Below is a list of the 1400+ links to FREE educational YouTube videos developed by Salman Khan who, before founding the Khan Academy, was the senior research analyst at a Bay Area investment fund. Khan has also held positions in product management at Xerox PARC and Oracle. He received his MBA from Harvard Business School where he was president of the student body. He also holds a Masters in computer science, a B.S. in computer science, and a B.S. in mathematics from MIT where he was president of the Class of 1998.

Khan’s YouTube videos cover a wide range of subjects: Algebra, Algebra 1, Arithmetic, Banking and Money, Biology, Brain Teasers, Calculus, California Standards Test: Algebra I, California Standards Test: Algebra II, California Standards Test: Geometry, Chemistry, Credit Crisis, Current Economics, Differential Equations, Finance, Geithner Plan, Geometry, History, Linear Algebra, Paulson Bailout, Physics, Pre-Algebra, Pre-Calculus, Probability, Statistics, Trigonometry, Valuation and Investing, and Venture Capital and Capital Markets.

In addition, he has some valuable insights into problem solving for actual test questions in the SAT and GMAT.

**[IMPORTANT NOTE: Using some of the utility programs to download YouTube videos to save them in your PC hard drive–one such FREE utility software is KEEPVID–you save yourself quite a chunk of online time and the occasional woes of waiting for the YouTube video to download while playing.]**

### New Videos from khanacademy (07/04/2010):

- Salman Khan Interview with Mixergy.com
- Probability of Dependent Events
- Probability of Dependent Events 2
- Permutations and Combinations 1
- Permutations and Combinations 4
- U12_L2_T2_we1 Independent Events 1
- Independent Events 2
- Independent Events 3
- Events and Outcomes 2
- Events and Outcomes 3

### New Videos from khanacademy (06/27/2010):

- Adding and Subtracting Rational Expressions 1
- Adding and Subtracting Rational Expressions 2
- Adding and Subtracting Rational Expressions 3

- Multiplying and Dividing Rational Expressions 1
- Multiplying and Dividing Rational Expressions 2
- Multiplying and Dividing Rational Expressions 3

**Arithmetic:**

- Basic Addition
- Addition 2
- Level 2 Addition
- Addition 3
- Addition 4
- Basic Subtraction
- Subtraction 2
- Subtraction 3: Introduction to Borrowing or Regrouping
- Alternate mental subtraction method
- Level 4 Subtraction
- Why borrowing works
- Adding Decimals
- Subtracting decimals
- Basic Multiplication
- Multiplication 2: The Multiplication Tables
- Multiplication 3: 10,11,12 times tables
- Multiplication 4: 2-digit times 1-digit number
- Multiplication 5: 2-digit times a 2-digit number
- Multiplication 6: Multiple Digit Numbers
- Multiplication 7: Old video giving more examples
- Mulitplication 8: Multiplying decimals (Old video)
- Lattice Multiplication
- Why Lattice Multiplication Works
- Division 1
- Division 2
- Division 3: More long division and remainder examples
- Level 4 division
- Converting fractions to decimals
- Percent and decimals
- Dividing decimal
- Ordering numeric expressions
- Greatest Common Divisor
- Least Common Multiple
- Equivalent fractions
- Mixed numbers and improper fractions

**Pre-algebra:**

- Adding and subtracting fractions
- Adding/Subtracting negative numbers
- Dividing fractions
- Exponent Rules Part 1
- Exponent Rules Part 2
- Introduction to logarithm properties
- Introduction to logarithm properties (part 2)
- Introduction to Logarithms
- Introduction to Order of Operations
- Introduction to Ratios (new HD version)
- Level 1 Exponents
- Level 2 Exponents
- Level 3 exponents
- More Complicated Order of Operations Example
- Multiplying and dividing negative numbers
- Multiplying fractions
- Negative Exponent Intuition
- Scientific Notation
- Scientific Notation Examples
- Simplifying radicals
- Speed translation
- Unit conversion
- Unit Conversion Example: Drug Dosage

**Algebra:**

- Algebra: Linear Equations 1
- Algebra: Linear Equations 1
- Absolute Value and Number Lines
- Absolute Value Equation Example
- Advanced ratio problems
- Age word problems 1
- Age word problems 2
- Age word problems 3
- Algebra: Linear Equations 2
- Algebra: Linear Equations 3
- Algebra: Linear Equations 4
- Algebra: Solving Inequalities
- Algebra: graphing lines 1
- Algebra: Slope and Y-intercept intuition
- Algebra: Slope
- Algebra: Slope 2
- Algebra: Slope 3
- Algebra: Equation of a line
- Algebraic Long Division
- Alternate Solution to Ratio Problem (HD Version)
- Another Percent Word Problem
- Averages
- Completing the square
- Complex Numbers (part 1)
- Complex Numbers (part 2)
- Conic Identification 3
- Conic Sections: Intro to Circles
- Conic Sections: Intro to Ellipses
- Conic Sections: Intro to Hyperbolas
- Conic Sections: Hyperbolas 2
- Conic Sections: Hyperbolas 3
- Domain of a function
- Early Train Word Problem
- Example of Solving for a Variable
- Foci of a Hyperbola
- Foci of an Ellipse
- Focus and Directrix of a Parabola 2
- Functions (part 4)
- Functions (Part III)
- Functions Part 2
- Geometric series sum to figure out mortgage payments
- Growing by a percentage
- i and Imaginary numbers
- Identifying Conics 1
- Identifying Conics 2
- Integer sums
- Interesting Polynomial Coefficient Problem
- Introduction to Conic Sections
- Introduction to functions
- Introduction to Ratios
- Introduction to Ratios (new HD version)
- Introduction to the quadratic equation
- Level 1 multiplying expressions
- More advanced ratio problem–with Algebra (HD version)
- More percent problems
- Officer on Horseback
- Overtaking Word Problem
- Parabola Focus and Directrix 1
- Partial Fraction Expansion 1
- Partial Fraction Expansion 2
- Partial Fraction Expansion 3
- Passed Bike Word Problem
- Passing Trains
- Proof: log a + log b = log ab
- Proof: A(log B) = log (B^A), log A – log B = log (A/B)
- Proof: log_a (B) = (log_x (B))/(log_x (A))
- Proof: Hyperbola Foci
- Quadratic Equation part 2
- Quadratic Formula (proof)
- Quadratic Inequalities
- Quadratic Inequalities (Visual Explanation)
- Ratio problem with basic algebra (new HD)
- Rational Inequalities
- Rational Inequalities 2
- Slope and Y-intercept Intuition
- Solving a quadratic by factoring
- systems of equations
- Taking percentages
- Two Passing Bicycles Word Problem

**Algebra 1:**

- A Third Example of Graphing a Rational Function
- Absolute Value Equations
- Absolute Value Inequalities
- Adding Rational Expressions Example 1
- Adding Rational Expressions Example 2
- Adding Rational Expressions Example 3
- Addition and Subtraction of Polynomials
- Addition of Rational Numbers
- Another Rational Function Graph Example
- Asymptotes of Rational Functions
- Average or Central Tendency: Arithmetic Mean, Median, and Mode
- Box-and-whisker Plot
- Compound Inequalities
- Direct Variation Models
- Discriminant of Quadratic Equations
- Distance Formula
- Distributive Property
- Division of Rational Numbers
- Domain and Range of a Function
- Equations and Inequalities
- Equations of Parallel and Perpendicular Lines
- Equations with Variables on Both Sides
- Exponent Properties Involving Products
- Exponent Properties Involving Quotients
- Exponential Decay Functions
- Exponential Growth Functions
- Extraneous Solutions to Radical Equations
- Factor by Grouping and Factoring Completely
- Factoring Quadratic Expressions
- Factoring Special Products
- Fitting a Line to Data
- Functions as Graphs
- Geometric Sequences (Introduction)
- Graphing Inequalities
- Graphing Using Intercepts
- Graphs of Linear Equations
- Graphs of Quadratic Functions
- Graphs of Square Root Functions
- Graphs Using Slope-Intercept Form
- Histograms
- How to Rationalize a Denominator
- Identifying Exponential Models
- Identifying Quadratic Models
- Inequalities Using Addition and Subtraction
- Inequalities Using Multiplication and Division
- Integers and Rational Numbers
- Khan Academy Vision and Social Return
- Linear Equations in Point Slope Form
- Linear Equations in Slope Intercept Form
- Linear Equations in Standard Form
- Linear Function Graphs
- Linear, Quadratic, and Exponential Models
- Midpoint Formula
- More Involved Radical Equation Example
- More Simplifying Radical Expressions
- Multiplication of Polynomials
- Multiplication of Rational Numbers
- Multiplying and Dividing Rational Expressions
- Multi-Step Equations
- Multi-Step Inequalities
- One Step Equations
- Order of Operations
- Patterns and Equations
- Percent Problems
- Polynomial Division
- Polynomial Equations in Factored Form
- Predicting with Linear Models
- Problem Solving Word Problems 2
- Proof of Quadratic Formula
- Proportionality
- Pythagorean Theorem
- Quadratic Regression
- Radical Equation Examples
- Radical Expressions with Higher Roots
- Range, Variance and Standard Deviation as Measures of Dispersion
- Ratio and Proportion
- Scale and Indirect Measurement
- Scientific Notation
- Simplifying Rational Expressions
- Slope and Rate of Change
- Solving Linear Systems by Graphing
- Solving Linear Systems by Substitution
- Solving Quadratic Equations by Completing the Square
- Solving Quadratic Equations by Graphing
- Solving Quadratic Equations by Square Roots
- Solving Rational Equations
- Solving Systems of Equations by Elimination
- Solving Systems of Equations by Multiplication
- Special Products of Binomials
- Special Types of Linear Systems
- Square Roots and Real Numbers
- Stem and Leaf Plots
- Subraction of Rational Numbers
- Surveys and Samples
- Systems of Linear Inequalities
- The Coordinate Plane
- Two more examples of solving rational equations
- Two-Step Equations
- Using a Linear Model
- Using the Quadratic Formula
- Variable Expressions
- Visual Pythagorean Theorem Proof
- Word Problem Solving 3
- Word Problem Solving 4
- Word Problem Solving- Exponential Growth and Decay
- Word Problem Solving Plan 1
- Word Problem Solving Strategies
- Zero, Negative, and Fractional Exponents

**California Standards Test: Algebra I:**

- CA Algebra I: Completing the Square
- CA Algebra I: Factoring Quadratics
- CA Algebra I: Functions
- CA Algebra I: Graphing Inequalities
- CA Algebra I: More Word Problems
- CA Algebra I: Number Properties and Absolute Value
- CA Algebra I: Quadratic Equation
- CA Algebra I: Quadratic Roots
- CA Algebra I: Rational Expressions
- CA Algebra I: Rational Expressions
- CA Algebra I: Simple Logical Arguments
- CA Algebra I: Simplifying Expressions
- CA Algebra I: Simplifying Expressions
- CA Algebra I: Slope and Y-intercept
- CA Algebra I: Systems of Inequalities
- CA Algebra I: Word Problems

