the curl of our vector field.

This video looks at Figuring out a parameterization of our surface and representing ds.

This video looks at Writing our surface integral as a double integral over the domain of our parameters.

This video looks at starting to work on the line integral about the surface.

This video looks at Parametrizing a surface that can be explictly made a function of x and y.