Courses
Math Notes -- Videos
This page will provide links to videos I make and post publicly.
They are collected in a couple of playlists on YouTube organized by topic.
Mandelbrot Set exploration in the TI-83/84
Complex Numbers in
the TI-83/84
Redundancy in a Network Graph
Roman Numerals
Algebra
What kind of
number is it?
Why
Division by Zero is undefined
Calculator Tricks
for Working with Fractions
Simplifying
Square Roots
Adding Square Roots
Rationalizing Square
Roots
Properties of
Exponents
Solving Linear
Equations involving Fractions
Solving Linear
Equation with Integer Coefficients
Plotting Points
in two dimensions
Graphing Basics in
the TI-83/84
Midpoint Formula
Distance Formula
Distance and
Midpoint Formulas
Equation of a
Circle, Completing the Square
Equations of a
Line
Parallel
and Perpendicular Lines
Finding Equations of
a Line
Percent
Increase/Decrease Problems
Setting up Mixture
Problems in 2 and 3 variables
Graphing Systems of
Linear Inequalities
Comparing Solutions
Methods for Systems of Equations
Variation Problems
Identifying
Polynomials
Factoring
Solving Quadratic Equations by Factoring
Solving Quadratic
Equations (Quadratic Formula, completing the square)
Combining Different
Roots into a single expression
Factoring with
Fractional Exponents
Open-Top Box
Problems
Graphing Quadratics with Intercepts, Vertex, Axis of Symmetry
Extending FOIL
beyond Binomials
Using the
Discriminant to Find Number of Zeros
Building Piecewise Functions and
Graphing in Graphfree (Graphfree)
Graphing Piecewise
Functions by Hand
Writing Functions of
Piecewise Graphs
Functions and
Relations
Domain and Range of Functions and Relations
Symmetry of
Functions and Relations
Symmetry of
Functions
Properties of Piecewise Functions from a Graph
Distance Between a
Function and a Point
Difference Quotient
with Polynomials
Difference Quotient
with Rational Function
Difference Quotient
with Radical Function
Average Rate of
Change
Relationship between the Average Rate of Change, the Difference Quotient
and the Instantanous Rate of Change
Simplifying a
Complex Fraction
Simplifying a
Complex Fraction with Radicals
Identifying
Transformations on Functions
Inverses with Domain
Restrictions
Finding Inverses of One-to-One Functions
Decomposing
Functions
Operations on Functions and Domains
Long Division of
Polynomials
Graphing Real Zeros of Polynomials
Graphing Rational
Functions
Applying Transformations to Functions and Points
Complex Numbers
Rational Zeros
Theorem
Synthetic Division
Remainder and Factor
Theorem
Graphs of Rational Functions
Binomial Theorem
Finding all the
Zeros of a Polynomial
Rational Zeros and
Rule of Signs
Equations of
Polynomials from their Zeros
Polynomial Zeros and
End Behavior
Long and Synthetic Division
Basic Operations on
Complex Numbers
Solving
Exponential and Log Equations
Finding the Inverse
of a Rational Function
Solving a Rational
Equation
Solving a Radical (Square Root) Equation
Solving an Absolute
Value Eqation
Solving a Linear
Inequality
Solving an Absolute Value Inequality (greater than)
Solving a Double
Inequality
Quadratic Inequalities
Rational
Inequalities
Complex Absolute Value Inequality Done Graphically
Inequalities
involving AND and OR
Solution Sets
Polynomial and
Rational Inequalities
Math of Finance
with Formulas
Math of Finance with
TVM Solver in TI-83/84
Sigma Notation
Basics
General