**California Standards Test: Algebra II:**

- Algebra II: Binomial Expansion and Combinatorics
- Algebra II: Binomial Expansions, Geometric Series Sum
- Algebra II: Circles and Logarithms
- Algebra II: Complex numbers and conjugates
- Algebra II: Conic Sections
- Algebra II: Functions and Probability
- Algebra II: Functions, Combinatorics
- Algebra II: Imaginary and Complex Numbers
- Algebra II: Logarithms and more
- Algebra II: Logarithms Exponential Growth
- Algebra II: Mean and Standard Deviation
- Algebra II: Probability and Statistics
- Algebra II: Quadratics and Shifts
- Algebra II: Shifting Quadratic Graphs
- Algebra II: Simplifying Polynomials
- CA Standards: Algebra II
- CA Standards: Algebra II (Algebraic Division/Multiplication)
- California Standards Test: Algebra II
- California Standards Test: Algebra II (Graphing Inequalities)

**Geometry:**

- Introduction to angles
- Angles (part 2)
- Angles (part 3)
- Angles of parallel lines
- The Angle Game
- Similar triangles
- Similar triangles (part 2)
- Angle Game (part 2)
- Area and Perimeter
- Circles: Radius, Diameter and Circumference
- Area of a circle
- Introduction to the Pythagorean Theorem
- Pythagorean Theorem II
- 45-45-90 Triangles
- Intro to 30-60-90 Triangles
- 30-60-90 Triangles II
- Heron’s Formula
- Part 1 of Proof of Heron’s Formula
- Part 2 of the Proof of Heron’s Formula
- An inscribed angle is half of a central angle that subtends the same arc
- Area of Inscribed Equilateral Triangle (some basic trig used)
- Right Triangles Inscribed in Circles (Proof)

**California Standards Test: Geometry:**

- CA Geometry: Area, Circumference, Volume
- CA Geometry: Area, Pythagorean Theorem
- CA Geometry: Basic Trigonometry
- CA Geometry: Circle Area Chords Tangent
- CA Geometry: Compass Construction
- CA Geometry: Deducing Angle Measures
- CA Geometry: deductive reasoning
- CA Geometry: Exterior Angles
- CA Geometry: More on congruent and similar triangles
- CA Geometry: More Proofs
- CA Geometry: More Trig
- CA Geometry: Proof by Contradiction
- CA Geometry: Pythagorean Theorem, Area
- CA Geometry: Pythagorean Theorem, Compass Constructions
- CA Geometry: Secants and Translations
- CA Geometry: Similar Triangles
- CA Geometry: Similar Triangles
- CA Geometry: Triangles and Parallelograms

**Trigonometry:**

- Basic Trigonometry
- Basic Trigonometry II
- Determining the equation of a trigonometric function
- Ferris Wheel Trig Problem
- Ferris Wheel Trig Problem (part 2)
- Fun Trig Problem
- Graph of the sine function
- Graphing trig functions
- Graphs of trig functions
- Inverse Trig Functions: Arccos
- Inverse Trig Functions: Arcsin
- Inverse Trig Functions: Arctan
- Law of cosines
- More trig graphs
- Navigation Word Problem
- Polar Coordinates 1
- Polar Coordinates 2
- Polar Coordinates 3
- Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)
- Proof: Law of Sines
- Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)
- Radians and degrees
- The unit circle definition of trigonometric function
- Trig identies part 3 (part 5 if you watch the proofs)
- Trig identities part 2 (parr 4 if you watch the proofs)
- Trigonometric Identities
- Trigonometry Identity Review/Fun
- Trigonometry word problems (part 1)
- Trigonometry word problems (part 2)
- Unit Circle Definition of Trig Functions
- Using Trig Functions
- Using Trig Functions Part II

**Precalculus:**

- Binomial Theorem (part 1)
- Binomial Theorem (part 2)
- Binomial Theorem (part 3)
- Combinations
- Compound Interest and e (part 2)
- Compound Interest and e (part 3)
- Compound Interest and e (part 4)
- Exponential Growth
- Interest (part 2)
- Introduction to compound interest and e
- Introduction to interest
- Introduction to Limits
- Limit Examples (part 1)
- Limit Examples (part 2)
- Limit Examples (part3)
- Limit Examples w/ brain malfunction on first prob (part 4)
- More Limits
- Parametric Equations 1
- Parametric Equations 2
- Parametric Equations 3
- Parametric Equations 4
- Permutations
- Polar Coordinates 1
- Polar Coordinates 2
- Polar Coordinates 3
- Proof: lim (sin x)/x
- Sequences and Series (part 1)
- Sequences and series (part 2)
- Squeeze Theorem

**Statistics:**

- Binomial Distribution 1
- Binomial Distribution 2
- Binomial Distribution 3
- Binomial Distribution 4
- Central Limit Theorem
- ck12.org Exercise: Standard Normal Distribution and the Empirical Rule
- ck12.org Normal Distribution Problems: Empirical Rule
- ck12.org Normal Distribution Problems: Qualitative sense of normal distributions
- ck12.org Normal Distribution Problems: z-score
- ck12.org: More Empirical Rule and Z-score practice
- Expected Value of Binomial Distribution
- Expected Value: E(X)
- Introduction to Random Variables
- Introduction to the Normal Distribution
- Law of Large Numbers
- Normal Distribution Excel Exercise
- Poisson Process 1
- Poisson Process 2
- Probability Density Functions
- Sampling Distribution of the Sample Mean
- Sampling Distribution of the Sample Mean 2
- Standard Error of the Mean
- Statistics: Alternate Variance Formulas
- Statistics: Sample Variance
- Statistics: Sample vs. Population Mean
- Statistics: Standard Deviation
- Statistics: The Average
- Statistics: Variance of a Population

**Probability:**

- Binomial Distribution 1
- Binomial Distribution 2
- Binomial Distribution 3
- Binomial Distribution 4
- Birthday Probability Problem
- Combinations
- Conditional Probability and Combinations
- Expected Value of Binomial Distribution
- Expected Value: E(X)
- Introduction to Random Variables
- Law of Large Numbers
- Permutations
- Poisson Process 1
- Poisson Process 2
- Probability (part 1)
- Probability (part 2)
- Probability (part 3)
- Probability (part 4)
- Probability (part 5)
- Probability (part 6)
- Probability (part 7)
- Probability (part 8)
- Probability and Combinations (part 2)
- Probability Density Functions
- Probability using Combinations

**Calculus:**

- âˆ«(2^ln x)/x dx Antiderivative Example
- Another u-subsitution example
- AP Calculus BC Exams: 2008 1 a
- AP Calculus BC Exams: 2008 1 b&c
- AP Calculus BC Exams: 2008 1 c&d
- AP Calculus BC Exams: 2008 1 d
- Approximating functions with polynomials (part 3)
- Calculus BC 2008 2 a
- Calculus BC 2008 2 b &c
- Calculus BC 2008 2d
- Calculus Graphing with Derivatives Example
- Calculus: Derivative of x^(x^x)
- Calculus: Derivatives 1
- Calculus: Derivatives 1 (new HD version)
- Calculus: Derivatives 2
- Calculus: Derivatives 2 (new HD version)
- Calculus: Derivatives 2.5 (new HD version)
- Calculus: Derivatives 3
- Calculus: Derivatives 4: The Chain Rule
- Calculus: Derivatives 5
- Calculus: Derivatives 6
- Calculus: Graphing Using Derivatives
- Calculus: Maximum and minimum values on an interval
- Closed Curve Line Integrals of Conservative Vector Fields
- Curl 1
- Curl 2
- Curl 3
- Definite integral with substitution
- Definite Integrals (area under a curve) (part III)
- Definite Integrals (part 4)
- Definite Integrals (part 5)
- Definite integrals (part II)
- Derivative of a position vector valued function
- Derivatives (part 7)
- Derivatives (part 8)
- Derivatives (part 9)
- Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
- Differential of a vector valued function
- Divergence 1
- Divergence 2
- Divergence 3
- Double Integral 1
- Double Integrals 2
- Double Integrals 3
- Double Integrals 4
- Double Integrals 5
- Double Integrals 6
- Epsilon Delta Limit Definition 1
- Epsilon Delta Limit Definition 2
- Equation of a tangent line
- Example of calculating a surface integral part 1
- Example of calculating a surface integral part 2
- Example of calculating a surface integral part 3
- Example of Closed Line Integral of Conservative Field
- Exponential Growth
- Extreme Derivative Word Problem (advanced)
- Gradient 1
- Gradient of a scalar field
- Graphing with Calculus
- Green’s Theorem Example 1
- Green’s Theorem Example 2
- Green’s Theorem Proof (part 2)
- Green’s Theorem Proof Part 1
- Implicit Differentiation
- Implicit Differentiation (part 2)
- Indefinite integrals (part II)
- Indefinite Integration (part 7)
- Indefinite Integration (part III)
- Indefinite Integration (part IV)
- Indefinite Integration (part V)
- Inflection Points and Concavity Intuition
- Integrals: Trig Substitution 1
- Integrals: Trig Substitution 2
- Integrals: Trig Substitution 3 (long problem)
- Integration by Parts (part 6 of Indefinite Integration)
- Introduction to definite integrals
- Introduction to differential equations
- Introduction to Limits
- Introduction to Parametrizing a Surface with Two Parameters
- Introduction to rate-of-change problems
- Introduction to the Line Integral
- Introduction to the Surface Integral
- Ladder rate-of-change problem
- Limit Examples (part 1)
- Limit Examples (part 2)
- Limit Examples (part3)
- Limit Examples w/ brain malfunction on first prob (part 4)
- Line Integral Example 1
- Line Integral Example 2 (part 1)
- Line Integral Example 2 (part 2)
- Line Integrals and Vector Fields
- Maxima Minima Slope Intuition
- Mean Value Theorem
- Monotonicity Theorem
- More chain rule and implicit differentiation intuition
- More implicit differentiation
- More Limits
- Optimization Example 4
- Optimization with Calculus 1
- Optimization with Calculus 2
- Optimization with Calculus 3
- Parametrization of a Reverse Path
- Partial Derivatives
- Partial Derivatives 2
- Partial Derivatives of Vector-Valued Functions
- Path Independence for Line Integrals
- Polynomial approximation of functions (part 1)
- Polynomial approximation of functions (part 2)
- Polynomial approximation of functions (part 4)
- Polynomial approximation of functions (part 5)
- Polynomial approximation of functions (part 6)
- Polynomial approximation of functions (part 7)
- Position Vector Valued Functions
- Proof: d/dx(e^x) = e^x
- Proof: d/dx(ln x) = 1/x
- Proof: d/dx(sqrt(x))
- Proof: d/dx(x^n)
- Proof: lim (sin x)/x
- Proofs of Derivatives of Ln(x) and e^x
- Rates-of-change (part 2)
- Scalar Field Line Integral Independent of Path Direction
- Second Example of Line Integral of Conservative Vector Field
- Sequences and Series (part 1)
- Sequences and series (part 2)
- Solid of Revolution (part 1)
- Solid of Revolution (part 2)
- Solid of Revolution (part 3)
- Solid of Revolution (part 4)
- Solid of Revolution (part 5)
- Solid of Revolution (part 6)
- Solid of Revolution (part 7)
- Solid of Revolution (part 8)
- Squeeze Theorem
- Taylor Polynomials
- The Indefinite Integral or Anti-derivative
- Trig Implicit Differentiation Example
- Triple Integrals 1
- Triple Integrals 2
- Triple Integrals 3
- Using a line integral to find the work done by a vector field example
- Vector Field Line Integrals Dependent on Path Direction
- Vector valued function derivative example

