Khan Academy
Khan Academy: Algebra: Radical Equivalent to Rational Exponents 2
Video simplifying the 4th root of an algebraic expression by writing it with fractional exponents and then simplifying further. [2:24]
Khan Academy
Khan Academy: Linear Algebra: Proof: Any Subspace Basis Has Same Number Elements
Video shows proof that any basis of a particular subspace has the same number of elements. Leads up to give the definition of dimension. This video also appears in the strand Algebra: Matrices. [21:25]
Khan Academy
Khan Academy: Differential Equations: Undetermined Coefficients 1
Video first shows the intuition that the general solution to a nonhomogeneous differential equation is the general solution of the homogenous equation plus a particular solution of the nonhomogeneous equation. Then shows an example of...
Khan Academy
Khan Academy: Algebra: Linear Equations 3
A video that demonstrates how to solve a multi-step linear equation. There are two sample problems that contain only integers. Practice problems available. [6:44]
Khan Academy
Khan Academy: Linear Algebra: Basis of a Subspace
Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....
Khan Academy
Khan Academy: Linear Algebra: Gram Schmidt Example With 3 Basis Vectors
Video using the Gram-Schmidt process to create an orthonormal basis from a specific basis with three basis vectors in four-dimensional space. [13:57]
Khan Academy
Khan Academy: Linear Algebra: Preimage of a Set
Video first reviews what the image under a transformation is and then introduces the concept of preimage. [5:23]
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Common Divisibility Examples
This video shows how to determine the prime factorization of a number to determine divisibility. Practice problems are available. [8:13]
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]