Properties of Matrices
Operations on
Matrices
Converting Systems of Equations into Matrix Form
Solving Systems of
Equations with Matrices
Solving a
Nonlinear System with Three Variables
Solving a Nonlinear
System with Two Variables
Partial Fraction
Decomposition
Calculator Tricks
for Working with Trig
Proving
Trigonometric Identities
Domain and Range of
Trig Functions and Inverses
Solving Equations
with Trig Functions
Simplifying
Expressions with Inverse Trig Expressions inside other Trig Functions
Law of Sines
Law of Cosines
Bearings Problems
Conic Sections
Converting Polar
Functions into Parametric Form
Polar Coordinates
Plotting Polar
Coordinates
Parametric Equations of an Ellipse
Algebra Playlist
Quantitative Reasoning and Statistics
Excel/Sheets examples for Spreadsheet Applications
Entering Data into
the TI-83/84
Descriptive Statistics in the TI-83/84
Descriptive
Statistics of Grouped Data in the TI-83/84
Expected Value in
the TI-83/84
Counting Formulas in the TI-83/84
Binomial
Distribution in the TI-83/84
Statistical Graphs
in the TI-83/84
Normal Distribution
in the TI-83/84
Geometric
Distribution in the TI-84
F-Distribution in
the TI-84
Chi-Squared Distribution in the TI-84
One-Sample
Confidence Intervals in the TI-83/84
One-Sample
Hypothesis Testing in the TI-83/84
Two-Sample Dependent
(Paired) T-Test in the TI-83/84
Two-Sample
Independent T-Test in the TI-83/84
Hypothesis Testing
for Two-Sample Proportions in the TI-83/84
Chi-Squared Test of
Independence in TI-83/84
Goodness-of-Fit Test
in the TI-84
One-Way ANOVA in the TI-83/84
Correlation and
Simple Linear Regression in the TI-83/84
Regression Slope
Confidence Interval in the TI-84
Linear Regression
T-Test in the TI-84
Basic Linear Regression in Excel
2016
One-Variable Regression Basics in Excel
Exploring
Scatterplots and Correlations in Excel
Making Predictions
and Finding Residuals for Regression in Excel
Calculating and
Interpreting Coefficient of Determination in Excel
Hypothesis Testing
for Regression in Excel
Confidence Intervals
on Regression Coefficients in Excel
Simulation of
Coefficients for Regression in Excel
Identifying Outliers
and Influential Points
Intrinsically Linear
Models in Excel
Exponential
Regression in Excel
Polynomial
Regression from a Scatterplot in Excel
Polynomial
Regression in Excel
Multiple Linear
Regression Basics in Excel
Backward Selection
for Multiple Regression
Creating Dummy
Variables in Excel
Two-Way Tables in Excel 2016 --
Basics
Two Way Tables in
Excel 2016 -- Multiple Questions
Frequency Tables
(one- and two-way tables) in Minitab
Percentiles in Excel 2016
Line Graphs in Excel 2016
Time Series Graphs in Minitab 19
Confidence Intervals from Raw
Data in Minitab 19
Worked
Example with Two Proportion Confidence Interval in Minitab 19
One-sample T-Test in TI-84
Example
One-sample T-Test in
Excel Example
One-sample
T-Test in Minitab 19 Example
One-sample Z-Test in TI-84
Example
One-sample Z-Test of
Summarized Data in Excel Example
One-sample Z-Test of Summarized
Data in Minitab 19
Two-Sample
Unpooled T-Tests from Summary Statistics in Excel
Two-Sample Pooled
T-Tests from Summary Statistics in Excel
Paired Two-Sample
T-Tests in Excel
Two-Sample
Independent T-Tests from Data in Excel
Two-Sample
T-Intervals in Excel
Chi-Squared Test
of Independence in Excel
Goodness-of-fit
Tests in Excel
One-Way ANOVA in
Excel
Which
Test do I Use?