**Differential Equations:**

- Introduction to differential equations
- Separable Differential Equations
- Separable differential equations 2
- Exact Equations Intuition 1 (proofy)
- Exact Equations Intuition 2 (proofy)
- Exact Equations Example 1
- Exact Equations Example 2
- Exact Equations Example 3
- Integrating factors 1
- Integrating factors 2
- First order homegenous equations
- First order homogenous equations 2
- 2nd Order Linear Homogeneous Differential Equations 1
- 2nd Order Linear Homogeneous Differential Equations 2
- 2nd Order Linear Homogeneous Differential Equations 3
- 2nd Order Linear Homogeneous Differential Equations 4
- Complex roots of the characteristic equations 1
- Complex roots of the characteristic equations 2
- Complex roots of the characteristic equations 3
- Repeated roots of the characteristic equation
- Repeated roots of the characterisitic equations part 2
- Undetermined Coefficients 1
- Undetermined Coefficients 2
- Undetermined Coefficients 3
- Undetermined Coefficients 4
- Laplace Transform 1
- Laplace Transform 2
- Laplace Transform 3 (L{sin(at)})
- Laplace Transform 4
- Laplace Transform 5
- Laplace Transform 6
- Laplace Transform to solve an equation
- Laplace Transform solves an equation 2
- More Laplace Transform tools
- Using the Laplace Transform to solve a nonhomogenous eq
- Laplace Transform of : L{t}
- Laplace Transform of t^n: L{t^n}
- Laplace Transform of the Unit Step Function
- Inverse Laplace Examples
- Laplace/Step Function Differential Equation
- Dirac Delta Function
- Laplace Transform of the Dirac Delta Function
- Introduction to the Convolution
- The Convolution and the Laplace Transform
- Using the Convolution Theorem to Solve an Initial Value Prob

**Linear Algebra:**

- Introduction to matrices
- Matrix multiplication (part 1)
- Matrix multiplication (part 2)
- Inverse Matrix (part 1)
- Inverting matrices (part 2)
- Inverting Matrices (part 3)
- Matrices to solve a system of equations
- Matrices to solve a vector combination problem
- Singular Matrices
- 3-variable linear equations (part 1)
- Solving 3 Equations with 3 Unknowns
- Linear Algebra: Introduction to Vectors
- Linear Algebra: Vector Examples
- Linear Algebra: Parametric Representations of Lines
- Linear Combinations and Span
- Linear Algebra: Introduction to Linear Independence
- More on linear independence
- Span and Linear Independence Example
- Linear Subspaces
- Linear Algebra: Basis of a Subspace
- Vector Dot Product and Vector Length
- Proving Vector Dot Product Properties
- Proof of the Cauchy-Schwarz Inequality
- Linear Algebra: Vector Triangle Inequality
- Defining the angle between vectors
- Defining a plane in R3 with a point and normal vector
- Linear Algebra: Cross Product Introduction
- Proof: Relationship between cross product and sin of angle
- Dot and Cross Product Comparison/Intuition
- Matrices: Reduced Row Echelon Form 1
- Matrices: Reduced Row Echelon Form 2
- Matrices: Reduced Row Echelon Form 3
- Matrix Vector Products
- Introduction to the Null Space of a Matrix
- Null Space 2: Calculating the null space of a matrix
- Null Space 3: Relation to Linear Independence
- Column Space of a Matrix
- Null Space and Column Space Basis
- Visualizing a Column Space as a Plane in R3
- Proof: Any subspace basis has same number of elements
- Dimension of the Null Space or Nullity
- Dimension of the Column Space or Rank
- Showing relation between basis cols and pivot cols
- Showing that the candidate basis does span C(A)
- A more formal understanding of functions
- Vector Transformations
- Linear Transformations
- Matrix Vector Products as Linear Transformations
- Linear Transformations as Matrix Vector Products
- Image of a subset under a transformation
- im(T): Image of a Transformation
- Preimage of a set
- Preimage and Kernel Example
- Sums and Scalar Multiples of Linear Transformations
- More on Matrix Addition and Scalar Multiplication
- Linear Transformation Examples: Scaling and Reflections
- Linear Transformation Examples: Rotations in R2
- Rotation in R3 around the X-axis
- Unit Vectors
- Introduction to Projections
- Expressing a Projection on to a line as a Matrix Vector prod
- Compositions of Linear Transformations 1
- Compositions of Linear Transformations 2
- Linear Algebra: Matrix Product Examples
- Matrix Product Associativity
- Distributive Property of Matrix Products
- Linear Algebra: Introduction to the inverse of a function
- Proof: Invertibility implies a unique solution to f(x)=y
- Surjective (onto) and Injective (one-to-one) functions
- Relating invertibility to being onto and one-to-one
- Determining whether a transformation is onto
- Linear Algebra: Exploring the solution set of Ax=b
- Linear Algebra: Matrix condition for one-to-one trans
- Linear Algebra: Simplifying conditions for invertibility
- Linear Algebra: Showing that Inverses are Linear
- Linear Algebra: Deriving a method for determining inverses
- Linear Algebra: Example of Finding Matrix Inverse
- Linear Algebra: Formula for 2×2 inverse
- Linear Algebra: 3×3 Determinant
- Linear Algebra: nxn Determinant
- Linear Algebra: Determinants along other rows/cols
- Linear Algebra: Rule of Sarrus of Determinants
- Linear Algebra: Determinant when row multiplied by scalar
- Linear Algebra: (correction) scalar muliplication of row
- Linear Algebra: Determinant when row is added
- Linear Algebra: Duplicate Row Determinant
- Linear Algebra: Determinant after row operations
- Linear Algebra: Upper Triangular Determinant
- Linear Algebra: Simpler 4×4 determinant
- Linear Algebra: Determinant and area of a parallelogram
- Linear Algebra: Determinant as Scaling Factor
- Linear Algebra: Transpose of a Matrix
- Linear Algebra: Determinant of Transpose
- Linear Algebra: Transposes of sums and inverses
- Linear Algebra: Transpose of a Vector
- Linear Algebra: Rowspace and Left Nullspace
- Lin Alg: Visualizations of Left Nullspace and Rowspace
- Linear Algebra: Orthogonal Complements
- Linear Algebra: Rank(A) = Rank(transpose of A)
- Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n
- Lin Alg: Representing vectors in Rn using subspace members
- Lin Alg: Orthogonal Complement of the Orthogonal Complement
- Lin Alg: Orthogonal Complement of the Nullspace
- Lin Alg: Unique rowspace solution to Ax=b
- Linear Alg: Rowspace Solution to Ax=b example
- Lin Alg: Showing that A-transpose x A is invertible
- Linear Algebra: Projections onto Subspaces
- Linear Alg: Visualizing a projection onto a plane
- Lin Alg: A Projection onto a Subspace is a Linear Transforma
- Linear Algebra: Subspace Projection Matrix Example
- Lin Alg: Another Example of a Projection Matrix
- Linear Alg: Projection is closest vector in subspace
- Linear Algebra: Least Squares Approximation
- Linear Algebra: Least Squares Examples
- Linear Algebra: Another Least Squares Example
- Linear Algebra: Coordinates with Respect to a Basis
- Linear Algebra: Change of Basis Matrix
- Lin Alg: Invertible Change of Basis Matrix
- Lin Alg: Transformation Matrix with Respect to a Basis
- Lin Alg: Alternate Basis Tranformation Matrix Example
- Lin Alg: Alternate Basis Tranformation Matrix Example Part 2
- Lin Alg: Changing coordinate systems to help find a transformation matrix
- Linear Algebra: Introduction to Orthonormal Bases
- Linear Algebra: Coordinates with respect to orthonormal bases
- Lin Alg: Projections onto subspaces with orthonormal bases
- Lin Alg: Finding projection onto subspace with orthonormal basis example
- Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix
- Lin Alg: Orthogonal matrices preserve angles and lengths
- Linear Algebra: The Gram-Schmidt Process
- Linear Algebra: Gram-Schmidt Process Example
- Linear Algebra: Gram-Schmidt example with 3 basis vectors
- Linear Algebra: Introduction to Eigenvalues and Eigenvectors
- Linear Algebra: Proof of formula for determining Eigenvalues
- Linear Algebra: Example solving for the eigenvalues of a 2×2 matrix
- Linear Algebra: Finding Eigenvectors and Eigenspaces example
- Linear Algebra: Eigenvalues of a 3×3 matrix
- Linear Algebra: Eigenvectors and Eigenspaces for a 3×3 matrix
- Linear Algebra: Showing that an eigenbasis makes for good coordinate systems

**Physics:**

- 2 dimensional projectile motion (part 1)
- 2 dimensional projectile motion (part 2)
- 2 dimensional projectile motion (part 4)
- 2-dimensional momentum problem
- 2-dimensional momentum problem (part 2)
- 2-dimensional projectile motion (part 3)
- 2-dimensional projectile motion (part 5)
- A more complicated friction/inclined plane problem
- Amplitude, Period, Frequency and Wavelength of Periodic Waves
- Calculating dot and cross products with unit vector notation
- Calculus Proof that a=v^2/r
- Capacitance
- Center of Mass
- Centripetal Acceleration (part 2)
- Centripetal Acceleration (part 3)
- Circuits (part 1)
- Circuits (part 2)
- Circuits (part 3)
- Circuits (part 4)
- Conservation of angular momentum
- Conservation of Energy
- Cross product 1
- Cross Product 2
- Cross Product and Torque
- Dot vs. Cross Product
- Electric Potential Energy
- Electric Potential Energy (part 2– involves calculus)
- Electrostatics (part 1): Introduction to Charge and Coulomb’s Law
- Electrostatics (part 2)
- Fluids (part 1)
- Fluids (part 10)
- Fluids (part 11)
- Fluids (part 12)
- Fluids (part 2)
- Fluids (part 3)
- Fluids (part 4)
- Fluids (part 5)
- Fluids (part 6)
- Fluids (part 7)
- Fluids (part 8)
- Fluids (part 9)
- Force with Vectors
- Friction on an inclined plane
- Gravitation (part 2)
- Harmonic Motion Part 2 (calculus)
- Harmonic Motion Part 3 (no calculus)
- Intro to springs and Hooke’s Law
- Introduction to angular velocity
- Introduction to centripetal acceleration (part 1)
- Introduction to friction
- Introduction to Harmonic Motion
- Introduction to Magnetism
- Introduction to mechanical advantage
- Introduction to Momentum
- Introduction to motion
- Introduction to motion (part 2)
- Introduction to motion (part 3)
- Introduction to Newton’s Law of Gravitation
- Introduction to Tension
- Introduction to Torque
- Introduction to Waves
- Introduction to work and energy
- Magnetism 10: Electric Motors
- Magnetism 11: Electric Motors
- Magnetism 12: Induced Current in a Wire
- Magnetism 2
- Magnetism 3
- Magnetism 4
- Magnetism 5
- Magnetism 6: Magnetic field due to current
- Magnetism 7
- Magnetism 8
- Magnetism 9: Electric Motors
- Mass on Inclined Plane
- Mechanical Advantage (part 2)
- Mechanical Advantage (part 3)
- Moments
- Moments (part 2)
- Momentum: Ice skater throws a ball
- Moving pulley problem (part 1)
- Moving pulley problem (part 2)
- Newton’s First Law of Motion
- Newton’s Laws
- Newton’s Laws and vectors
- Newton’s Laws Examples (part 2)
- Newton’s Laws Problems (part 1)
- Newton’s Second Law of Motion
- Newton’s Third Law of Motion
- Potential energy stored in a spring
- Projectile motion (part 1)
- Projectile motion (part 10)
- Projectile motion (part 2)
- Projectile motion (part 3)
- Projectile motion (part 4)
- Projectile motion (part 5)
- Projectile motion (part 6)
- Projectile motion (part 7)
- Projectile motion (part 8)
- Projectile motion (part 9)
- Projectile Motion with Ordered Set Notation
- Projectile Motion with Unit Vectors
- Projectile Motion with Unit Vectors (part 2)
- Proof (Advanced): Field from infinite plate (part 1)
- Proof (Advanced): Field from infinite plate (part 2)
- Spring potential energy example (mistake in math)
- Tension (part 2)
- Tension in an accelerating system and pie in the face
- The dot product
- Thermodynamics (part 1)
- Thermodynamics (part 2)
- Thermodynamics (part 3)
- Thermodynamics (part 4)
- Thermodynamics (part 5)
- Unit Vector Notation
- Unit Vector Notation (part 2)
- Visual Proof: a= v^2/r
- Voltage
- Work and Energy (part 2)
- Work/Energy problem with Friction

