Class Videos

• Calculus 1

  Limits and Continuity

  • Limits and Limit Laws
    • Speed and Limits
    • Tangents and Limits
    • Limits and Limit Laws
    • Limits of Rational Functions
    • Limits of Complex Rational Functions
    • Limits with Conjugates
    • Limits with the Difference Quotient
  • One-Sided Limits
    • One-sided Limits
    • (Sin θ)/θ
    • Special Trig Limits
  • Limits involving infinity and asymptotes
    • Concepts with 1/x
    • Vertical asymptotes of a rational function
    • Limits at infinity with rational function - motivation
    • Limits at infinity with rational functions
    • A function with two horizontal asymptotes
    • A horizontal asymptote and an exponential function
    • An oblique asymptote
    • sin(x)/x
    • Asymptotes and trig, exponential, and logarithmic functions
  • Continuity
    • The Definition of Continuity
    • Classifying Discontinuities
    • The Intermediate Value Theorem
  • Definition of the Limit
    • The Definition of the Limit
    • Proofs with the Definition of the Limit

  Differentiation

  • Slopes, tangents, and the derivative
    • The slope of a curve and tangent lines
    • A tangent to the square root function
    • A tangent to x-cubed
    • The definition of the derivative
    • The derivative of 1/x
    • The derivative of the square root function
    • An alternative form of the derivative
    • Differentiability and continuity
    • The derivative and the shape of a curve
  • Derivative rules
    • Overview of derivative rules
    • Derivative of a polynomial
    • Product rule example
    • Quotient rule example
    • Product and quotient rule
    • Higher order derivatives
    • Velocity and the derivative
  • Derivative rule derivations
    • The derivative of a constant
    • The power rule
    • The derivative of the exponential function
    • The derivative of sin(x)
    • The derivative of tan(x)
    • The constant multiple rule
    • The sum and difference rules
    • The product rule
    • The quotient rule
  • The Chain Rule
    • Chair Rule Overview
    • A Power
    • A Root
    • Tangent
    • Exponential
    • Nested functions
    • Sine squared
    • A chain and a product
    • Another chain and a product
    • A chain and a quotient
    • Another chain and a quotient
    • Proof concept for chain rule
  • Implicit Differentiation
    • Implicit differentiation introduction
    • Folium
    • Trig and product example
    • Quotient example
    • Cotangent example
    • Example with a third variable
    • Area of a circle
    • Volume of a cone
  • Related Rates
    • A related rates problem with a cone
    • A sphere
    • A trig function
    • Pythagorean Theorem
  • Inverse Functions and Logarithms
    • Inverse Functions
    • The Derivative of ln(x)
    • The Derivative of ln|x|
    • Chain Rule and ln(x)
    • A Derivative with ln(x)
    • A Derivative with ln(x)
    • Derivatives and Log Properties
    • Logarithmic Differentiation 1
    • Logarithmic Differentiation 2
    • Other Bases
    • The Power Rule
    • e As a Limit
  • Derivatives of Inverse Trig Functions
    • Restricting Domains
    • Evaluating Inverse Trig Functions
    • Trig Functions and Inverse Trig Functions
    • Derivative of Arcsine
    • Derivative of Arctangent
    • Derivative of Arcsecant
    • Inverse Trig Derivative Example
    • Inverse Trig Derivative Example
    • Inverse Trig Derivative Example
    • Inverse Trig Derivative Example
  • Linearization and Differentials
    • Blank
  • Extreme Values
    • Extreme Values
    • Optimization on a closed interval
    • Optimization on a closed interval 2
  • Mean Value Theorem
    • Rolle's Theorem
    • Rolle's Theorem Example
    • Mean Value Theorem
    • Mean Value Theorem Example
    • Two Theorems
  • Analysis
    • Overview of Analysis
    • Analysis Example
    • Analysis Example 2
    • Analysis Example 3
    • Analysis Example 4
    • Proof of First Derivative Test
  • L'Hopital's Rule
    • Indeterminate Forms
    • Form 0/0
    • Form ∞/∞
    • Products and Differences
    • Indeterminate Powers
    • A proof of a version of L'Hopital's Rule
  • Applied Optimization
    • Rectangular Pen
    • Minimum Distance
    • Maximum Volume, Fixed Surface Area
    • Minimum Surface Area, Fixed Volume
    • Inscribed Rectangle
    • Poster
  • Newton's Method
    • Blank