COVID-19 and Exponential Growth
(Excel sheet)
Making Frequency Tables (Pivot
Tables) in Excel
Making Pie
Charts in Excel
Making Bar
Graphs in Excel
Making Bar
Graphs from Two-Way Tables in Excel
Making Comparative Box Plots in
Excel
Making Histograms and
Boxplots in Excel
Making Maps in Excel
Bar Graphs in
Minitab
Pie
Charts in Minitab
Histograms in
Minitab
Boxplots in Minitab
Making Correlograms
in Minitab
Scatterplots in Minitab
Adding Trend
(Regression) or Smoothing to Scatterplot in Minitab
Bubble Plots in
Minitab
Binned Scatterplots in Minitab
Marginal Plots in
Minitab
Dotplots & Stem-and-Leaf Plots in Minitab
Probability Plots &
Empirical CDF graphs in Minitab
Plotting Probabilty
Distributions in Minitab
3D Scatterplots in
Minitab
Venn Diagrams and
Set Notation
Venn Diagrams and Probability
Importing Data
into Excel from the Web
Recoding Data in
Excel for a Database
Cell Reference Basics in Excel
Using IF statements in Excel
Formatting Numbers in Excel for
Proportions
Coin Toss Simulation in Excel
Fair Die Roll Simulation in Excel
Random Simulation in
Excel and Minitab
Finding Probabilties from
Two-Way tables with Probability Rules
Counting Rules in Excel
Using Excel to Evaluate
Mathematical and Statistical Formulas
Using Excel to Graph Functions
Stats with Pivot Tables in Excel
Calculating Descriptive Statistics
in Excel
Calculating a
Weighted Average in Excel
Calculated Expected Values and Standard Deviation for a Discrete
Probability Distribution in Excel
Doing Binomial Probabilities in
Excel
Empirical Rule and
Standard Score
Calculating
Normal Probabilities in Excel
Calculating Probabilities and
Cut-off Values for T-Distribution in Excel
Central Limit Theorem Simulation
Calculating Probabilities with
Sampling Distributions
Finding Confidence intervals for
Means and Proportions (one-sample) in Excel
Finding Sample Sizes for one-sample
confidence intervals (means and proportins) in Excel
Math of Finance: Simple Interest
in Excel
Math of
Finance: Calculating Future Values (Compound Interest)
Math of Finance: Calculating
Present Value (Compound Interest)
Math of Finance: Calculating
Payments in Excel (Compound Interest)
Math of Finance: A simple
amortization table in Excel
Math of Finance: Creating Amortization Tables in Excel
Math of Finance: Calculating
Effective Rates in Excel
Math of Finance: Continuous Compounding in Excel
Exponential vs. Linear Growth
Linear Programming in Two
Variables, Solve Graphically with Desmos
Linear Programming in Two
Variables, Solve with Solver in Excel 2016
Playlists:
Spreadsheet Application Tutorials
Excel Basics for Quantitative/Mathematical Reasoning
Statistics with Excel
Statistics with Minitab
Statistics with the TI-83/84
Liberal Arts Math
Single-Variable Calculus
How to Draw the
Greek Letters
Epsilon-Delta
Definition of a Limit Proof -- Linear
Epsilon-Delta
Definition of a Limit Proof -- Nonlinear
Squeeze Theorem
Numerical Limits in
Excel
Limit Definition
of a Derivative -- Polynomial
Limit Definition of
a Derivative -- Radical
Limit Definition of
a Derivative -- Rational
Derivative of the
Sine Function
Hyperbolic Trig
Functions: Quick Intro
Properties of
Derivatives
Using
Combinations of the product rule, quotient rule and chain rules: easy
version
Using
Combinations of the product, quotient and chain rules: harder version
Logarithmic
Differentiation
Implicit
Differentiation: worked example in x and y
Newton's Method
Bisection Algorithm
in Excel
Related Rates
Estimating Values
using Differentials
Estimating Area
under a Curve -- Riemann Sums, Fixed Rectangles
Finding Area Under a
Curve -- Riemann Sums, Limit Definition
Mathematical
Induction: proving the sum of i-squared formula
Deriving the
Formula for the Arc Length
Volume of Solid
of Revolution -- around x-axis
Volume of Solid of
Revolution -- around y-axis
Volume of Solid of
Revoution -- around y=c
Volume of Solid of
Revolution -- around x=c
Surface Area of
Revolution
Work: springs and
gravity
Work:
winding up a chain
Work: pumping out
tanks (various shapes)
Center of Mass
Change of
Variable (one-variable)
Substitution (u-sub,
one-variable)
Integration by
Parts, overview
Integration by Parts
with u-substitution
Integration by Parts
with looping integrals
Integration by Parts
using the tabular method
Trigonometric
Integrals: sine and cosine
Trigonometric
Integrals: tangent and secant
Trig Substitution
Integrating Products
of Trig Functions with Different Angles
Integrating
Rational Functions: Overview and Strategy
Which Integration
Strategy to use?