**Biology:**

- Anatomy of a muscle cell
- Anatomy of a Neuron
- ATP: Adenosine Triphosphate
- B Lymphocytes (B cells)
- Bacteria
- C-4 Photosynthesis
- CAM Plants
- Cancer
- Chromosomes, Chromatids, Chromatin, etc.
- Circulatory System and the Heart
- Cytotoxic T Cells
- Diffusion and Osmosis
- DNA
- Electron Transport Chain
- Electrotonic and Action Potentials
- Embryonic Stem Cells
- Evolution Clarification
- Glycolysis
- Hardy-Weinberg Principle
- Helper T Cells
- Hemoglobin
- Inflammatory Response
- Intelligent Design and Evolution
- Introduction to Cellular Respiration
- Introduction to Evolution and Natural Selection
- Introduction to Heredity
- Krebs / Citric Acid Cycle
- Mitosis, Meiosis and Sexual Reproduction
- Myosin and Actin
- Natural Selection and the Owl Butterfly
- Neuronal Synapses (Chemical)
- Oxidation and Reduction in Cellular Respiration
- Oxidation and Reduction Review From Biological Point-of-View
- Oxidative Phosphorylation and Chemiosmosis
- Parts of a cell
- Phases of Meiosis
- Phases of Mitosis
- Photorespiration
- Photosynthesis
- Photosynthesis: Calvin Cycle
- Photosynthesis: Light Reactions 1
- Photosynthesis: Light Reactions and Photophosphorylation
- Professional Antigen Presenting Cells (APC) and MHC II complexes
- Punnett Square Fun
- Red blood cells
- Review of B cells, CD4+ T cells and CD8+ T cells
- Role of Phagocytes in Innate or Nonspecific Immunity
- Role of the Sarcoplasmic Reticulum in Muscle Cells
- Saltatory Conduction in Neurons
- Secondary Active Transport in the Nephron
- Sex-Linked Traits
- Sodium Potassium Pump
- The Kidney and Nephron
- The Lungs and Pulmonary System
- Tropomyosin and troponin and their role in regulating muscle contraction
- Types of immune responses: Innate and Adaptive. Humoral vs. Cell-Mediated
- Variation in a Species
- Viruses

**Chemistry:**

- A look at a seductive but wrong Gibbs/Spontaneity Proof
- Acid Base Introduction
- Another mass composition problem
- Another Stoichiometry Example in a Solution
- Balancing Chemical Equations
- Boiling Point Elevation and Freezing Point Suppression
- Buffers
- Carnot Cycle and Carnot Engine
- Carnot Efficiency 2: Reversing the Cycle
- Carnot Efficiency 3: Proving that it is the most efficient
- Chilling Water Problem
- Conjugate Acids and Bases
- Covalent Networks, Metallic, and Ionic Crystals
- Efficiency of a Carnot Engine
- Electron Configurations
- Electron Configurations 2
- Empirical and Molecular Formulas from Stoichiometry
- Enthalpy
- Entropy Intuition
- Example of Finding Reactant Empirical Formula
- Exponential Decay Formula Proof (can skip, involves Calculus)
- First Law of Thermodynamics/ Internal Energy
- Formula from Mass Composition
- Galvanic Cells
- Gibbs Free Energy and Spontaneity
- Gibbs Free Energy Example
- Groups of the Periodic Table
- Half Equivalence Point
- Half-Life
- Heat of Formation
- Hess’s Law and Reaction Enthalpy Change
- Heterogenous Equilibrium
- Hydrogen Peroxide Correction
- Ideal Gas Equation Example 1
- Ideal Gas Equation Example 2
- Ideal Gas Equation Example 3
- Ideal Gas Equation: PV=nRT
- Ideal Gas Example 4
- Introduction to Exponential Decay
- Introduction to Kinetics
- Introduction to Oxidation States
- Introduction to pH, pOH, and pKw
- Introduction to the atom
- Ionic, Covalent, and Metallic Bonds
- Keq derivation intuition (can skip; bit mathy)
- Keq Intuition (mathy and not necessary to progress)
- Le Chatelier’s Principle
- Limiting Reactant Example Problem 1
- Macrostates and Microstates
- Maxwell’s Demon
- Mini-Video on Ion Size
- Molecular and Empirical Formulas
- More Exponential Decay Examples
- More on Entropy
- More on Internal Energy
- More on orbitals and electron configuration
- More on Oxidation States
- More rigorous Gibbs Free Energy/ Spontaneity Relationship
- Orbitals
- Other Periodic Table Trends
- Partial Pressure
- Periodic Table Trends: Ionization Energy
- pH of a Weak Acid
- pH of a Weak Base
- pH, pOH of Strong Acids and Bases
- Phase Diagrams
- pKa and pKb Relationship
- Proof: S (or Entropy) is a valid state variable
- Proof: U=(3/2)PV or U=(3/2)nRT
- Proof: Volume Ratios in a Carnot Cycle
- PV-diagrams and Expansion Work
- Quasistatic and Reversible Processes
- Reactions in Equilibrium
- Reconciling Thermodynamic and State Definitions of Entropy
- Redox Reactions
- Solubility
- Specific Heat, Heat of Fusion and Vaporization
- States of Matter
- States of Matter Follow-Up
- Stoichiometry
- Stoichiometry Example Problem 1
- Stoichiometry Example Problem 2
- Stoichiometry of a Reaction in Solution
- Stoichiometry: Limiting Reagent
- Strong Acid Titration
- Suspensions, Colloids and Solutions
- The Mole and Avogadro’s Number
- Thermodynamic Entropy Definition Clarification
- Titration Roundup
- Types of Decay
- Valence Electrons
- Van Der Waals Forces
- Vapor Pressure
- Weak Acid Titration
- Work Done by Isothermic Process
- Work from Expansion

**History:**

- French Revolution (Part 1)
- French Revolution (Part 2)
- French Revolution (Part 3) – Reign of Terror
- French Revolution (Part 4) – The Rise of Napoleon Bonaparte
- Haitian Revolution (Part 1)
- Haitian Revolution (Part 2)
- Napoleon and the War of the Fourth Coalition
- Napoleon and the War of the Third Coalition
- Napoleon and the Wars of the First and Second Coalitions
- Napoleon Forced to Abdicate
- Napoleon’s Peninsular Campaigns

**Banking and Money:**

- Banking 1
- Banking 10: Introduction to leverage (bad sound)
- Banking 11: A reserve bank
- Banking 12: Treasuries (government debt)
- Banking 13: Open Market Operations
- Banking 14: Fed Funds Rate
- Banking 15: More on the Fed Funds Rate
- Banking 16: Why target rates vs. money supply
- Banking 17: What happened to the gold?
- Banking 18: Big Picture Discussion
- Banking 2: A bank’s income statement
- Banking 3: Fractional Reserve Banking
- Banking 4: Multiplier effect and the money supply
- Banking 5: Introduction to Bank Notes
- Banking 6: Bank Notes and Checks
- Banking 7: Giving out loans without giving out gold
- Banking 8: Reserve Ratios
- Banking 9: More on Reserve Ratios (Bad sound)
- Federal Reserve Balance Sheet
- Fractional Reserve Banking Commentary 1
- FRB Commentary 2: Deposit Insurance
- FRB Commentary 3: Big Picture
- Repurchase Agreements (Repo transactions)
- The Discount Rate

**Finance:**

- 401(k)s
- An IPO
- Annual Percentage Rate (APR) and Effective APR
- Bailout 1: Liquidity vs. Solvency
- Bailout 10: Moral Hazard
- Bailout 11: Why these CDOs could be worth nothing
- Bailout 12: Lone Star Transaction
- Bailout 13: Does the bailout have a chance of working?
- Bailout 14: Possible Solution
- Bailout 15: More on the solution
- Bailout 2: Book Value
- Bailout 3: Book value vs. market value
- Bailout 4: Mark-to-model vs. mark-to-market
- Bailout 5: Paying off the debt
- Bailout 6: Getting an equity infusion
- Bailout 7: Bank goes into bankruptcy
- Bailout 8: Systemic Risk
- Bailout 9: Paulson’s Plan
- Banking 1
- Banking 2: A bank’s income statement
- Banking 3: Fractional Reserve Banking
- Banking 4: Multiplier effect and the money supply
- Bonds vs. Stocks
- Chapter 11: Bankruptcy Restructuring
- Chapter 7:Bankruptcy Liquidation
- Collateralized Debt Obligation (CDO)
- Compound Interest and e (part 2)
- Compound Interest and e (part 3)
- Compound Interest and e (part 4)
- Credit Default Swaps
- Credit Default Swaps 2
- Getting a seed round from a VC
- Going back to the till: Series B
- Home equity loans
- Housing Conundrum (part 4)
- Housing price conundrum (part 2)
- Housing Price Conundrum (part 3)
- Institutional Roles in Issuing and Processing Credit Cards
- Interest (part 2)
- Introduction to Balance Sheets
- Introduction to Bonds
- Introduction to Compound Interest
- Introduction to compound interest and e
- Introduction to interest
- Introduction to Mortgage Loans
- Introduction to Present Value
- Introduction to the yield curve
- Investment vs. Comsumption 2
- Investment vs. Consumption 1
- More on balance sheets and equity
- More on IPOs
- Mortgage-Backed Securities I
- Mortgage-backed securities II
- Mortgage-backed securities III
- Payday Loans
- Personal Bankruptcy: Chapters 7 and 13
- Ponzi Schemes
- Present Value 2
- Present Value 3
- Present Value 4 (and discounted cash flow)
- Raising money for a startup
- Relationship between bond prices and interest rates
- Renting vs. Buying (detailed analysis)
- Renting vs. Buying a home
- Renting vs. buying a home (part 2)
- Return on capital
- Roth IRAs
- The housing price conundrum
- The Rule of 72 for Compound Interest
- Traditional IRAs
- Wealth Destruction 1
- Wealth Destruction 2
- What it means to buy a company’s stock

