Khan Academy
Khan Academy: Calculus: Path Independence for Line Integrals
Video lesson introducing conservative vector fields and the multivariable chain rule. Shows that a vector field is conservative if the line integral is the same for the same starting and ending point regardless of the path taken. [17:14]
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Khan Academy: Brain Teasers: Alien Abduction Brain Teaser
Video explains how to solve a brain teaser involving ten people who have been abducted by aliens. The people are arranged single-file, facing the same direction. Each person is wearing either a purple or green hat. No one can see the...
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Khan Academy: Calculus: 2011 Calculus Bc Free Response #6C
Video shows how to use the Taylor series of a function which was found in the previous video to find the sixth derivative of the function at 0. [2:58]
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Khan Academy: Brain Teasers: Toggler Brain Teaser
Video explaining how to solve a brain teaser involving five people. Four of the people are togglers--they alternate between lying and telling the truth--and the fifth person always tells the truth. The goal of the teaser is to figure out...
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Khan Academy: Calculus: Green's Theorem Proof Part 1
Video starting to derive Green's theorem by showing that the closed line integral in a vector field with vectors only in the x-direction is equal to the negative double integral over the region contained within the closed curve of the...
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Khan Academy: Calculus: Sine Taylor Series at 0 (Maclaurin)
Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. [6:33]
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Khan Academy: Calculus: 2011 Calculus Bc Free Response #3 (B & C)
Video shows how to use the disk method to find the volume of a solid of rotation. Also shows how to use the chain rule to find the rate of change of the volume as the length of the solid changes. [8:26]
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Khan Academy: Calculus: Second Example of Line Integral of Conservative Field
Video lesson solving a line integral of a vector field by showing that the vector field is conservative and using the idea of path independence to solve the integral. [10:18]
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Khan Academy: Calculus: 2011 Calculus Bc Free Response #6D
Video shows how to calculate the Lagrange error bound for a Taylor series polynomial approximation. [11:52]
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Khan Academy: Calculus: Euler's Formula and Euler's Identity
Video lesson using the polynomial approximations for the sine, cosine and exponential functions from Maclaurin series to derive Euler's formula and Euler's identity. [11:27]
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Khan Academy: Calculus: Calculus: Derivative of X^(x^x)
Video demonstrating the derivative of the functions y = x^x and y = x^(x^x) using natural logarithms and implicit differentiation. [9:02]
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Khan Academy: Calculus: Vector Representation of a Surface Integral
Video using the information about unit normal vectors to represent the surface integral for finding flux through a surface in two dimensions in a different way. The video also uses partial derivatives and the second definition of the...
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Khan Academy: Calculus: 2011 Calculus Bc Free Response #6B
Video shows how to find the first four nonzero terms of a Taylor series of cos x. Also shows how to combine Taylor series for parts of a function to create a Taylor series for the entire function. [9:59]
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Khan Academy: Calculus: Calculus Bc 2008 #2D
Video lesson solving the fourth part of a free response problem from the 2008 AP Calculus BC exam about people waiting in line to purchase tickets. Solution involves finding a definite integral using a graphing calculator. [4:28]
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Khan Academy: Calculus: Intro to Parametrizing a Surface With Two Parameters
Video showing how to paramatrize a torus using two parameters by first visually showing the parameters without using equations. [19:02]
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Khan Academy: Calculus: Surface Integral Ex2 Pt1: Parameterizing the Surface
First part of a two-part video series on calculating the surface integral of a surface that can be described as a function of x and y. Video shows parameterizing the surface. [5:10]
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Khan Academy: Calculus: Example of Closed Line Integral of Conservative Field
Video lesson solving a closed line integral by first showing that the vector field is conservative and then knowing based on the information in the previous video that the closed line integral is equal to zero. [11:02]
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Khan Academy: Calculus: Green's Theorem Proof (Part 2)
Video finishing the derivation of Green's theorem by showing that the closed line integral in a vector field with vectors only in the y-direction is equal to the double integral over the region contained within the closed curve of the...
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Khan Academy: Calculus: Example of Calculating a Surface Integral Part 2
Part 2 of a 3-part video series showing how to calculate the surface integral of a torus. Video continues to find the surface area of the torus by calculating a cross product. [10:29]
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Khan Academy: Calculus: Line Integral Example 2 (Part 2)
Video lesson continuing the problem from the previous video on finding the surface area along a closed curve using line integrals. Two line integrals are set up and solved and added to the area found previously. [9:58]
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Khan Academy: Calculus: Conceptual Clarification for 2 D Divergence Theorem
Video revisits the 2-D divergence theorem to involve mass density and velocity and find the mass exiting the closed curve. [9:28]
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Khan Academy: Calculus: Calculus: Derivatives 1
Video introducing a derivative as the slope of a tangent line by reviewing the concept of the slope of a line and using that to find the slope of a secant line. Includes link to additional practice problems. [9:25]
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Khan Academy: Brain Teasers: Blue Forehead Room
Video explains the following brain teaser: One-hundred perfect logicians are blindfolded and each has their forehead painted blue. They all enter a room with the lights off, sit in a circle, and the lights are turned on. Each logician...
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Khan Academy: Calculus: Example of Calculating a Surface Integral Part 3
This is part 3 of a 3-part video series showing how to calculate the surface integral of a torus.