Integrating with
Tables
Improper
Integrals
Trapezoidal Rule
Errors and finding n
for the Trapezoidal Rule
Simpson's Rule
Errors and finding n
for Simpson's Rule
Sequence Formulas
Series Tests: Nth
term (divergence) and Alternating
Series Tests:
Telescoping and P-Series
Series Tests:
Integral and Geometric
Series Tests: Root
and Ratio
Series Tests: Limit and Direct Comparison
Errors on the
Integral Test and Alternating Series Tests
Power Series
Convergence
Power Series Convergence at the Endpoints
Functions as Power
Series
Derivatives of the Power Series formula to find more power series
Generating Taylor
polynomials
Working with Taylor polynomials
Doing Approximations
with Taylor polynomials
First and Second
Derivatives with Parametric Functions
Area Under a
Parametric Curve
Surface Area of
Revolution of a Parametric Curve
Derivative with
Polar Functions
Finding the Area of
a Petal of a Polar Curve
Finding the Area of
the Inner Loop of a Polar Curve
Area Between Two
Polar Curves
Area Between Two Polar Curves (Example 2)
Eccentricity of
Conics (Rectangular and Polar)
Exploring Polar
Curves
Elasticity of
Demand
Consumer and Producer Surplus
Continuous Income
Stream
Average Value of
a Function
Playlist:
Single Variable Calculus
Multivariable Calculus
Vector Operations
for Multivariable Calculus
Plotting Points in
3D
Domain and
Range of Multivariable Functions
Quadric
Surfaces
Distance between a Point and a Plane
Distance between a
Point and a Line
Equation of a Line
in 3-space
Lines in 3-space: Skew, Parallel or Intersecting
Equation of the
Intersection of Planes
Angle of
Intersection of Planes
Equation of a Plane
in 3-space
Equation of a Plane from different starting points
Level Curves and Traces
Gradients and Level
Curves
Writing Surfaces in Parametric Form
Converting
Coordinate Systems: Converting Functions: Rectangular, Cylindrical,
Spherical
Converting Coordinate Systems: Converting Points: Rectangular,
Cylindrical, Spherical
Del
Notation
Curvature
Parametrizing
Intersection of Surfaces
Angle of
Intersection of Two Surfaces
Domain of a
Parametric Function
Rewriting Parametric
Functions in terms of their Arc Length
Tangents and
Normal Vectors for Space Curves
Tangent Planes and
Normal Lines for Surfaces in Rectangular Coordinates
Tangent Planes and
Normal Lines for Parametric Surfaces
Orientable Surfaces
Limits
in 2 or more Variables
Multivariable Chain
Rule
Relative
Extrema in 2 Variables
Absolute Extrema in
2 Variables
Implicit Differentiation using the Definition
Implicit
Differentiation using Partial Derivatives
Lagrange
Multipliers
Triple Integrals
Finding the Mass
of a Wire
Mass of a lamina in a plane
Mass of a lamina
over a surface
Mass of a volume
Center of Mass in
two dimensions (two variables)
Center of Mass in
three dimensions
Changing
Variables/Jacobians
Changing Limits of
Integration in 2D
Changing Limits of
Integration in 3D
Vector Fields and
Potential Functions
Line Integrals
with Parametrized Curves
Green's Theorem
Stokes' Theorem
Fundamental Theorem
of Line Integrals
Finding Area Under a
Curve with Line Integrals
Surface Integrals
Playlist:
Multivariable Calculus
Probability and Statistics (Calculus-based)
Continuous
Probability Distributions -- Probability, Cumulative, Percentiles
Continuous
Probability Distributions -- Expected Value and Variance
Maximum Likelihood
Functions: Part 1
Maximum Likelihood
Functions: Part 2
Maximum Likelihood
Functions: Part 3
Playlist:
Probability and Stats (Calculus topics)
Differential Equations
Classifying Differential
Equations (order, linearity, some homogeneous)
Slope Fields
Separable Differential Equations
using Partial Fractions Example
Separable Differential Equations
