Khan Academy
Khan Academy: Calculus: Periodic Definite Integral
Video lesson solving a 2010 IIT JEE calculus problem about finding the definite integral of a periodic function. The function in the problem is composed of a cosine function and a greatest integer function. The problem is solved using...
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Khan Academy: Calculus: Proof: D/dx (X^n)
Video lesson proving the power rule for finding a derivative using the limit defintion of a derivative and the binomial theorem. [7:03]
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Khan Academy: Calculus: Surface Integral Ex 1 Pt 1: Parameterize the Unit Sphere
Part 1 of a 3-part video series showing how to calculate the surface integral of the unit sphere. The first part shows how to parameterize the unit sphere. [11:05]
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Khan Academy: Calculus: Derivative of a Position Vector Valued Function
Video lesson defining the derivative of a position vector valued function by visualizing it and setting it up. [14:45]
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Khan Academy: Linear Algebra: Formula for 2 X 2 Inverse
A video lesson in which a formula is derived for finding the inverse of a 2 x 2 matrix. Addresses that a 2 x 2 matrix is only invertible if the determinant is not equal to 0. Defines the determinant and shows two examples of calculating...
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Khan Academy: Calculus: Parametrization of a Reverse Path
Video lesson showing how to find the parameterization for a curve going in the opposite direction. Concept is being set up to use with line integrals in the next two videos. [7:26]
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Khan Academy: Calculus: Newton, Leibniz, and Usain Bolt
Video lesson explaining the use of differential equations by exploring the speed at which Usain Bolt runs. Explains the difference between average speed and instantaneous speed. [9:07]
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Khan Academy: Calculus: Surface Integral Ex3 Pt1: Parameterize the Outer Surface
Part 1 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The first video sets up the surface integral for the entire surface, evaluates the first surface and parametrizes and finds the...
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Khan Academy: Calculus: Maclaurin and Taylor Series Intuition
Video lesson showing how to approximate a function at 0 using a polynomial by deriving the formula for a Maclaurin series. [12:58]
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Khan Academy: Calculus: Integrals: Trig Substitution 2
Video lesson solving an indefinite integral by substituting a trigonometric identity. Includes the derivation of the trigonometric identity used. [8:11]
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Khan Academy: Calculus: Epsilon Delta Limit Definition 2
Video lesson proving a limit by using the epsilon delta definition of a limit. [10:56]
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Khan Academy: Calculus: Vector Field Line Integrals Dependent on Path Direction
Video lesson using line integrals in a vector field for a path in opposite directions. Gives the intuition and then shows that the results will have opposite signs. [15:51]
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Khan Academy: Calculus: Differential of a Vector Valued Function
Video lesson reviewing position vector valued functions and their derivatives. Explanation does not contain any specific examples. [5:04]
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Khan Academy: Calculus: Green's Theorem Example 1
Video lesson solving a closed line integral of a vector field by using Green's theorem. [10:31]
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Khan Academy: Calculus: Calculus: Derivatives 2.5 (New Hd Version)
Video lesson finding the slope of a tangent line of a general quadratic function for any point and then using the function to find the slope at specific points. [11:05]
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Khan Academy: Calculus: Calculus: Graphing Using Derivatives
Video lesson using the first and second derivatives to find critical and inflection points and to graph a polynomial function. [20:31]
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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]
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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...
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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...
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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]
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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]