  Integration

  • Antiderivatives
    • Antiderivatives
    • Antiderivatives with Powers
    • Antiderivatives with Trig and Exponentials
    • Initial Value Problem - First Derivative
    • Initial Value Problem - Second Derivative
    • Initial Value Problem - Projectile
  • Estimating Area
    • Approximating area with rectangles - example
    • Approximating area with rectangles -
    • Approximating distance from velocity - example
    • Approximating distance from velocity
    • Approximating average value
  • Sigma Notation
    • Sigma notation
    • Sigma notation algebra rules
    • Using sigma notation algebra rules
  • Limit of Riemann Sums
    • Area, distance, and average value as limits of sums
    • Finding area as a limit of sums
  • The Definite Integral
    • Definition and interpretations of the definite integral
    • Properties of the definite integral
  • The Fundamental Theorem of Calculus
    • The Fundamental Theorem of Calculus
    • A Proof of the Fundamental Theorem of Calculus
    • Evaluating an integral examples
    • Area examples
    • Derivative of an integral examples
  • Integration by Substitution
    • Substitution examples
    • More substitution examples
    • Even more substitution examples
    • Definite integrals and substitution
  • Area Between Curves
    • Derivations
    • Simple area between curves
    • Two points of intersection
    • Three points of intersection
    • A region bounded by three functions
    • An integral with respect to y
    • An area which is easier with respect to y

• Calculus 2

  Integration

  • Definite Integrals and the Fundamental Theorem of Calculus
    • Area, distance, and average value as limits of sums and definite integrals
    • Definition and interpretations of the definite integral
    • The Fundamental Theorem of Calculus
    • Evaluating an integral examples
    • Area examples
  • Integration by Substitution
    • Substitution examples
    • More substitution examples
    • Even more substitution examples
    • Definite integrals and substitution

  Applications of Integration

  • Area Between Curves
    • Derivations
    • Simple area between curves
    • Two points of intersection
    • Three points of intersection
    • A region bounded by three functions
    • An integral with respect to y
    • An area which is easier with respect to y
  • Volumes by cross sections
    • Derivations
    • A pyramid
    • A wedge
    • Given cross sections
  • Volumes of solids of revolution
    • Derivations
    • Disks with respect to x
    • Shells with respect to x
    • Shells with respect to y
    • Disks (washers) with respect to y
    • Shells with respect to x
  • Arc Length
    • Derivations
    • Basic arc length
    • Perfect square
    • Arc length with respect to y
  • Surfaces of Revolution
    • Derivations
    • Around the x-axis with respect to x
    • Around the y-axis with respect to y
    • Around the y-axis with respect to x
  • Work
    • Derivations
    • Springs
    • Cable/Rope
    • A cable lifting a leaking bucket
  • Pumping problems
    • Revisiting cables and ropes
    • A rectangular tank
    • A conical tank
  • Fluid Force
    • Force on a horizontal plate
    • Force on a vertical plate
  • Center of Mass
    • Center of mass of a discrete system of point masses
    • Center of mass of a region
    • Theorem of Pappus
    • Theorem of Pappus Example
    • Centroids and fluid force

  Integrals and Transcendental Functions

  • The Logarithm as an Integral
    • The problem with early transcendentals
    • The definition of ln(x)
    • The definition of exp(x)
    • General exponentials and logarithms
  • Exponential Change
    • Differential equations
    • Exponential change derivation
    • Population growth
    • Radioactive decay
    • Newton's Law of Cooling

  Integration Techniques

  • Integration by Parts
    • Derivation
    • x sin(x)
    • x ln(x)
    • x² e^x
    • Tabular Integration
    • Tabular Integration 2
    • Arctan (definite integral)
    • A circle
  • Trig Integrals
    • Peel off Introduction
    • Cosine Cubed
    • sin⁶(x)
    • sec⁴(x) tan²(x)
    • sec³(x) tan³(x)
    • A square root
    • Secant Cubed
    • Tangent Squared
    • Tangent Cubed
    • Tangent to the Fourth
  • Trig Substitution
    • Introduction
    • Example 1
    • Example 2
    • Example 3
    • Example 4
  • Getting Ready for Partial Fractions
    • Rational function with a linear denominator
    • Rational function with repeated linear denominator
    • Rational function with a quadratic denominator
    • Rational function with a quadratic denominator 2
    • Completing the square
    • Long Division
  • Partial Fractions
    • Forms
    • Distinct Linear Factors
    • Repeated Linear Factors
    • Quadratic Factors
  • Improper Integrals
    • Definitions and convergent with infinite limit
    • Divergent with infinite limits
    • Two infinite limits
    • P integrals
    • Discontinuity
    • Two sided discontinuity
    • Tests for convergence
  • Numerical Integration
    • Derivations
    • Numerical Examples
    • Simpson's Rule Derivations

