Khan Academy
Khan Academy: Calculus: Double Integrals 5
Video lesson showing how to compute the double integral to find the volume under a specific surface when the bounds are variable. Includes a visual representation. Shows how to set up the integral but not how to evaluate it. [9:51]
Khan Academy
Khan Academy: Calculus: Derivative Intuition Module
Video lesson exploring how to use a module for finding the derivative of a function. Module can be accessed by clicking on the "Practice this concept" link at the top of the video. [3:58]
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Khan Academy: Calculus: Closed Curve Line Integral of Conservative Vector Field
Video extending the idea of a conservative vector field to show that a closed curve line integral will be equal to zero by showing that the difference of a line integral of a path and a line integral of a path with the same end points...
Khan Academy
Khan Academy: Calculus: Surface Integral Ex2 Pt2: Evaluating Integral
Second 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 evaluates the surface integral. [9:51]
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Khan Academy: Calculus: Conceptual Understanding of Flux in Three Dimensions
Video explaining flux through a two-dimensional surface by relating it to line integrals in two dimensions. Sets up a surface integral of the dot product of the product of a mass density function and velocity function with the unit...
Khan Academy
Khan Academy: Geometry: Pi Is (Still) Wrong
An argument about why tau would be a better, more intuitive circle constant to use instead of pi. [5:17]
Khan Academy
Khan Academy: Brain Teasers: Forehead Numbers Brain Teaser
Video sets up and solves the following brain teaser: Three people with infallible logic are in a room together. Each has a number painted on their forehead. The numbers are unique, greater than zero, and one number is the sum of the...
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Khan Academy: Calculus: Taylor Series at 0 (Maclaurin) for E to the X
Video lesson using a Maclaurin series to approximate an exponential function by using a polynomial function and relates its polynomial approximation to that for the sine and cosine functions. [6:10]
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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...
Khan Academy
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]
Khan Academy
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...
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]