**Valuation and Investing:**

- Amortization
- Depreciation
- Earnings and EPS
- EBITDA
- Enterprise Value
- Introduction to the Income Statement
- Introduction to the Price-to-Earnings Ratio
- P/E Conundrum
- P/E Discussion
- Price and Market Capitalization
- ROA Discussion 1
- ROA Discussion 2

**Venture Capital and Capital Markets:**

- Raising money for a startup
- Getting a seed round from a VC
- Going back to the till: Series B
- An IPO
- More on IPOs
- Equity vs. Debt
- Bonds vs. Stocks
- Chapter 7:Bankruptcy Liquidation
- Chapter 11: Bankruptcy Restructuring

**Current Economics**

- Economics of a Cupcake Factory
- Cupcake Economics 2
- Cupcake Economics 3
- Inflation, Deflation & Capacity Utilization
- Inflation, Deflation & Capacity Utilization 2
- Inflation & Deflation 3: Obama Stimulus Plan
- Unemployment
- CPI Index
- Simple Analysis of Cost per Job Saved from Stimulus
- Unemployment Rate Primer

**Credit Crisis:**

- The housing price conundrum
- Housing price conundrum (part 2)
- Housing Price Conundrum (part 3)
- Housing Conundrum (part 4)
- Mortgage-Backed Securities I
- Mortgage-backed securities II
- Mortgage-backed securities III
- Collateralized Debt Obligation (CDO)
- Bailout 13: Does the bailout have a chance of working?
- Credit Default Swaps
- Credit Default Swaps 2
- Wealth Destruction 1
- Wealth Destruction 2

**Geithner Plan:**

- Geithner Plan I
- Geithner Plan II
- Geithner Plan 2.5
- Geithner Plan III
- Geithner Plan IV
- Geithner 5: A better solution

**Paulson Bailout:**

- Bailout 1: Liquidity vs. Solvency
- Bailout 2: Book Value
- Bailout 3: Book value vs. market value
- Bailout 4: Mark-to-model vs. mark-to-market
- Bailout 5: Paying off the debt
- Bailout 6: Getting an equity infusion
- Bailout 7: Bank goes into bankruptcy
- Bailout 8: Systemic Risk
- Bailout 9: Paulson’s Plan
- Bailout 10: Moral Hazard
- Bailout 11: Why these CDOs could be worth nothing
- Bailout 12: Lone Star Transaction
- Bailout 14: Possible Solution
- Bailout 15: More on the solution

**Brain Teasers:**

- 3-D Path Counting Brain Teaser
- Alien Abduction Brain Teaser
- Blue Forehead Room Solution
- Brain Teaser: Blue Forehead Room
- Forehead Numbers Brain Teaser
- Liar Truthteller Brain Teaser
- Light Bulb Switching Brain Teaser
- Path Counting Brain Teaser
- Toggler Brain Teaser

Here are the links to the SAT and GMAT Preparation guides:

The following is an alphabetized **INDEX** of the entire Khan Academy library of YouTube videos:

2 dimensional projectile motion (part 1)

2 dimensional projectile motion (part 2)

2 dimensional projectile motion (part 4)

2-dimensional momentum problem

2-dimensional momentum problem (part 2)

2-dimensional projectile motion (part 3)

2-dimensional projectile motion (part 5)

2nd Order Linear Homogeneous Differential Equations 1

2nd Order Linear Homogeneous Differential Equations 2

2nd Order Linear Homogeneous Differential Equations 3

2nd Order Linear Homogeneous Differential Equations 4

30-60-90 Triangles II

3-D Path Counting Brain Teaser

3-variable linear equations (part 1)

401(k)s

45-45-90 Triangles

A look at a seductive but wrong Gibbs/Spontaneity Proof

A more complicated friction/inclined plane problem

A more formal understanding of functions

A Third Example of Graphing a Rational Function

âˆ«(2^ln x)/x dx Antiderivative Example

Absolute Value and Number Lines

Absolute Value Equation Example

Absolute Value Equations

Absolute Value Inequalities

Acid Base Introduction

Adding and subtracting fractions

Adding Decimals

Adding Rational Expressions Example 1

Adding Rational Expressions Example 2

Adding Rational Expressions Example 3

Adding/Subtracting negative numbers

Addition 2

Addition 3

Addition 4

Addition and Subtraction of Polynomials

Addition of Rational Numbers

Advanced ratio problems

Age word problems 1

Age word problems 2

Age word problems 3

Algebra II: Binomial Expansion and Combinatorics

Algebra II: Binomial Expansions, Geometric Series Sum

Algebra II: Circles and Logarithms

Algebra II: Complex numbers and conjugates

Algebra II: Conic Sections

Algebra II: Functions and Probability

Algebra II: Functions, Combinatorics

Algebra II: Imaginary and Complex Numbers

Algebra II: Logarithms and more

Algebra II: Logarithms Exponential Growth

Algebra II: Mean and Standard Deviation

Algebra II: Probability and Statistics

Algebra II: Quadratics and Shifts

Algebra II: Shifting Quadratic Graphs

Algebra II: Simplifying Polynomials

Algebra: Equation of a line

Algebra: graphing lines 1

Algebra: Linear Equations 1

Algebra: Linear Equations 2

Algebra: Linear Equations 3

Algebra: Linear Equations 4

Algebra: Slope

Algebra: Slope 2

Algebra: Slope 3

Algebra: Slope and Y-intercept intuition

Algebra: Solving Inequalities

Algebraic Long Division

Alien Abduction Brain Teaser

Alternate mental subtraction method

Alternate Solution to Ratio Problem (HD Version)

Amortization

Amplitude, Period, Frequency and Wavelength of Periodic Waves

An inscribed angle is half of a central angle that subtends the same arc

An IPO

An IPO

Anatomy of a muscle cell

Anatomy of a Neuron

Angle Game (part 2)

Angles (part 2)

Angles (part 3)

Angles of parallel lines

Annual Percentage Rate (APR) and Effective APR

Another mass composition problem

Another Percent Word Problem

Another Rational Function Graph Example

Another Stoichiometry Example in a Solution

Another u-subsitution example

AP Calculus BC Exams: 2008 1 a

AP Calculus BC Exams: 2008 1 b&c

AP Calculus BC Exams: 2008 1 c&d

AP Calculus BC Exams: 2008 1 d

Approximating functions with polynomials (part 3)

Area and Perimeter

Area of a circle

Area of Inscribed Equilateral Triangle (some basic trig used)

Asymptotes of Rational Functions

ATP: Adenosine Triphosphate

Average or Central Tendency: Arithmetic Mean, Median, and Mode

Averages

B Lymphocytes (B cells)

Bacteria

Bailout 1: Liquidity vs. Solvency

Bailout 1: Liquidity vs. Solvency

Bailout 10: Moral Hazard

Bailout 10: Moral Hazard

Bailout 11: Why these CDOs could be worth nothing

Bailout 11: Why these CDOs could be worth nothing

Bailout 12: Lone Star Transaction

Bailout 12: Lone Star Transaction

Bailout 13: Does the bailout have a chance of working?

Bailout 13: Does the bailout have a chance of working?

Bailout 14: Possible Solution

Bailout 14: Possible Solution

Bailout 15: More on the solution

Bailout 15: More on the solution

Bailout 2: Book Value

Bailout 2: Book Value

Bailout 3: Book value vs. market value

Bailout 3: Book value vs. market value

Bailout 4: Mark-to-model vs. mark-to-market

Bailout 4: Mark-to-model vs. mark-to-market

Bailout 5: Paying off the debt

Bailout 5: Paying off the debt

Bailout 6: Getting an equity infusion

Bailout 6: Getting an equity infusion

Bailout 7: Bank goes into bankruptcy

Bailout 7: Bank goes into bankruptcy

Bailout 8: Systemic Risk

Bailout 8: Systemic Risk

Bailout 9: Paulson’s Plan

Bailout 9: Paulson’s Plan

Balancing Chemical Equations

Banking 1

Banking 1

Banking 10: Introduction to leverage (bad sound)

Banking 11: A reserve bank

Banking 12: Treasuries (government debt)

Banking 13: Open Market Operations

Banking 14: Fed Funds Rate

Banking 15: More on the Fed Funds Rate

Banking 16: Why target rates vs. money supply

Banking 17: What happened to the gold?

Banking 18: Big Picture Discussion

Banking 2: A bank’s income statement

Banking 2: A bank’s income statement

Banking 3: Fractional Reserve Banking

Banking 3: Fractional Reserve Banking

Banking 4: Multiplier effect and the money supply

Banking 4: Multiplier effect and the money supply

Banking 5: Introduction to Bank Notes

Banking 6: Bank Notes and Checks

Banking 7: Giving out loans without giving out gold

Banking 8: Reserve Ratios

Banking 9: More on Reserve Ratios (Bad sound)

Basic Addition

Basic Multiplication

Basic Subtraction

Basic Trigonometry

Basic Trigonometry II

Binomial Distribution 1

Binomial Distribution 1

Binomial Distribution 2

Binomial Distribution 2

Binomial Distribution 3

Binomial Distribution 3

Binomial Distribution 4

Binomial Distribution 4

Binomial Theorem (part 1)

Binomial Theorem (part 2)

Binomial Theorem (part 3)

Birthday Probability Problem

Blue Forehead Room Solution

Boiling Point Elevation and Freezing Point Suppression

Bonds vs. Stocks

Bonds vs. Stocks

Box-and-whisker Plot

Brain Teaser: Blue Forehead Room

Buffers

C-4 Photosynthesis

CA Algebra I: Completing the Square

CA Algebra I: Factoring Quadratics

CA Algebra I: Functions

CA Algebra I: Graphing Inequalities

CA Algebra I: More Word Problems

CA Algebra I: Number Properties and Absolute Value

CA Algebra I: Quadratic Equation

CA Algebra I: Quadratic Roots

CA Algebra I: Rational Expressions

CA Algebra I: Rational Expressions

CA Algebra I: Simple Logical Arguments

CA Algebra I: Simplifying Expressions

CA Algebra I: Simplifying Expressions

CA Algebra I: Slope and Y-intercept

CA Algebra I: Systems of Inequalities

CA Algebra I: Word Problems

CA Geometry: Area, Circumference, Volume

CA Geometry: Area, Pythagorean Theorem

CA Geometry: Basic Trigonometry

CA Geometry: Circle Area Chords Tangent

CA Geometry: Compass Construction

CA Geometry: Deducing Angle Measures

CA Geometry: deductive reasoning

CA Geometry: Exterior Angles

CA Geometry: More on congruent and similar triangles

CA Geometry: More Proofs

CA Geometry: More Trig

CA Geometry: Proof by Contradiction

CA Geometry: Pythagorean Theorem, Area

CA Geometry: Pythagorean Theorem, Compass Constructions

CA Geometry: Secants and Translations

CA Geometry: Similar Triangles

CA Geometry: Similar Triangles

CA Geometry: Triangles and Parallelograms

CA Standards: Algebra II

CA Standards: Algebra II (Algebraic Division/Multiplication)

Calculating dot and cross products with unit vector notation

Calculus BC 2008 2 a

Calculus BC 2008 2 b &c

Calculus BC 2008 2d

Calculus Graphing with Derivatives Example

Calculus Proof that a=v^2/r

Calculus: Derivative of x^(x^x)

Calculus: Derivatives 1

Calculus: Derivatives 1 (new HD version)

Calculus: Derivatives 2

Calculus: Derivatives 2 (new HD version)

Calculus: Derivatives 2.5 (new HD version)

Calculus: Derivatives 3

Calculus: Derivatives 4: The Chain Rule

Calculus: Derivatives 5

Calculus: Derivatives 6

Calculus: Graphing Using Derivatives

Calculus: Maximum and minimum values on an interval

California Standards Test: Algebra II

California Standards Test: Algebra II (Graphing Inequalities)

CAM Plants

Cancer

Capacitance

Carnot Cycle and Carnot Engine

Carnot Efficiency 2: Reversing the Cycle

Carnot Efficiency 3: Proving that it is the most efficient

Center of Mass

Central Limit Theorem

Centripetal Acceleration (part 2)

Centripetal Acceleration (part 3)

Chapter 11: Bankruptcy Restructuring

Chapter 11: Bankruptcy Restructuring

Chapter 7:Bankruptcy Liquidation

Chapter 7:Bankruptcy Liquidation

Chilling Water Problem

Chromosomes, Chromatids, Chromatin, etc.

