This video looks at the mean Value Theorem and differentiability.
This video looks at using a tangent line to extrapolate a function from a known initial condition.
This video looks at using the second derivative to judge whether an approximation with the tangent line is an overestimate or underestimate.
This video looks at solving a differential equation using separation of variables.
This video looks at the continuity of piecewise-defined functions.
This video looks at the derivative of a piecewise-defined function.
This video looks at the average value of a piecewise-defined function on an interval.
This video looks at the Velocity and acceleration vectors for particle.
This video looks at the Position and slope of particle's path at a given time.
This video looks at the arc length for a curve.
This video looks at the arc length of a function.
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 video looks at another substitution with x=sin (theta).