This video looks at the Volume of a solid of rotation and chain Rule for rates of change.
This video looks at the Taylor series approximation of sin(x).
This video looks at the Taylor series for cos x at x=0.
This video looks at calculating the 6th derivative at 0 from the Taylor series approximation.
This video looks at the Lagrange error bound for Taylor Polynomial approximation.
This video looks at using Green's Theorem to establish a two dimensional version of the divergence Theorem.
This 9-minute video lesson gives an antiderivative example.
An earlier tutorial used Green's theorem to prove the divergence theorem in 2-D, this tutorial gives us the 3-D version (what most people are talking about when they refer to the "divergence theorem"). We will get an intuition for it (that the flux through a close surface--like a balloon--should be equal to the divergence across it's volume). We will use it in examples. We will prove it in another tutorial.
This series of videos focusing on calculus covers sample questions from the A.P, Calculus AB and AC exams (both multiple choice and free answer).
The Calculus BC AP exam is a super set of the AB exam. It covers everything in AB as well as some of the more advanced topics in integration, sequences and function approximation. This tutorial is great practice for anyone looking to test their calculus mettle!
This video looks at another substitution with x=sin (theta).
Tnis 6-minute video lesson examines finding the antiderivative using u-substitution.
This video looks at the antiderivative of hairier expression.
This video looks at the antiderivative of x^-1.
This video looks at the antiderivative of xcosx using integration by parts.
You are very familiar with taking the derivative of a function. Now we are going to go the other way around--if I give you a derivative of a function, can you come up with a possible original function. In other words, we'll be taking the anti-derivative!
This 9-minute video lectures covers Part 1a of the 2008 BC free response.
This 10-minute video lesson looks at parts B and C of problem 1 (free response) of the AP Calculus BC Exams.
This 9-minute video lesson looks at parts C&D of problem 1 in the 2008 AP Calculus BC free response.
This 5-minute video lesson looks at part 1D of the 2008 AP Calculus BC exam (free response).