Circles: Radius, Diameter and Circumference

Circuits (part 1)

Circuits (part 2)

Circuits (part 3)

Circuits (part 4)

Circulatory System and the Heart

ck12.org Exercise: Standard Normal Distribution and the Empirical Rule

ck12.org Normal Distribution Problems: Empirical Rule

ck12.org Normal Distribution Problems: Qualitative sense of normal distributions

ck12.org Normal Distribution Problems: z-score

ck12.org: More Empirical Rule and Z-score practice

Closed Curve Line Integrals of Conservative Vector Fields

Collateralized Debt Obligation (CDO)

Collateralized Debt Obligation (CDO)

Column Space of a Matrix

Combinations

Combinations

Completing the square

Complex Numbers (part 1)

Complex Numbers (part 2)

Complex roots of the characteristic equations 1

Complex roots of the characteristic equations 2

Complex roots of the characteristic equations 3

Compositions of Linear Transformations 1

Compositions of Linear Transformations 2

Compound Inequalities

Compound Interest and e (part 2)

Compound Interest and e (part 2)

Compound Interest and e (part 3)

Compound Interest and e (part 3)

Compound Interest and e (part 4)

Compound Interest and e (part 4)

Conditional Probability and Combinations

Conic Identification 3

Conic Sections: Hyperbolas 2

Conic Sections: Hyperbolas 3

Conic Sections: Intro to Circles

Conic Sections: Intro to Ellipses

Conic Sections: Intro to Hyperbolas

Conjugate Acids and Bases

Conservation of angular momemtum

Conservation of Energy

Converting fractions to decimals

Covalent Networks, Metallic, and Ionic Crystals

CPI Index

Credit Default Swaps

Credit Default Swaps

Credit Default Swaps 2

Credit Default Swaps 2

Cross product 1

Cross Product 2

Cross Product and Torque

Cupcake Economics 2

Cupcake Economics 3

Curl 1

Curl 2

Curl 3

Cytotoxic T Cells

Defining a plane in R3 with a point and normal vector

Defining the angle between vectors

Definite integral with substitution

Definite Integrals (area under a curve) (part III)

Definite Integrals (part 4)

Definite Integrals (part 5)

Definite integrals (part II)

Depreciation

Derivative of a position vector valued function

Derivatives (part 7)

Derivatives (part 8)

Derivatives (part 9)

Determining a Position Vector-Valued Function for a Parametrization of Two Parameters

Determining the equation of a trigonometric function

Determining whether a transformation is onto

Differential of a vector valued function

Diffusion and Osmosis

Dimension of the Column Space or Rank

Dimension of the Null Space or Nullity

Dirac Delta Function

Direct Variation Models

Discriminant of Quadratic Equations

Distance Formula

Distributive Property

Distributive Property of Matrix Products

Divergence 1

Divergence 2

Divergence 3

Dividing decimal

Dividing fractions

Division 1

Division 2

Division 3: More long division and remainder examples

Division of Rational Numbers

DNA

Domain and Range of a Function

Domain of a function

Dot and Cross Product Comparison/Intuition

Dot vs. Cross Product

Double Integral 1

Double Integrals 2

Double Integrals 3

Double Integrals 4

Double Integrals 5

Double Integrals 6

Early Train Word Problem

Earnings and EPS

EBITDA

Economics of a Cupcake Factory

Efficiency of a Carnot Engine

Electric Potential Energy

Electric Potential Energy (part 2– involves calculus)

Electron Configurations

Electron Configurations 2

Electron Transport Chain

Electrostatics (part 1): Introduction to Charge and Coulomb’s Law

Electrostatics (part 2)

Electrotonic and Action Potentials

Embryonic Stem Cells

Empirical and Molecular Formulas from Stoichiometry

Enterprise Value

Enthalpy

Entropy Intuition

Epsilon Delta Limit Definition 1

Epsilon Delta Limit Definition 2

Equation of a tangent line

Equations and Inequalities

Equations of Parallel and Perpendicular Lines

Equations with Variables on Both Sides

Equity vs. Debt

Equivalent fractions

Evolution Clarification

Exact Equations Example 1

Exact Equations Example 2

Exact Equations Example 3

Exact Equations Intuition 1 (proofy)

Exact Equations Intuition 2 (proofy)

Example of calculating a surface integral part 1

Example of calculating a surface integral part 2

Example of calculating a surface integral part 3

Example of Closed Line Integral of Conservative Field

Example of Finding Reactant Empirical Formula

Example of Solving for a Variable

Expected Value of Binomial Distribution

Expected Value of Binomial Distribution

Expected Value: E(X)

Expected Value: E(X)

Exponent Properties Involving Products

Exponent Properties Involving Quotients

Exponent Rules Part 1

Exponent Rules Part 2

Exponential Decay Formula Proof (can skip, involves Calculus)

Exponential Decay Functions

Exponential Growth

Exponential Growth

Exponential Growth Functions

Expressing a Projection on to a line as a Matrix Vector prod

Extraneous Solutions to Radical Equations

Extreme Derivative Word Problem (advanced)

Factor by Grouping and Factoring Completely

Factoring Quadratic Expressions

Factoring Special Products

Federal Reserve Balance Sheet

Ferris Wheel Trig Problem

Ferris Wheel Trig Problem (part 2)

First Law of Thermodynamics/ Internal Energy

First order homegenous equations

First order homogenous equations 2

Fitting a Line to Data

Fluids (part 1)

Fluids (part 10)

Fluids (part 11)

Fluids (part 12)

Fluids (part 2)

Fluids (part 3)

Fluids (part 4)

Fluids (part 5)

Fluids (part 6)

Fluids (part 7)

Fluids (part 8)

Fluids (part 9)

Foci of a Hyperbola

Foci of an Ellipse

Focus and Directrix of a Parabola 2

Force with Vectors

Forehead Numbers Brain Teaser

Formula from Mass Composition

Fractional Reserve Banking Commentary 1

FRB Commentary 2: Deposit Insurance

FRB Commentary 3: Big Picture

French Revolution (Part 1)

French Revolution (Part 2)

French Revolution (Part 3) – Reign of Terror

French Revolution (Part 4) – The Rise of Napoleon Bonaparte

Friction on an inclined plane

Fun Trig Problem

Functions (part 4)

Functions (Part III)

Functions as Graphs

Functions Part 2

Galvanic Cells

Geithner 5: A better solution

Geithner Plan 2.5

Geithner Plan I

Geithner Plan II

Geithner Plan III

Geithner Plan IV

Geometric Sequences (Introduction)

Geometric series sum to figure out mortgage payments

Getting a seed round from a VC

Getting a seed round from a VC

Gibbs Free Energy and Spontaneity

Gibbs Free Energy Example

Glycolysis

GMAT Preparation

Going back to the till: Series B

Going back to the till: Series B

Gradient 1

Gradient of a scalar field

Graph of the sine function

Graphing Inequalities

Graphing trig functions

Graphing Using Intercepts

Graphing with Calculus

Graphs of Linear Equations

Graphs of Quadratic Functions

Graphs of Square Root Functions

Graphs of trig functions

Graphs Using Slope-Intercept Form

Gravitation (part 2)

Greatest Common Divisor

Green’s Theorem Example 1

Green’s Theorem Example 2

Green’s Theorem Proof (part 2)

Green’s Theorem Proof Part 1

Groups of the Periodic Table

Growing by a percentage

Haitian Revolution (Part 1)

Haitian Revolution (Part 2)

Half Equivalence Point

Half-Life

Hardy-Weinberg Principle

Harmonic Motion Part 2 (calculus)

Harmonic Motion Part 3 (no calculus)

Heat of Formation

Helper T Cells

Hemoglobin

Heron’s Formula

Hess’s Law and Reaction Enthalpy Change

Heterogenous Equilibrium

Histograms

Home equity loans

Housing Conundrum (part 4)

Housing Conundrum (part 4)

Housing price conundrum (part 2)

Housing price conundrum (part 2)

Housing Price Conundrum (part 3)

Housing Price Conundrum (part 3)

How to Rationalize a Denominator

Hydrogen Peroxide Correction

i and Imaginary numbers

Ideal Gas Equation Example 1

Ideal Gas Equation Example 2

Ideal Gas Equation Example 3

Ideal Gas Equation: PV=nRT

Ideal Gas Example 4

Identifying Conics 1

Identifying Conics 2

Identifying Exponential Models

Identifying Quadratic Models

im(T): Image of a Transformation

Image of a subset under a transformation

Implicit Differentiation

Implicit Differentiation (part 2)

Indefinite integrals (part II)

Indefinite Integration (part 7)

Indefinite Integration (part III)

Indefinite Integration (part IV)

Indefinite Integration (part V)

Inequalities Using Addition and Subtraction

Inequalities Using Multiplication and Division

Inflammatory Response

Inflation & Deflation 3: Obama Stimulus Plan

Inflation, Deflation & Capacity Utilization

Inflation, Deflation & Capacity Utilization 2

Inflection Points and Concavity Intuition

Institutional Roles in Issuing and Processing Credit Cards

Integer sums

Integers and Rational Numbers

Integrals: Trig Substitution 1

Integrals: Trig Substitution 2

Integrals: Trig Substitution 3 (long problem)

Integrating factors 1

Integrating factors 2

Integration by Parts (part 6 of Indefinite Integration)

Intelligent Design and Evolution

Interest (part 2)

Interest (part 2)

Interesting Polynomial Coefficient Problem

Intro to 30-60-90 Triangles

Intro to springs and Hooke’s Law

Introduction to angles

Introduction to angular velocity

Introduction to Balance Sheets

Introduction to Bonds

Introduction to Cellular Respiration

Introduction to centripetal acceleration (part 1)

Introduction to Compound Interest

Introduction to compound interest and e

Introduction to compound interest and e

Introduction to Conic Sections

Introduction to definite integrals

Introduction to differential equations

Introduction to differential equations

Introduction to Evolution and Natural Selection

Introduction to Exponential Decay

Introduction to friction

Introduction to functions

Introduction to Harmonic Motion

Introduction to Heredity

Introduction to interest

Introduction to interest

Introduction to Kinetics

Introduction to Limits

Introduction to Limits

Introduction to logarithm properties

Introduction to logarithm properties (part 2)

Introduction to Logarithms

Introduction to Magnetism

Introduction to matrices

Introduction to mechanical advantage

Introduction to Momentum

Introduction to Mortgage Loans

Introduction to motion

Introduction to motion (part 2)

