This 10-minute video lesson looks at finding the sum of an infinite geometric series.
- Author:
- Khan, Salman
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This 10-minute video lesson take the revolution around something other than one of the axes.
- Author:
- Khan, Salman
This 4-minute video lesson looks at the last part of the problem in part 7 (see previous video lesson).
- Author:
- Khan, Salman
This video looks at the example showing how to find the volume of a solid of revolution (constructed by rotating around the x-axis) using the shell method (this could have been done with the disk method as well).
- Author:
- Khan, Salman
You want to rotate a function around a vertical line, but do all your integrating in terms of x and f(x), then the shell method is your new friend. It is similarly fantastic when you want to rotate around a horizontal line but integrate in terms of y.
- Author:
- Khan, Salman
This 9-minute video lesson uses the \shell method\ to rotate about the y-axis.
- Author:
- Khan, Salman
This video covers using the shell method to rotate around a vertical line.
- Author:
- Khan, Salman
This video looks at the shell method with two functions of y.
- Author:
- Khan, Salman
This video looks at showing explicit and implicit differentiation give same result.
- Author:
- Khan, Salman
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.
- Author:
- Khan, Salman
This 7-minute video lesson examines the Sine Taylor Series at 0 (Maclaurin).
- Author:
- Khan, Salman
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).
- Author:
- Khan, Salman
This video looks at the speed of shadow of diving bird.
- Author:
- Khan, Salman
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 _ 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.
- Author:
- Khan, Salman
This video looks at converting the surface integral to a double integral.
- Author:
- Khan, Salman
This video looks at Finding the curl of the vector field and then evaluating the double integral in the parameter domain.
- Author:
- Khan, Salman
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".
- Author:
- Khan, Salman
This video covers The beginning of a proof of stokes' theorem for a special class of surfaces. Finding the curl of our vector field.
- Author:
- Khan, Salman
This video looks at Figuring out a parameterization of our surface and representing ds.
- Author:
- Khan, Salman