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Algebra
- Adding and Subtraction Functions
- Algebra Word Problem: Distance rate, time
- Averages
- Complex Numbers - Graphing, Adding and Subtracting
- Complex Numbers - Multiplying and Dividing
- Composition of Functions
- Descarte's Rule of Signs
- Domain and Range - Basic Idea - Reading the Domain and Range from Two Graphs
- Equation of a line
- Evaluating Numbers Raised to Fractional Exponents
- Finding the Domain of a Function (not from a graph)
- Function Notation
- Growing by a percentage
- Integer sums
- Intermediate Value Theorem
- Linear Equations 1
- Linear Equations 2
- Linear Equations 3
- Linear Equations 4
- Long Division of Polynomials
- Long Division of Polynomials - Slightly Harder Example
- More percent problems
- Multplying and Dividing Functions
- Negative Exponents and Fractional Exponents
- Properties of Logarithms - Logarithmic Functions (algebra stuff!!)
- Simplifying Numbers Under Square Roots
- Slope
- Slope 2
- Slope 3
- Slope and Y-intercept intuition
- Solving Inequalities
- Synthetic Division - Example 1
- Synthetic Division - Example 2
- Taking percentages
- The Basic Rules
- The Distance Formula
- The Midpoint Formula
- The Pythagorean Theorem
Arithmetic
- Absolute Value
- Adding and Subtracting Fractions
- Adding and Subtracting Polynomials
- Adding Decimals
- Basic Addition
- Basic Multiplication
- Basic Subtraction
- Converting fractions to decimals
- Dividing Decimal
- Dividing Decimals II
- Equivalent fractions
- Factoring Numbers
- Finding the Greatest Common Factor, GCF
- Finding the Least Common Multiple, LCM
- Finding the Percent of a Number
- Greatest Common Divisor
- Least Common Multiple
- Level 2 Addition
- Level 4 Division
- Level 4 Subtraction
- Mixed numbers and improper fractions
- 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
- Multiplying and Dividing Fractions
- Multiplying Decimals
- Ordering numeric expressions
- Percent and decimals
- Radical Notation
- Rationalizing the Denominator of a Fraction - A few basic examples
- Rationalizing the Denominator of a Fraction - A harder example
- Subtracting Decimals
- Why Borrowing Works
Calculus
- Basic Derivative Examples
- Basic Derivative Formulas
- Chain Rule - Harder Example # 1
- Chain Rule - Harder Example # 2
- Chain Rule - Harder Example # 3
- Continuity - Basic Idea and Types of Discontinuities
- Continuity - Examples of Finding Discontinuities of Piecewise Functions
- Derivatives involving Exponential Functions - e^x, a^x, etc
- Derivatives Involving Inverse Trigonometric Functions
- Derivatives Involving Logarithmic Functions - ln(x), log (x), etc.
- Derivatives Using Implicit Differentiation
- Derivatives Using Implicit Differentiation - More Examles #2
- Derivatives Using Implicit Differentiation - More Examples #1
- Derivatives Using the Chain Rule
- Derivatives Using the Product Rule
- Derivatives Using the Quotient Rule
- Find the Linearization at a Point
- Finding Partial Derivatives
- Finding the Derivative Using the Definition of the Derivative
- Finding the Equation of a Tangent Line
- Inverse Trigonometric Derivative Example 1
- Inverse Trigonometric Derivative Example 2
- Inverse Trigonometric Derivative Example 3
- Logarithmic Differentiation - Basic Idea and Example
- Logarithmic Differentiation Example 2
- More Chain Rule Examples
- More Complicated Derivative Examples
- More Complicated Derivative Examples - Part 2
- More Examples Involving Inverse Trig Functions
- More Examples Using the Product Rule
- More Examples Using the Quotient Rule
- Newton's Method
- Related Rates - A point moving on a graph
- Related Rates - Baseball Diamond Example
- Related Rates - With Trigonometry
- Related Rates Involving a Cone
- Related Rates Problems and Implicit Differentiation
- Sketching the Derivative of a Function
- The General Chain Rule - Part 1
- The General Chain Rule - Part 2
- The Mean Value Theorem
- Using the Product and Chain Rule to Find a Derivative - Then Factoring and Simplifying
Calculus - Multivariable
- Calculating the Dot Product Between Two Vectors
- Cross Product - Finding the Cross Product of Two Vectors
- Directional Derivatives
- Finding the Domain of a Vector Function
- Finding the Limit of a Vector Function
- Finding the Magnitude or Length of a Vector
- Finding the Scalar Equation of a Plane
- Finding the Vector Equation of a Line
- Sketching a Vector Field
- Tangent Plane Approximations
- The Arc Length of a Vector Function
- The Gradient Vector - Notation and Definition
- The Jacobian
- Torque - An Application of the Cross Product
- Vector Basics - Algebraic Representations - Part 2
- Vector Basics - Algebraic Representations - Part 2-2
- Vector Basics - Drawing Vectors and Vector Addition
Differential equations
- 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
- Exact Equations Example 1
- Exact Equations Example 2
- Exact Equations Example 3
- Exact Equations Intuition 1 (proofy)
- Exact Equations Intuition 2 (proofy)
- First order homegenous equations
- Integrating factors 1
- Integrating factors 2
- Introduction to differential equations
- Repeated roots of the characteristic equation 1
- Repeated roots of the characteristic equation 2
- Separable Differential Equations
- Separable differential equations 2
- Undetermined Coefficients 1
- Undetermined Coefficients 2
- Undetermined Coefficients 3
- Undetermined Coefficients 4
Geometry
- 30-60-90 Triangles II
- 45-45-90 Triangles
- Angles (part 2)
- Angles (part 3)
- Angles of parallel lines
- Area and Perimeter
- Area of a circle
- Circles: Radius, Diameter and Circumference
- Intro to 30-60-90 Triangles
- Introduction to angles
- Introduction to the Pythagorean Theorem
- Pythagorean Theorem II
- Similar triangles
- Similar triangles (part 2)
- The Angle Game
- The Angle Game (part 2)
Graphing
- A quick sketch of about 10 basic graphs you should know!
