This video looks at using Green's Theorem to complete the proof.
This video looks at Parametrizing a surface that can be explictly made a function of x and y.
This video looks at evaluating the surface integral.
This video looks at breaking apart a larger surface into its components.
This video looks at evaluating the surface integral over the outside of the chopped cylinder.
This video looks at Parametrizing the top surface.
This video looks at evaluating the third surface integral and coming to the final answer.
This video looks at Visualizing a suitable parameterization.
This video looks at Taking the cross product to calculate the surface differential in terms of the parameters.
This video looks at using a few trigonometric identities to finally calculate the value of the surface integral.
This series of videos focusing on calculus covers parameterizing a surface, surface integrals, stokes' theorem.
You can parameterize a line with a position vector valued function and understand what a differential means in that context already. This tutorial will take things further by parametrizing surfaces (2 parameters baby!) and have us thinking about partial differentials.
You know what Stokes' theorem is and how to apply it, but are craving for some real proof that it is true. Well, you've found the right tutorial!
Finding line integrals to be a bit boring? Well, this tutorial will add new dimension to your life by explore what surface integrals are and how we can calculate them.
This video covers swapping the bounds for definite integral.
This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.
You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.
Discover what magic we can derive when we take a derivative, which is the slope of the tangent line at any point on a curve.
The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.
We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!