Khan Academy
Khan Academy: Differential Equations: Exact Equations Example 1
Video first gives example of determining if an equation is an exact equation and then shows how to solve it. [12:09]
Khan Academy
Khan Academy: Algebra: Logarithm of a Power
Explains the property of a logarithm of a power that states the log base b of m to the n power is equal to n times log base b of m. [4:49]
Khan Academy
Khan Academy: Geometry: Common Orthocenter and Centroid
Proves that if the orthocenter and centroid are the same point in a triangle then the triangle is a right triangle. [6:25]
Khan Academy
Khan Academy: Linear Algebra: Linear Transformations as Matrix Vector Products
Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....
Khan Academy
Khan Academy: Linear Algebra: Linear Transformations as Matrix Vector Products
Video first introduces the identity matrix and shows that when any vector is multiplied by the identity matrix the result is the original vector. Also shows that the columns of the identity matrix are called the standard basis for R^n....
Khan Academy
Khan Academy: Trigonometry: Law of Cosines
This is a video showing how to derive the law of cosines. [9:27]
Khan Academy
Khan Academy: Linear Algebra: Introduction to Eigenvalues and Eigenvectors
Video defining eigenvectors as scaled vectors and eigenvalues as their scale value and explaining their significance. Video references the example from a previous video about changing coordinate systems to make finding the transformation...
Khan Academy
Khan Academy: Linear Algebra: Transformation Matrix With Respect to a Basis
Video discussing transformation matrices and how a vector is able to be mapped to the same resulting vector by using a transformation matrix with respect to the standard basis as well as one with respect to a different basis. Reviews how...
Khan Academy
Khan Academy: Linear Algebra: Cross Product Introduction
Video explains the vector cross product and gives examples of finding it. Also discusses the usefulness and limitations of vector cross products and the differences from the dot product. [15:47]
Khan Academy
Khan Academy: Linear Algebra: Linear Subspaces
Video defines a vector subspace by its three criteria: containing the zero vector, closure under scalar multiplication and closure under vector addition. Gives examples of vector sets and testing to see if they are vector subspaces. Then...
Khan Academy
Khan Academy: Algebra: Inequalities Using Multiplication and Division
Video demonstrates through several examples how to solve inequalities using multiplication and division of positive and negative numbers. Practice problems available. This video is also found in the strand Algebra: ck12.org. [10:27]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Ab Free Response #1A
Video shows how to determine whether the speed of a particle is increasing or decreasing at a given time by using the velocity and acceleration functions and reasoning about the signs of the functions when evaluated at the given time....
Khan Academy
Khan Academy: Algebra: Complex Numbers: Iit Jee Complex Numbers (Part 2)
Video shows working a problem from the IIT JEE test which involves algebraic manipulation and using what the argument of complex numbers is to visually reason if two given equations about arguments are true. [7:26]
Khan Academy
Khan Academy: Linear Algebra: Example Finding the Eigenvalues of a 2x2 Matrix
Video using the conclusion from the previous video to find the eigenvalues of a specific 2x2 matrix. Part of the process requires finding the determinant of a matrix and solving a quadratic equation. [5:39]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform of T^n: L{t^n}
Video demonstrates finding the Laplace transform of t^n using integration by parts and using a pattern of values to develop a general formula. [10:16]
Khan Academy
Khan Academy: Perpendicular Radius Bisects Chord
Proof that if a radius is perpendicular to a chord then it bisects the chord. This video also appears in the Geometry: Circles strand. [6:57]
Khan Academy
Khan Academy: Linear Algebra: Rowspace and Left Nullspace
Video reviewing two fundamental subspaces of a matrix (null space and column space) and introducing two more (row space and left null space). Finds each of these subspaces for a specific 2x3 matrix and its transpose. Demonstrates that...
Khan Academy
Khan Academy: Linear Algebra: Row Space Solution to Ax = B Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Algebra: Graphical Relations and Functions
Video determing whether the graph of a set of points is a function, which in this case it is not. Includes an overview of what a function is. Describes the vertical line test. [4:07]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform of : L{t}
Video first reviews the Laplace transform of L{1} then uses it to help determine the Laplace transform of L{t}. [9:06]
Khan Academy
Khan Academy: Linear Algebra: Relating Invertibility to Onto and One to One
Video first reviews that a function is invertible if and only if there is a unique solution to f(x) = y for any y. Extends this to show that a function is invertible if and only if it is surjective (onto) and injective (one-to-one). [6:31]
Khan Academy
Khan Academy: Linear Algebra: Another Least Squares Example
A video lesson on using the least squares approximation to find the line of best fit for a set of points. Includes a concrete example dealing with a set of 4 points. Finds the equation to the line that is the best approximation of a line...
Khan Academy
Khan Academy: Linear Algebra: Linear Combination and Spans
Video explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...
Khan Academy
Khan Academy: Linear Algebra: Orthogonal Complements as Subspaces
Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null...