  Sequences and Series

  • Sequences
    • Intro to sequences
    • Convergent sequences
    • Limits of sequences
    • L'Hopital's Rule
    • Factorials
    • Recursively defined sequences
    • Bounded monotonic sequences
  • Series
    • Intro to series
    • Telescoping series
    • Geometric series
    • Some theorems
  • Integral Test
    • Integral Test Proof
    • P-Series
    • Example
    • Example
    • Example
  • Comparison Tests
    • Direct Comparison Test
    • Example
    • Example
    • Example
    • Limit Comparison Test
    • Example
    • Example
  • Ratio and Root Tests
    • Ratio Test
    • Example
    • Example
    • P-Series
    • Root Test
    • Example
    • Example
  • Alternating Series and Absolute Convergence
    • Alternating Series Test
    • Absolute and Conditional Convergence
    • Strategy
  • Taylor and Maclaurin Polynomials
    • Taylor Polynomial Intro
    • Taylor Polynomials for Sin(x)
    • Graphs of Taylor Polynomials for Sin(x)
    • Taylor Series for Sin(x)
    • Taylor Polynomial for exp(x)
    • Taylor Series for exp(x)
    • Taylor Polynomial for (1/x)
  • Power Series
    • Power Series Intro
    • Interval of Convergence Ex.
    • Interval of Convergence Ex.
    • Interval of Convergence Ex.
    • Interval of Convergence Ex.
    • Derivatives of Power Series
    • Integrals of Power Series
  • Taylor Series Convergence
    • Taylor's Formula
    • An Integral
    • A Limit
    • Euler's Identity

  Parametric Equations

  • Parametric Equations
    • Parametric equations introduction
    • A parametric line
    • Parametric circles and ellipses
    • Parametric cycloid
  • Calculus with Parametric Equations
    • Derivatives
    • Area
    • Arc length
    • Surface area

• Math for Elementary Teachers 1

  • 01 Operations with Tallies
    • Introduction to Tallies
    • Operations with Tallies
  • 02 Comparing Numbers with Tallies
    • Introduction to Comparing Sets
    • Children Counting
  • 03 Base Ten Notation
    • Base Ten Notation
  • 04 Bar Models
    • Basic Bar Models
    • Changing Amounts
    • Comparing Quantities
    • Equal Size Groups
    • Bar Models for Complex Relationships
  • 05 Properties of Addition and Subtraction
    • Properties of Addition
    • Properties of Subtraction
    • Mental Arithmetic
  • 06 Addition Algorithm
    • Addition Algorithm
  • 07 Subtraction Algorithm
    • Subtraction Algorithm
  • 08 Properties of Multiplication and Division
    • Properties of Multiplication
    • Properties of Division
    • Summary of Properties of Multiplication and Division
  • 09 Multiplication Algorithm
    • Rewriting Products with the Distributive Law
    • Multiplication Algorithms
    • Counting with Multiplication
    • Counting Ordered Pairs
    • Counting Pairs with Order and Repetition
  • 10 Division Algorithm
    • Division with Tallies
    • Toward a Division Algorithm
    • Bar Models and Division
  • 11 Number Lines and Negative Numbers
    • Number Lines
    • Addition on the Number Line
    • Subtraction on the Number Line
    • Multiplication on the Number Line
  • 12 Comparing Numbers
    • Comparing Numbers
    • Comparing Numbers on the Number Line
    • Rounding
    • Approximation with Rounding
  • 13 Order of Operations
    • Order of Operations
  • 14 Fractions
    • Introduction to Fractions
    • Fractions on the Number Line
    • Fractions and Division
    • Fraction Word Problems
  • 15 Forms of Fractions
    • Equivalent Fractions
    • Improper Fractions
    • Comparing Fractions
    • Ordering Fractions
  • 16 Operations with Fractions
    • Adding Fractions
    • Multiplying Fractions
    • Dividing Fractions
    • Fraction Arithmetic
    • Find the Fraction Shaded
    • More Fraction Word Problems
  • 17 Ratios and Proportions
    • Ratios and Proportions
    • Snakes and Lizards
    • Unit Rates
    • Proportional and Inversely Proportional Relationships
  • 18 Decimals
    • Decimal Notation
    • Comparing Decimals
    • Adding Decimals
    • Multiplying Decimals
    • Converting between Decimals and Fractions
  • 19 Scientific Notation
    • Scientific Notation
    • Converting from Scientific Notation
    • Converting to Scientific Notation
    • Multiplying in Scientific Notation
    • Adding in Scientific Notation
  • 20 Percents
    • Introduction to Percents
    • Converting with Percents
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent word problem
    • Percent Increase/Decrease
    • Percent Increase/Decrease
    • Percent Increase/Decrease
    • Percent Increase/Decrease
    • Percent Increase/Decrease
    • Percent Increase/Decrease
    • Percent Increase/Decrease
  • 21 Expressions
    • Expressions
    • Expression Example
    • Expression Example
    • Expression Example
    • Algebraic Expressions
    • Algebraic Expression Example
    • Algebraic Expression Example
    • Algebraic Expression Example
  • 22 Equations
    • Equations
    • Solving Equations
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
    • Word Problem Example
  • 23 Sequences
    • Sequences
    • Repeating Patterns
    • Counting Repeating Patterns
    • Arithmetic Sequences
    • Geometric Sequences
    • Continuing Patterns
  • 24 Functions
    • Functions
    • Tables for Functions
    • Not a Function
    • Equations for Functions
    • Graphing Functions
    • Reading Graphs
    • Change in Graphs
    • Pollen Count
    • Something is Wrong Here
  • 25 Linear Functions
    • Linear Functions
    • Graphing Lines
    • Equations from Tables
    • Nightlights

