ALGEBRA AND TRIGONOMETRY
THE BASICS
Sets of Numbers: N,Z,Q,I,R
Order of Operations
Rules of Signs
Multiplications and Divisions of Fractions
Adding and Subtracting Fractions
Rules of Exponents
Roots
Roots.Part II
Polynomials
Factoring
Polynomial Division and Synthetic Division
Intervals
EQUATIONS AND INEQUALITIES
Linear Equations
Quadratic Equations
Solving Inequalities
Inequalities with Absolute Values
Polynomial and Rational Inequalities
Radical Equations
DISTANCE, MIDPOINTS, STRAIGHT LINES
Distance, Midpoint and Slope
Straight Lines
Parallel and Perpendicular Lines
FUNCTIONS
Functions
Domain of a Function
More Domains
Transformations
Quadratic Functions
Quadratic Functions. Part II
Quadratic Functions. Part III
Polynomial Functions
Polynomial Functions Part II
Polynomial Behavior Near Zeros
The Fundamental Theorem of Algebra
Graphing Rational Functions
Domains, Holes and Asymptotes
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Composition of Functions
Inverse Functions
Exponential Functions
Exponential Equations
Logarithms
Properties of Logs
Exponential Equations Part II
Logarithmic Equations
Compound Interest
Exponential Growth and Decay
TRIGONOMETRY
Right Triangle Trigonometry
Trigonometric Functions of General Angles
Trigonometric Identities
Trigonometric Functions of Real Numbers
Graphs of the Sine and the Cosine
Graphs of the Tangent and the Cotangent
Graphs of the Secant and Cosecant
Transformations of Sine and Cosine
Example of Transformations of the Sine
The Inverse Sine Function
The Inverse Cosine Function
The Inverse Tangent Function
The Inverse Cotangent Function
The Inverse Secant Function
The Inverse Cosecant Function
Sum and Difference Formulas
Double Angle Formulas
Half Angle Formulas
Product-to-Sum and Sum-to-Product Formulas
The Law of Sines
The Law of Sines: The Ambiguous Case
The Law of Cosines
CONIC SECTIONS
The Circle
The Parabola
The Ellipse
The Hyperbola
POLAR COORDINATES
Polar Coordinates
Polar Equations and Graphs
COMPLEX NUMBERS
Complex Numbers part I
Complex Numbers part II
Quadratic Equations with Complex Solutions
MATRICES AND SYTEMS OF EQUATIONS
Systems of Equations. Substitution
Substitution: Larger Systems
Substitution: Larger Dependent Systems
Method of Elimination
Matrix Methods. Part I
Matrix Methods. Part II
Determinants: Cramer's Rule
Systems of Equations with the TI-83/84
Matrix Algebra
Inverse of a Square Matrix
FINITE MATH
LOGIC
Introduction to Logic
Logic Exercises
Bigger Truth Tables
More on the Conditional. The Biconditional
Logical Arguments
Euler Diagrams
SETS
Sets
Applications of Sets
PROBABILITY AND STATISTICS
Counting Methods
Permutations of Non Distinct Objects
Introduction to Probability
Conditional Probabilities
Independent Events
Baye's Formula
Deck of Cards Problems
Probabilities. Ex-1
Probabilities. Ex-2
Probabilities. Ex-3
Probabilities. Ex-4
Mean, Median and Mode
Standard Deviation
Standard Deviation with the TI-30XIIS
Std Dev with the TI-30XS Multiview
Standard Deviation with the TI-83 or 84
Discrete vs Continuous
Binomial Random Variables
Expected Value and Std Dev of Discrete Random Variables
Binomial Tables
The Normal Distribution
The Normal Approximation to the Binomial
LINEAR EQUATIONS
Linear Equations
Distance, Midpoint and Slope
Straight Lines
Parallel and Perpendicular Lines
SYSTEMS OF LINEAR EQUATIONS
Systems of Equations. Substitution
Substitution: Larger Systems
Substitution: Larger Dependent Systems
LINEAR PROGRAMMING
Graphing Linear Inequalities (2 var)
Systems of Linear Inequalities
Linear Programming Part I
Linear Programming Part II
DISCRETE MATH
