Khan Academy
Khan Academy: Calculus: Introduction to the Line Integral
Video lesson first reviews the definite integral and then introduces the line integral. Shows how to visualize a line integral and set it up. [18:48]
Khan Academy
Khan Academy: Calculus: Constructing a Unit Normal Vector to a Curve
Video showing how to construct the unit normal vector for any point on a curve by first finding the tangent vector, using it to find any normal vector and from there finding the unit normal vector. [10:08]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #3A
Video shows how to use integrals to write a formula for the perimeter of an area bounded on one side by a function. Includes showing how to derive the arc length formula. [5:41]
Khan Academy
Khan Academy: Calculus: Ap Calculus Bc Exams: 2008 #1C & D
Video lesson solving the third part and introducing the fourth part of a free response problem from the 2008 AP Calculus BC exam about finding the area between two curves. Solution involves finding the volume of a solid whose...
Khan Academy
Khan Academy: Calculus: Double Integrals 6
Video lesson finishing an example of how to evaluate the double integral to find the volume under a specific surface when the bounds are variable. Initially integrates with respect to x first and then solves the problem again integrating...
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #6A
Video shows how to write the first four nonzero terms of the Taylor series for a function. [7:42]
Khan Academy
Khan Academy: Trigonometry: Tau Versus Pi
This video explores pi and tau, and their relationship to the length of the arc of a circle, the sine graph, and Euler's formula. [16:22]
Khan Academy
Khan Academy: Calculus: Generalized Taylor Series Approximation
Video lesson showing how to approximate a function at any value using a polynomial by deriving the formula for a Taylor series. [7:27]
Khan Academy
Khan Academy: Calculus: Proofs of Derivatives of Ln(x) and E^x
Video lesson proving the derivative of the natural logarithm of x function using the limit definition of a derivative and proving the derivative of the exponential function by using the derivative of the natural logarithm of x function....
Khan Academy
Khan Academy: Brain Teasers: Liar Truthteller Brain Teaser
Video explains how to solve a brain teaser involving two doors, with treasure behind one of the doors. Two people guard the doors. The first is honest and always tells the truth. The second lies and never tells the truth. What question,...
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #1 (B & C)
Video shows how to find the slope of the tangent line to a particles path using the derivatives of the parametric equations representing the particle. Also shows how to integrate the derivatives of the parametric equations along with...
Khan Academy
Khan Academy: Calculus: Proof: D/dx (Sqrt(x))
Video lesson proving the derivative of the square root of x function using the limit definition of a derivative. Shows that the derivative of the square root of x follows the general power rule. [5:07]
Khan Academy
Khan Academy: Calculus: Example of Calculating a Surface Integral Part 1
Part 1 of a 3-part video series showing how to calculate the surface integral of a torus. Video first reviews the parametrization of the torus and then starts to use it to find the surface area of the torus by finding partial...
Khan Academy
Khan Academy: Calculus: Double Integral 1
Video lesson introducing double integrals by first reviewing definite integrals. Includes an understanding of how to use double integrals to calculate the volume under a surface using a visual representation but no mathematical...
Khan Academy
Khan Academy: Calculus: Visualizing Taylor Series Approximations
Video lesson using the Wolfram Alpha website to show the graphs of the Maclaurin series expansion of the sine function, demonstrating that approximations with more terms are better approximations of the sine curve. [6:01]
Khan Academy
Khan Academy: Calculus: Scalar Field Line Integral Independent of Path Direction
Video lesson using line integrals to find the area along a parametric curve in both directions. Shows that the results are the same for either direction by using substitution. [16:22]
Khan Academy
Khan Academy: Calculus: Introduction to the Surface Integral
Video introducing surface integrals by building on the partial derivatives of vector-valued functions from the previous video and showing how to visualize a surface integral. Surface area is found by taking the magnitude of the cross...
Khan Academy
Khan Academy: Calculus: Using Line Integrals to Find Work Done by a Vector Field
Video lesson using a line integral to find the work done on a particle on a specific path in a specific vector field. Solution results in negative work. [11:32]
Khan Academy
Khan Academy: Calculus: Visualizing Taylor Series for E^x
Video lesson using a Taylor series to approximate e^x around x=3 by using a polynomial function and then showing some of the graphs of the expansion by using the Wolfram Alpha website. [6:38]
Khan Academy
Khan Academy: Calculus: Calculus: Derivatives 2
Video lesson finding the slope of a tangent line of a general quadratic function at a point by finding the limit of the slope of the secant line. Continues on to find the derivative of the function for any point. Includes link to...
Khan Academy
Khan Academy: Calculus: Mean Value Theorem
Video lesson introducing the mean value theorem by providing the theorem and explaining it visually with an arbitrary graph and an example about driving. Includes an example of using the mean value theorem with a specific function. [16:48]
Khan Academy
Khan Academy: Calculus: Surface Integral Ex3 Pt4: Home Stretch
Part 4 of a 4-part video series solving for the surface integral of a surface made of three separate parts. This video finishes evaluating the surface integral of the third surface and adds the results together. [4:02]
Khan Academy
Khan Academy: Calculus: Functions for Parametrization With Two Parameters
Video continuing to show how to parameterize a torus using two parameters by writing the position vector valued functions. [16:32]
Khan Academy
Khan Academy: Calculus: Partial Derivatives of Vector Valued Functions
Video showing how to take the partial derivatives of a generalized vector-valued function by taking the partial derivative of each part of the function. Video is meant as a build-up to the videos on surface integrals. [10:07]