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...
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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]
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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]
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...
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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...
Khan Academy
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]
Khan Academy
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]
Khan Academy
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...
Khan Academy
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]
Khan Academy
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]
Khan Academy
Khan Academy: Calculus: Epsilon Delta Limit Definition 2
Video lesson proving a limit by using the epsilon delta definition of a limit. [10:56]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]
Khan Academy
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]