Khan Academy
Khan Academy: Geometry: Koch Snowflake Fractal
Explanation of the Koch Snowflake and why it has an infinite perimeter but a finite area. [9:11]
Khan Academy
Khan Academy: Linear Algebra: Projection Is Closest Vector in Subspace
A video lesson proving that the projection of a vector is actually the closest vector in the subspace to the original vector. [9:05]
Khan Academy
Khan Academy: Linear Algebra: Vector Triple Product Expansion (Very Optional)
Video deriving the triple product expansion by expanding the cross product of 3 vectors and then simplifying it to the difference of dot products. [14:25]
Khan Academy
Khan Academy: Algebra: Multiplying Polynomials 3
Video shows how to use polynomial multiplication to find the volume of a cylinder of given dimensions. The problem requires multiplying a binomial and a trinomial. [4:19]
Khan Academy
Khan Academy: Chemistry: Titration Roundup
An explanation of how pH changes during various acid-base titrations. [11:02]
Khan Academy
Khan Academy: Differential Equations: Inverse Laplace Examples
Video first reviews properties of the Laplace transform that were shown in previous videos as well as Laplace transform table values that have been shown in previous videos. Then uses the properties and inverse Laplace transforms to find...
Khan Academy
Khan Academy: Arithmetic and Pre Algebra: Inverse Property of Addition
This video demonstrates the inverse property of addition. Practice problems are available. [2:59]
Khan Academy
Khan Academy: Linear Algebra: Transposes of Sums and Inverses
Video explaining two properties of transpose matrices: that the transpose of the sum of two matrices is equivalent to the sum of the transpose of each matrix and that the inverse of the transpose of a matrix is equivalent to the...
Khan Academy
Khan Academy: Algebra: Rational Equations
A step-by-step breakdown to solve a rational equations and find the excluded values. [4:16]
Khan Academy
Khan Academy: Linear Algebra: Compositions of Linear Transformations 2
Video shows that the transformation matrix of the composition of linear functions is the product of the transformation matrices of each linear transformation in the composition. [16:30]
Khan Academy
Khan Academy: Geometry: Ca Geometry: Similar Triangles 1
This video tutorial [12:55] demonstrates solutions to problems #10-14 of California Geometry released state test questions. Problems address understanding of counterexamples, properties of quadrilateral diagonals, and similar triangles.
Khan Academy
Khan Academy: Intro to Complex Number Conjugates
An instructional video describing complex conjugates. Complex conjugates are defined and then used to simplify a problem in which a complex number is divided by another complex number. [8:03]
Khan Academy
Khan Academy: Algebra: Conic Sections: Tangent Line Hyperbola Relationship
A video lesson showing the algebraic relationship between the equation of an arbitrary hyperbola and its arbitrary tangent line. [10:04]
Khan Academy
Khan Academy: Biology: Sodium Potassium Pump
A detailed explanation of how a neuron transmits information from a dendrite to an exon. [13:53]
Khan Academy
Khan Academy: Linear Algebra: Why Eigenbases Make for Good Coordinate Systems
Video creating a basis out of n linearly independent eigenvectors. Reviews transformations and change of basis matrices. Shows that when the eigenbasis is used as an alternate coordinate system, the transformation is a diagonal matrix...
Khan Academy
Khan Academy: Calculus: (2^Ln X)/x Antiderivative Example
Video lesson showing how to solve for the antiderivative of (2^ln x)/x by using u-substitution. [8:40]
Khan Academy
Khan Academy: Differential Equations: Laplace Transform 4
Video continues the lesson from the previous video finding a Laplace transform table value which involves integration by parts twice. [9:13]
Khan Academy
Khan Academy: Biology: The Kidney and Nephron
An explanation of how the kidney functions at its smallest level, the nephron. [18:38]
Khan Academy
Khan Academy: Algebra: Applying the Metric System
A step-by-step breakdown on how to solve a real-world application problem involving converting units within the metric system. [5:43]
Khan Academy
Khan Academy: Chemistry: Ionic, Covalent, and Metallic Bonds
A video lecture investigating the basics of chemical bonding. The video shows how bonds are formed by giving up or taking an electron, sharing electrons, and between metals. Examples of each type (ionic, metallic, and covalent) are...
Khan Academy
Khan Academy: Linear Algebra: Showing That the Candidate Basis Does Span C(a)
Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...
Khan Academy
Khan Academy: Algebra: Quadratic Formula 2
Demonstrates how to solve a quadratic equation that begins in the form ax^2 + bx = c using the quadratic formula. [6:40]
Khan Academy
Khan Academy: Algebra: Algebraic Word Problem
This video shows how to write and solve a multi-step equation based on an algebraic word problem. [8:02]
Khan Academy
Khan Academy: Linear Algebra: Introduction to Linear Independence
Video explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]