- Finding the Domain and Range of the Above Piecewise Defined Function
- Finding the Equation of a Line Using Point-Slope Form
- Finding the Equation of an Exponential Function from a Graph
- Finding the Formula of a Piecewise Defined Function from a Graph
- Finding the Slope between Two Points
- Graph of the sine function
- Graph Transformations - Basic Formulas and Vertical Stretching/Compressing is Discussed
- Graph Transformations - Horizontal and Vertical shifts
- Graph Transformations - Horizontal and Vertical Stretching/Compressing is Discussed
- Graph Transformations - Putting it All Together!! Example 1
- Graph Transformations - Putting it All Together!! Example 2
- Graph Transformations - Reflections about the X - Axis and Y-Axis are discussed - Basic Idea!
- Graphing Linear Functions by Finding X and Y Intercepts
- Graphing Linear Systems of Inequalities - Example 1
- Graphing Linear Systems of Inequalities - Example 2
- Graphing Piecewise Defined Functions
- Graphing Quadratic Functions
- Graphing the Great Integer Function also known as the Floor Function
- Graphs of trig functions
- More trig graphs
Integration
- Approximating a Definite Integral Using Rectangles
- Basic Antiderivate Examples (Indefinite Integrals)
- Basic Integration Formulas (high volume, turn down speakers)
- Basic Integration Problems 2
- Calculating a Definite Integral Using Riemann Sums - Part 1
- Calculating a Definite Integral Using Riemann Sums - Part 2
- Simpson's Rule and Error Bounds
- Simpson's Rule to Approximate a Definite Integral
- Summation Notation
- The Definite Integral - Understanding the Definition
- Trapezoidal Rule to Approximate a Definite Integral
Limits
- Basic Limit at Infinity Example and 'Shortcut' Information
- Basic Limit Information
- Calculating Limits by Expanding and Cancelling
- Calculating Limits by Factoring and Cancelling
- Calculating Limits by Getting Common Denominators
- Calculating Limits by Multiplying by a Conjugate
- Calculating Limits by using: limit x--> 0 [sin(x)/x] = 1
- Calculating Limits Involving Absolute Value
- First order homegenous equations 2
- Infinite Limits
- Limit at Infinity Example with Radicals Present - Two Examples
- The Squeeze Theorem For Limits
Linear Algebra
- 3-variable linear equations (part 1)
- Basis of a Subspace
- Defining the angle between vectors
- Introduction to Linear Independence
- Introduction to matrices
- Introduction to Vectors
- Inverse Matrix (part 1)
- Inverting matrices (part 2)
- Inverting Matrices (part 3)
- Linear Combinations and Span
- Linear independence (more)
- Linear Independence and Span Example
- Linear Subspaces
- Matrices to solve a system of equations
- Matrices to solve a vector combination problem
- Matrix multiplication (part 1)
- Matrix multiplication (part 2)
- Parametric Representations of Lines
- Proof of the Cauchy-Schwarz Inequality
- Proving Vector Dot Product Properties
- Singular Matrices
- Solving 3 Equations with 3 Unknowns
- Vector Dot Product and Vector Length
- Vector Examples
- Vector Triangle Inequality
Statistics
- Alternate Variance Formulas
- Binomial Distribution 1
- Binomial Distribution 2
- Binomial Distribution 3
- Binomial Distribution 4
- Expected Value of Binomial Distribution
- Expected Value: E(X)
- Introduction to the Normal Distribution
- Law of Large Numbers
- Normal Distribution Excel Exercise
- Poisson Process 1
- Poisson Process 2
- Probability Density Functions
- Sample Variance
- Sample vs. Population Mean
- Standard Deviation
- The Average
- Variance of a Population
Trigonometry
- Basic Trigonometry
- Basic Trigonometry 2
- Determining the equation of a trigonometric function
- Ferris Wheel Trig Problem
- Ferris Wheel Trig Problem (part 2)
- Fun Trig Problem
- Inverse Trig Functions: Arccos
- Inverse Trig Functions: Arcsin
- Inverse Trig Functions: Arctan
- Law of cosines
- 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
- Trig identies part 3 (part 5 if you watch the proofs)
- Trig identities part 2 (part 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 Part 2