using Exponential Rules Example
Bernoulli Solution to a
Differential Equation (previously solved by separation of variables)
Solving Bernoulli Equations
Solving First Order Homogeneous
Differential Equations
Solving Homogeneous ODEs with Substitution (previously solved by Exact
integrating factors)
Solving First Order Linear ODEs
with Method of Integrating Factors
Solving an Exact Differential
Equation
Solving Exact
Differential Equations with Integrating Factors
Concentration
Problems (one variable)
Solving Cauchy-Euler
Second-Order Equations with Real Roots
Solving Cauchy-Euler Second-Order
Equation with Repeated Roots
Solving Cauchy-Euler Second-Order
Equation with Complex Roots
Solving Constant Coefficient
Second-Order Equation with Real Roots
Solving Constant Coefficient
Second-Order Equation with Repeated Roots
Solving Constant Coefficient
Second-Order Equation with Complex Roots
Euler's Formula for Complex
Roots: Rewriting Complex Exponentials as Real Solutions
Variation of Parameters
Method of Undetermined
Coefficients, Example 1
Method of Undetermined Coefficients, Example 2
Method of Undetermined
Coefficients, Example 3
Reduction of Order
Laplace Transforms: Using the
Definition
Laplace
Transforms: Using the Definition on Piecewise Functions
Using a Table to Find Common
Laplace Transforms
Using a
Table to Find Common Inverse Laplace Transforms
Solving Second-Order ODEs with
Laplace Transforms, Example 1
Solving Second-Order ODEs with
Laplace Transforms, Example 2
Spring Problems,
Part 1
Spring
Problems, Part 2
Systems of Springs
Systems of ODEs,
real roots
Systems of ODEs, complex roots
Boundary Value
Problems: Eigenvalues and Eigenfunctions
Series Solutions
for ODEs
Singular Points
Extending Fourier
Series
Fourier Series: Even Function
Fourier Series: Odd
Function
Fourier Series: Asymmetric Piecewise Function
Playlist:
Differential Equations
LinearAlgebra
Loop Currents
Eigenvalues and
Eigenvectors
Inner Products
Linear
Transformations
Matrix Operations in
the TI-83/84
Writing Proofs
Coordinate Systems
Discrete Dynamical
Systems
Matrix of a Linear Transformation
Markov Chains
Homogeneous
Solutions and Null Spaces
Vector Spaces and
Subspaces
Dimensions for Subspaces of a Matrix
Basis for Row and
Column Space of a Matrix
Basis
Linear Independence
General
Properties of Matrices
Operations on
Matrices
Converting Systems of Equations into Matrix Form
Solving Systems of
Equations with Matrices
Finding an
Interpolating Polynomial
Solving a 2-variable
system with inverses and row-reducing
Solving a 3-variable
system with Cramer's Rule
Solving a 3-variable
independent system with row-reducing
Dependent Solutions
(2 free variables)
Input-Output System
Proving a Vector is
in the Span
Determining if Vectors with an Unknown are Independent
Solving A System
with Inverses
Complex
Similarity Transformations and Rotations
Similarity
Transformations and Diagonalization
Finding a 4x4
Determinant: Comparing Methods
Applications of
Determinants to Geometry
Finding a 5x5
Determinant through Row Reducing
Determinant of a 3x3
Matrix
Finding Eigenspace for 2x2, 3x3 matrices
Properties of
Determinants
Gram-Schmidt
Projection onto a
Subspace & Orthogonal Complement
Find a Basis for
W-perp/Extending an Orthogonal Basis to R^n
Orthogonal Bases
Regression with
Linear Algebra
Playlist:
Linear Algebra
Discrete Math
Logic Gates
Counting Formulas
Writing Proofs
Converting Base-10
to Base-2 and Hexadecimal
Conveting from
Base-10 to Other Bases
Decimal
Representations in Other Bases
Doing Arithmetic in
Other Bases
Creating Addition and Multiplication Tables in Other Bases
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