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]
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Khan Academy: Chemistry: Keq Derivation Intuition
A video lecture showing how the equilibrium constant was derived. Follow the derviation using the Haber process as an example. [15:05]
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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]
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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]
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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]
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Khan Academy: Chemistry: Spectrophotometry Introduction
A video lecture describing how spectrophotometry works in terms of absorbance and transmittance. All terms are defined using examples and detailed explanations. Also explored is how the Beer-Lambert law can be applied to find an unknown...
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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...
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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...
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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]
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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]
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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]
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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...
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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...
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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...
Khan Academy
Khan Academy: Chemistry: Phase Diagrams
Need help reading those phase diagrams given in chemistry class? This video module provides a good review of how to read the diagrams which show the different states of matter and when they transition to another state according to...
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Khan Academy: Arithmetic and Pre Algebra: Adding Fractions With Different Signs
This video shows how to add three fractions, one of which has a negative sign. Practice problems are available. [6:22]
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Khan Academy: Linear Algebra: Subpsace Projection Matrix Example
An instructional video that works through a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace. Matrix operations are used along with the...
Khan Academy
Khan Academy: Linear Algebra: Simpler 4x4 Determinant
Video demonstrating how to find the determinant of a 4x4 matrix by using row operations and row replacements to get the matrix into upper triangular form. [9:13]
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Khan Academy: Geometry: Intro to 30 60 90 Triangles
Solves an example problem in which the length of the hypotenuse is known and the length of a side must be determined. Explains the special relationship of the lengths of the sides of a 30-60-90 triangle using the Pythagorean theorem....
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Khan Academy: Biology: Intelligent Design and Evolution
Evolution is described as the most "intelligent design." [11:35]
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Khan Academy: Differential Equation: Laplace/step Function Differential Equation
Video demonstrates using the Laplace transform and inverse Laplace transform to solve a differential equation. [19:12]
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Khan Academy: Linear Algebra: Proof of the Cauchy Schwarz Inequality
Video first explains what the Cauchy-Schwarz inequality is and then shows a proof of it. [16:55]
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Khan Academy: Calculus: 2011 Calculus Ab Free Response #5C
Video shows how to find the particular solution to a separable differential equation. [9:15]
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Khan Academy: Algebra: Proof of Quadratic Formula
Demonstrates how to derive the quadratic formula from the standard form of a quadratic equation by completing the square. This video also appears in the Algebra: ck12.org strand. [7:44]