Introduction to motion (part 3)

Introduction to Newton’s Law of Gravitation

Introduction to Order of Operations

Introduction to Oxidation States

Introduction to Parametrizing a Surface with Two Parameters

Introduction to pH, pOH, and pKw

Introduction to Present Value

Introduction to Projections

Introduction to Random Variables

Introduction to Random Variables

Introduction to rate-of-change problems

Introduction to Ratios

Introduction to Ratios (new HD version)

Introduction to Ratios (new HD version)

Introduction to Tension

Introduction to the atom

Introduction to the Convolution

Introduction to the Income Statement

Introduction to the Line Integral

Introduction to the Normal Distribution

Introduction to the Null Space of a Matrix

Introduction to the Price-to-Earnings Ratio

Introduction to the Pythagorean Theorem

Introduction to the quadratic equation

Introduction to the Surface Integral

Introduction to the yield curve

Introduction to Torque

Introduction to Waves

Introduction to work and energy

Inverse Laplace Examples

Inverse Matrix (part 1)

Inverse Trig Functions: Arccos

Inverse Trig Functions: Arcsin

Inverse Trig Functions: Arctan

Inverting matrices (part 2)

Inverting Matrices (part 3)

Investment vs. Comsumption 2

Investment vs. Consumption 1

Ionic, Covalent, and Metallic Bonds

Keq derivation intuition (can skip; bit mathy)

Keq Intuition (mathy and not necessary to progress)

Khan Academy Vision and Social Return

Krebs / Citric Acid Cycle

Ladder rate-of-change problem

Laplace Transform 1

Laplace Transform 2

Laplace Transform 3 (L{sin(at)})

Laplace Transform 4

Laplace Transform 5

Laplace Transform 6

Laplace Transform of : L{t}

Laplace Transform of t^n: L{t^n}

Laplace Transform of the Dirac Delta Function

Laplace Transform of the Unit Step Function

Laplace Transform solves an equation 2

Laplace Transform to solve an equation

Laplace/Step Function Differential Equation

Lattice Multiplication

Law of cosines

Law of Large Numbers

Law of Large Numbers

Le Chatelier’s Principle

Least Common Multiple

Level 1 Exponents

Level 1 multiplying expressions

Level 2 Addition

Level 2 Exponents

Level 3 exponents

Level 4 division

Level 4 Subtraction

Liar Truthteller Brain Teaser

Light Bulb Switching Brain Teaser

Limit Examples (part 1)

Limit Examples (part 1)

Limit Examples (part 2)

Limit Examples (part 2)

Limit Examples (part3)

Limit Examples (part3)

Limit Examples w/ brain malfunction on first prob (part 4)

Limit Examples w/ brain malfunction on first prob (part 4)

Limiting Reactant Example Problem 1

Lin Alg: A Projection onto a Subspace is a Linear Transforma

Lin Alg: Alternate Basis Tranformation Matrix Example

Lin Alg: Alternate Basis Tranformation Matrix Example Part 2

Lin Alg: Another Example of a Projection Matrix

Lin Alg: Changing coordinate systems to help find a transformation matrix

Lin Alg: Example using orthogonal change-of-basis matrix to find transformation matrix

Lin Alg: Finding projection onto subspace with orthonormal basis example

Lin Alg: Invertible Change of Basis Matrix

Lin Alg: Orthogonal Complement of the Nullspace

Lin Alg: Orthogonal Complement of the Orthogonal Complement

Lin Alg: Orthogonal matrices preserve angles and lengths

Lin Alg: Projections onto subspaces with orthonormal bases

Lin Alg: Representing vectors in Rn using subspace members

Lin Alg: Showing that A-transpose x A is invertible

Lin Alg: Transformation Matrix with Respect to a Basis

Lin Alg: Unique rowspace solution to Ax=b

Lin Alg: Visualizations of Left Nullspace and Rowspace

Line Integral Example 1

Line Integral Example 2 (part 1)

Line Integral Example 2 (part 2)

Line Integrals and Vector Fields

Linear Alg: Projection is closest vector in subspace

Linear Alg: Rowspace Solution to Ax=b example

Linear Alg: Visualizing a projection onto a plane

Linear Algebra: (correction) scalar muliplication of row

Linear Algebra: 3×3 Determinant

Linear Algebra: Another Least Squares Example

Linear Algebra: Basis of a Subspace

Linear Algebra: Change of Basis Matrix

Linear Algebra: Coordinates with Respect to a Basis

Linear Algebra: Coordinates with respect to orthonormal bases

Linear Algebra: Cross Product Introduction

Linear Algebra: Deriving a method for determining inverses

Linear Algebra: Determinant after row operations

Linear Algebra: Determinant and area of a parallelogram

Linear Algebra: Determinant as Scaling Factor

Linear Algebra: Determinant of Transpose

Linear Algebra: Determinant when row is added

Linear Algebra: Determinant when row multiplied by scalar

Linear Algebra: Determinants along other rows/cols

Linear Algebra: dim(V) + dim(orthogonoal complelent of V)=n

Linear Algebra: Duplicate Row Determinant

Linear Algebra: Eigenvalues of a 3×3 matrix

Linear Algebra: Eigenvectors and Eigenspaces for a 3×3 matrix

Linear Algebra: Example of Finding Matrix Inverse

Linear Algebra: Example solving for the eigenvalues of a 2×2 matrix

Linear Algebra: Exploring the solution set of Ax=b

Linear Algebra: Finding Eigenvectors and Eigenspaces example

Linear Algebra: Formula for 2×2 inverse

Linear Algebra: Gram-Schmidt example with 3 basis vectors

Linear Algebra: Gram-Schmidt Process Example

Linear Algebra: Introduction to Eigenvalues and Eigenvectors

Linear Algebra: Introduction to Linear Independence

Linear Algebra: Introduction to Orthonormal Bases

Linear Algebra: Introduction to the inverse of a function

Linear Algebra: Introduction to Vectors

Linear Algebra: Least Squares Approximation

Linear Algebra: Least Squares Examples

Linear Algebra: Matrix condition for one-to-one trans

Linear Algebra: Matrix Product Examples

Linear Algebra: nxn Determinant

Linear Algebra: Orthogonal Complements

Linear Algebra: Parametric Representations of Lines

Linear Algebra: Projections onto Subspaces

Linear Algebra: Proof of formula for determining Eigenvalues

Linear Algebra: Rank(A) = Rank(transpose of A)

Linear Algebra: Rowspace and Left Nullspace

Linear Algebra: Rule of Sarrus of Determinants

Linear Algebra: Showing that an eigenbasis makes for good coordinate systems

Linear Algebra: Showing that Inverses are Linear

Linear Algebra: Simpler 4×4 determinant

Linear Algebra: Simplifying conditions for invertibility

Linear Algebra: Subspace Projection Matrix Example

Linear Algebra: The Gram-Schmidt Process

Linear Algebra: Transpose of a Matrix

Linear Algebra: Transpose of a Vector

Linear Algebra: Transposes of sums and inverses

Linear Algebra: Upper Triangular Determinant

Linear Algebra: Vector Examples

Linear Algebra: Vector Triangle Inequality

Linear Combinations and Span

Linear Equations in Point Slope Form

Linear Equations in Slope Intercept Form

Linear Equations in Standard Form

Linear Function Graphs

Linear Subspaces

Linear Transformation Examples: Rotations in R2

Linear Transformation Examples: Scaling and Reflections

Linear Transformations

Linear Transformations as Matrix Vector Products

Linear, Quadratic, and Exponential Models

Macrostates and Microstates

Magnetism 10: Electric Motors

Magnetism 11: Electric Motors

Magnetism 12: Induced Current in a Wire

Magnetism 2

Magnetism 3

Magnetism 4

Magnetism 5

Magnetism 6: Magnetic field due to current

Magnetism 7

Magnetism 8

Magnetism 9: Electric Motors

Mass on Inclined Plane

Matrices to solve a system of equations

Matrices to solve a vector combination problem

Matrices: Reduced Row Echelon Form 1

Matrices: Reduced Row Echelon Form 2

Matrices: Reduced Row Echelon Form 3

Matrix multiplication (part 1)

Matrix multiplication (part 2)

Matrix Product Associativity

Matrix Vector Products

Matrix Vector Products as Linear Transformations

Maxima Minima Slope Intuition

Maxwell’s Demon

Mean Value Theorem

Mechanical Advantage (part 2)

Mechanical Advantage (part 3)

Midpoint Formula

Mini-Video on Ion Size

Mitosis, Meiosis and Sexual Reproduction

Mixed numbers and improper fractions

Molecular and Empirical Formulas

Moments

Moments (part 2)

Momentum: Ice skater throws a ball

Monotonicity Theorem

More advanced ratio problem–with Algebra (HD version)

More chain rule and implicit differentiation intuition

More Complicated Order of Operations Example

More Exponential Decay Examples

More implicit differentiation

More Involved Radical Equation Example

More Laplace Transform tools

More Limits

More Limits

More on balance sheets and equity

More on Entropy

More on Internal Energy

More on IPOs

More on IPOs

More on linear independence

More on Matrix Addition and Scalar Multiplication

More on orbitals and electron configuration

More on Oxidation States

More percent problems

More rigorous Gibbs Free Energy/ Spontaneity Relationship

More Simplifying Radical Expressions

More trig graphs

Mortgage-Backed Securities I

Mortgage-Backed Securities I

Mortgage-backed securities II

Mortgage-backed securities II

Mortgage-backed securities III

Mortgage-backed securities III

Moving pulley problem (part 1)

Moving pulley problem (part 2)

Mulitplication 8: Multiplying decimals (Old video)

Multiplication 2: The Multiplication Tables

Multiplication 3: 10,11,12 times tables

Multiplication 4: 2-digit times 1-digit number

Multiplication 5: 2-digit times a 2-digit number

Multiplication 6: Multiple Digit Numbers

Multiplication 7: Old video giving more examples

Multiplication of Polynomials

Multiplication of Rational Numbers

Multiplying and dividing negative numbers

Multiplying and Dividing Rational Expressions

Multiplying fractions

Multi-Step Equations

Multi-Step Inequalities

Myosin and Actin

Napoleon and the War of the Fourth Coalition

Napoleon and the War of the Third Coalition

Napoleon and the Wars of the First and Second Coalitions

Napoleon Forced to Abdicate

Napoleon’s Peninsular Campaigns

Natural Selection and the Owl Butterfly

Navigation Word Problem

Negative Exponent Intuition

Neuronal Synapses (Chemical)

Newton’s First Law of Motion

Newton’s Laws

Newton’s Laws and vectors

Newton’s Laws Examples (part 2)

Newton’s Laws Problems (part 1)