• Math for Elementary Teachers 2

  • 26 Odd and Even Numbers
    • Blank Topic
    • Blank Topic
  • 27 Divisibility
    • Blank Topic
    • Blank Topic
  • 28 Prime Numbers
    • Blank Topic
    • Blank Topic
  • 29 Common Factors and Multiples
    • Blank Topic
    • Blank Topic
  • 30 Rational and Irrational Numbers
    • Blank Topic
    • Blank Topic
  • 31 Geometry
    • Blank Topic
    • Blank Topic
  • 32 Angles
    • Blank Topic
    • Blank Topic
  • 33 Triangles
    • Blank Topic
    • Blank Topic
  • 34 Quadrilaterals and Other Polygons
    • Blank Topic
    • Blank Topic
  • 35 Measurement
    • Blank Topic
    • Blank Topic
  • 36 Unit Conversions
    • Blank Topic
    • Blank Topic
  • 37 Area
    • Blank Topic
    • Blank Topic
  • 38 Circles
    • Blank Topic
    • Blank Topic
  • 39 Pythagorean Theorem
    • Pythagorean Theorem Introduction
    • Vi Hart and Pythagoras
    • Vi Hart Pythagorean Theorem Proof
    • Door Example
    • Boat Example
    • Shed Example
    • Equilateral Triangle Example
    • Pyramid Example
    • Cube Example
  • 40 Polyhedra
    • Polyhedra Introduction
    • Platonic Solids
    • Some shapes that are not polyhedra
    • Euler's Formula
  • 41 Nets and Surface Area
    • Nets
    • Surface Area
    • Box
    • Prism
    • Pyramid
    • Cylinder
    • Sphere
  • 42 Volume
    • Volume
    • Box
    • Prism
    • Pyramid
    • Cylinder
    • House
    • Sphere
  • 43 Transformations and Symmetry
    • Transformations
    • Reflection
    • Translation
    • Rotation
    • Symmetry
    • Finding Symmetries
    • Finding Symmetries
    • Finding Symmetries
    • Finding Symmetries
    • Completing a Pattern
    • Completing a Pattern
  • 44 Congruence and Similarity
    • Congruence
    • Similarity
    • Four Approaches to Similarity Problems
    • Four Approaches to Similarity Problems
    • Thumb
    • Shadow
    • Scaling Area and Volume
    • Area
    • Weight
  • 45 Data and Statistics
    • Data
    • Displaying Data
    • Types of Data
  • 46 Summarizing and Comparing Data
    • Centers
    • Weighted Averages
    • Quartiles
    • Percentiles
  • 47 Variation and Relative Standing
    • Variation
    • Standard Deviation
    • Range Rule of Thumb
  • 48 Probability
    • Probability and Events
    • Empirical Probability
    • Probability and Simple Events
    • Rolling Dice
  • 49 Multistage Experiments and Counting
    • Two Stage Experiments
    • Three Children
    • Marbles in a Bowl
    • Complements
    • Counting
    • Independent Events
    • Redundancy
    • More Marbles
    • Fish
    • Three More Children
    • Even More Marbles
    • Counting Codes

• Linear Algebra

  • Linear Equations
    • Systems of linear equations
    • Row reduction echelon forms
    • Vector equations
    • Matrix equations
    • Solutions sets of linear systems
    • Some applications
    • Linear independence
    • Introduction to linear transformations
    • The matrix of a linear transformation
  • Matrix Algebra
    • Matrix operations
    • The inverse of a matrix
    • Characterizations of invertible matrices
    • Subspaces of Rⁿ
    • Dimension and rank
  • Determinants
    • Introduction to determinants
    • Properties of determinants
    • Applications of determinants
  • Vector Spaces
    • Vector spaces and subspaces
    • The fundamental subspaces and linear transformations
    • Linearly independent sets and bases
    • Coordinate systems
    • Dimension
  • Eigenvalues and Eigenvectors
    • Eigenvalues and eigenvectors
    • The characteristic equation
    • Diagonalization
  • Orthogonality and Projections
    • Inner product, length, and orthogonality
    • Orthogonal sets
    • Orthogonal projections
    • Gram Schmidt orthogonalization