Newton’s Second Law of Motion

Newton’s Third Law of Motion

Normal Distribution Excel Exercise

Null Space 2: Calculating the null space of a matrix

Null Space 3: Relation to Linear Independence

Null Space and Column Space Basis

Officer on Horseback

One Step Equations

Optimization Example 4

Optimization with Calculus 1

Optimization with Calculus 2

Optimization with Calculus 3

Orbitals

Order of Operations

Ordering numeric expressions

Other Periodic Table Trends

Overtaking Word Problem

Oxidation and Reduction in Cellular Respiration

Oxidation and Reduction Review From Biological Point-of-View

Oxidative Phosphorylation and Chemiosmosis

P/E Conundrum

P/E Discussion

Parabola Focus and Directrix 1

Parametric Equations 1

Parametric Equations 2

Parametric Equations 3

Parametric Equations 4

Parametrization of a Reverse Path

Part 1 of Proof of Heron’s Formula

Part 2 of the Proof of Heron’s Formula

Partial Derivatives

Partial Derivatives 2

Partial Derivatives of Vector-Valued Functions

Partial Fraction Expansion 1

Partial Fraction Expansion 2

Partial Fraction Expansion 3

Partial Pressure

Parts of a cell

Passed Bike Word Problem

Passing Trains

Path Counting Brain Teaser

Path Independence for Line Integrals

Patterns and Equations

Payday Loans

Percent and decimals

Percent Problems

Periodic Table Trends: Ionization Energy

Permutations

Permutations

Personal Bankruptcy: Chapters 7 and 13

pH of a Weak Acid

pH of a Weak Base

pH, pOH of Strong Acids and Bases

Phase Diagrams

Phases of Meiosis

Phases of Mitosis

Photorespiration

Photosynthesis

Photosynthesis: Calvin Cycle

Photosynthesis: Light Reactions 1

Photosynthesis: Light Reactions and Photophosphorylation

pKa and pKb Relationship

Poisson Process 1

Poisson Process 1

Poisson Process 2

Poisson Process 2

Polar Coordinates 1

Polar Coordinates 1

Polar Coordinates 2

Polar Coordinates 2

Polar Coordinates 3

Polar Coordinates 3

Polynomial approximation of functions (part 1)

Polynomial approximation of functions (part 2)

Polynomial approximation of functions (part 4)

Polynomial approximation of functions (part 6)

Polynomial approximation of functions (part 7)

Polynomial approximations of functions (part 5)

Polynomial Division

Polynomial Equations in Factored Form

Ponzi Schemes

Position Vector Valued Functions

Potential energy stored in a spring

Predicting with Linear Models

Preimage and Kernel Example

Preimage of a set

Present Value 2

Present Value 3

Present Value 4 (and discounted cash flow)

Price and Market Capitalization

Probability (part 1)

Probability (part 2)

Probability (part 3)

Probability (part 4)

Probability (part 5)

Probability (part 6)

Probability (part 7)

Probability (part 8)

Probability and Combinations (part 2)

Probability Density Functions

Probability Density Functions

Probability using Combinations

Problem Solving Word Problems 2

Professional Antigen Presenting Cells (APC) and MHC II complexes

Projectile motion (part 1)

Projectile motion (part 10)

Projectile motion (part 2)

Projectile motion (part 3)

Projectile motion (part 4)

Projectile motion (part 5)

Projectile motion (part 6)

Projectile motion (part 7)

Projectile motion (part 8)

Projectile motion (part 9)

Projectile Motion with Ordered Set Notation

Projectile Motion with Unit Vectors

Projectile Motion with Unit Vectors (part 2)

Proof (Advanced): Field from infinite plate (part 1)

Proof (Advanced): Field from infinite plate (part 2)

Proof of Quadratic Formula

Proof of the Cauchy-Schwarz Inequality

Proof: A(log B) = log (B^A), log A – log B = log (A/B)

Proof: Any subspace basis has same number of elements

Proof: cos(a+b) = (cos a)(cos b)-(sin a)(sin b)

Proof: d/dx(e^x) = e^x

Proof: d/dx(ln x) = 1/x

Proof: d/dx(sqrt(x))

Proof: d/dx(x^n)

Proof: Hyperbola Foci

Proof: Invertibility implies a unique solution to f(x)=y

Proof: Law of Sines

Proof: lim (sin x)/x

Proof: lim (sin x)/x

Proof: log a + log b = log ab

Proof: log_a (B) = (log_x (B))/(log_x (A))

Proof: Relationship between cross product and sin of angle

Proof: S (or Entropy) is a valid state variable

Proof: sin(a+b) = (cos a)(sin b) + (sin a)(cos b)

Proof: U=(3/2)PV or U=(3/2)nRT

Proof: Volume Ratios in a Carnot Cycle

Proofs of Derivatives of Ln(x) and e^x

Proportionality

Proving Vector Dot Product Properties

Punnett Square Fun

PV-diagrams and Expansion Work

Pythagorean Theorem

Pythagorean Theorem II

Quadratic Equation part 2

Quadratic Formula (proof)

Quadratic Inequalities

Quadratic Inequalities (Visual Explanation)

Quadratic Regression

Quasistatic and Reversible Processes

Radians and degrees

Radical Equation Examples

Radical Expressions with Higher Roots

Raising money for a startup

Raising money for a startup

Range, Variance and Standard Deviation as Measures of Dispersion

Rates-of-change (part 2)

Ratio and Proportion

Ratio problem with basic algebra (new HD)

Rational Inequalities

Rational Inequalities 2

Reactions in Equilibrium

Reconciling Thermodynamic and State Definitions of Entropy

Red blood cells

Redox Reactions

Relating invertibility to being onto and one-to-one

Relationship between bond prices and interest rates

Renting vs. Buying (detailed analysis)

Renting vs. Buying a home

Renting vs. buying a home (part 2)

Repeated roots of the characterisitic equations part 2

Repeated roots of the characteristic equation

Repurchase Agreements (Repo transactions)

Return on capital

Review of B cells, CD4+ T cells and CD8+ T cells

Right Triangles Inscribed in Circles (Proof)

ROA Discussion 1

ROA Discussion 2

Role of Phagocytes in Innate or Nonspecific Immunity

Role of the Sarcoplasmic Reticulum in Muscle Cells

Rotation in R3 around the X-axis

Roth IRAs

Saltatory Conduction in Neurons

Sampling Distribution of the Sample Mean

Sampling Distribution of the Sample Mean 2

SAT Preparation

Scalar Field Line Integral Independent of Path Direction

Scale and Indirect Measurement

Scientific Notation

Scientific Notation

Scientific Notation Examples

Second Example of Line Integral of Conservative Vector Field

Secondary Active Transport in the Nephron

Separable Differential Equations

Separable differential equations 2

Sequences and Series (part 1)

Sequences and Series (part 1)

Sequences and series (part 2)

Sequences and series (part 2)

Sex-Linked Traits

Showing relation between basis cols and pivot cols

Showing that the candidate basis does span C(A)

Similar triangles

Similar triangles (part 2)

Simple Analysis of Cost per Job Saved from Stimulus

Simplifying radicals

Simplifying Rational Expressions

Singular Matrices

Slope and Rate of Change

Slope and Y-intercept Intuition

Sodium Potassium Pump

Solid of Revolution (part 1)

Solid of Revolution (part 2)

Solid of Revolution (part 3)

Solid of Revolution (part 4)

Solid of Revolution (part 5)

Solid of Revolution (part 6)

Solid of Revolution (part 7)

Solid of Revolution (part 8)

Solubility

Solving 3 Equations with 3 Unknowns

Solving a quadratic by factoring

Solving Linear Systems by Graphing

Solving Linear Systems by Substitution

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Graphing

Solving Quadratic Equations by Square Roots

Solving Rational Equations

Solving Systems of Equations by Elimination

Solving Systems of Equations by Multiplication

Span and Linear Independence Example

Special Products of Binomials

Special Types of Linear Systems

Specific Heat, Heat of Fusion and Vaporization

Speed translation

Spring potential energy example (mistake in math)

Square Roots and Real Numbers

Squeeze Theorem

Squeeze Theorem

Standard Error of the Mean

States of Matter

States of Matter Follow-Up

Statistics: Alternate Variance Formulas

Statistics: Sample Variance

Statistics: Sample vs. Population Mean

Statistics: Standard Deviation

Statistics: The Average

Statistics: Variance of a Population

Stem and Leaf Plots

Stoichiometry

Stoichiometry Example Problem 1

Stoichiometry Example Problem 2

Stoichiometry of a Reaction in Solution

Stoichiometry: Limiting Reagent

Strong Acid Titration

Subraction of Rational Numbers

Subtracting decimals

Subtraction 2

Subtraction 3: Introduction to Borrowing or Regrouping

Sums and Scalar Multiples of Linear Transformations

Surjective (onto) and Injective (one-to-one) functions

Surveys and Samples

Suspensions, Colloids and Solutions

systems of equations

Systems of Linear Inequalities

Taking percentages

Taylor Polynomials

Tension (part 2)

Tension in an accelerating system and pie in the face

The Angle Game

The Convolution and the Laplace Transform

The Coordinate Plane

The Discount Rate

The dot product

The housing price conundrum

The housing price conundrum

The Indefinite Integral or Anti-derivative

The Kidney and Nephron

The Lungs and Pulmonary System

The Mole and Avogadro’s Number

The Rule of 72 for Compound Interest

The unit circle definition of trigonometric function

Thermodynamic Entropy Definition Clarification

Thermodynamics (part 1)

Thermodynamics (part 2)

Thermodynamics (part 3)

Thermodynamics (part 4)

Thermodynamics (part 5)

Titration Roundup

Toggler Brain Teaser

Traditional IRAs

Trig identies part 3 (part 5 if you watch the proofs)

Trig identities part 2 (parr 4 if you watch the proofs)

Trig Implicit Differentiation Example

Trigonometric Identities

Trigonometry Identity Review/Fun

Trigonometry word problems (part 1)

Trigonometry word problems (part 2)

Triple Integrals 1

Triple Integrals 2

Triple Integrals 3

Tropomyosin and troponin and their role in regulating muscle contraction

Two more examples of solving rational equations

Two Passing Bicycles Word Problem

Two-Step Equations

Types of Decay

Types of immune responses: Innate and Adaptive. Humoral vs. Cell-Mediated

Undetermined Coefficients 1

Undetermined Coefficients 2

Undetermined Coefficients 3

Undetermined Coefficients 4

Unemployment

Unemployment Rate Primer

Unit Circle Definition of Trig Functions

Unit conversion

Unit Conversion Example: Drug Dosage

Unit Vector Notation

Unit Vector Notation (part 2)

Unit Vectors

Using a line integral to find the work done by a vector field example

Using a Linear Model

Using the Convolution Theorem to Solve an Initial Value Prob

Using the Laplace Transform to solve a nonhomogenous eq

Using the Quadratic Formula

Using Trig Functions

Using Trig Functions Part II

Valence Electrons

Van Der Waals Forces

Vapor Pressure

Variable Expressions

Variation in a Species

Vector Dot Product and Vector Length

Vector Field Line Integrals Dependent on Path Direction

Vector Transformations

Vector valued function derivative example

Viruses

Visual Proof: a= v^2/r

Visual Pythagorean Theorem Proof

Visualizing a Column Space as a Plane in R3

Voltage

Weak Acid Titration

Wealth Destruction 1

Wealth Destruction 1

Wealth Destruction 2

Wealth Destruction 2

What it means to buy a company’s stock

Why borrowing works

Why Lattice Multiplication Works

Word Problem Solving 3

Word Problem Solving 4

Word Problem Solving- Exponential Growth and Decay

Word Problem Solving Plan 1

Word Problem Solving Strategies

Work and Energy (part 2)

Work Done by Isothermic Process

Work from Expansion

Work/Energy problem with Friction

Zero, Negative, and Fractional Exponents

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