NUMBER SYSTEMS
The Binary Number System
SETS AND LOGIC
Sets
Introduction to Logic
Logic Exercises
Bigger Truth Tables
More on the Conditional. The Biconditional
Logical Arguments
Euler Diagrams
PERMUTATIONS AND COMBINATIONS
Permutations and Combinations
Permutations of Non Distinct Objects
PROBABILITY
Introduction to Probability
Conditional Probabilities
Independent Events
Baye's Formula
STATISTICS
Expected Value and Std Dev of Discrete Random Variables
CALCULUS I
Notion of Limit
Four Basic Limits
More Limits
The Number e
Continuity
Derivatives Part I
Product and Quotient Rule
The Chain Rule
Implitit Differentiation
Related Rates Part I
Related Rates Part II
Local Linear Approximations
Error Propagation
Derivatives of Log and Exponential Functions
Logarithmic differentiation
Derivatives of Trig and Inverse Trig Functions
Indeterminate Forms
L'Hopital's Rule Part I
L'Hopital's Rule Part II
Increasing and Decreasing Functions
Maximum and Minimum
Second Derivative Test
Concavity and Inflection Points
Absolute Maximum and Minimum
CALCULUS II
Antiderivatives
The Fundamental Theorem of Calculus
Integration by Substitution
Area as a Limit
The Definite Integral
Definite Integrals by Substitution
TECHNIQUES OF INTEGRATION
Integration by Parts
Trigonometric Integrals. Part I
Trigonometric Integrals. Part II
Trigonometric Integrals. Part III
Trigonometric Integrals. Part IV
Trigonometric Integrals. Part V
Trigonometric Integrals. Part VI
Trigonometric Integrals. Part VII
Integrals Involving a Quadratic Expression
Trigonometric-Substitutions
Partial Fractions I
Partial Fractions II
Partial Fractions III
Partial Fractions IV
Improper Integrals
Numerical Integration
APPLICATIONS OF INTEGRATION
Area Between Curves
Area Between Curves. Part II
Solids of Revolution. Method of Disks
Solids of Revolution. Method of Washers
Method of Washers. Integrating on Y
Method of Shells
Work Done by a Variable Force
INFINITE SERIES
Infinite Sequences
Infinite Sequences. Part II
Infinite Sequences. Part III
Infinite Series 1
Infinite Series 2. Telescoping
Harmonic Series
The-Divergence-Test
CALCULUS FOR BUSINESS
BUSINESS CONCEPTS
Demand-Revenue-Cost-Profit
Equilibrium
Break Even
Break Even Example
Optimal Selling Price Example
Property Tax Bill Example
LIMITS AND DERIVATIVES
Notion of Limit
APPLICATIONS OF DERIVATIVES
Related Rates Part I
Related Rates Part II
Increasing and Decreasing Functions
Concavity and Inflection Points
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Composition of Functions
Inverse Functions
Exponential Functions
Exponential Equations
Logarithms
Properties of Logs
Exponential Equations Part II
Logarithmic Equations
Compound Interest
Exponential Growth and Decay
Derivatives of Log and Exponential Functions
Logarithmic differentiation
INTEGRATION
Definite Integrals by Substitution
Integration by Parts
STATS I AND STATS FOR BUSINESS AND ECONOMICS
Permutations of Non Distinct Objects
Standard Deviation with the TI-30XIIS
Std Dev with the TI-30XS Multiview
Standard Deviation with the TI-83 or 84
Expected Value and Std Dev of Discrete Random Variables
Binomial Tables
Bar Graphs vs Histograms
Steps to Construct a Histogram
The Empirical Rule
Chebyshef's Rule
The Poisson Distribution
Hypergeometric Distribution
Expected Value and Std Dev of Discrete Random Variables
The Uniform Distribution
The Normal Approximation to the Binomial
The Exponential Distribution
Percentiles
Boxplots
Sampling Distributions
Central Limit Theorem
INFERENCES BASED ON A SINGLE SAMPLE
Confidence Intervals Part I
Confidence Intervals Part II
Degrees of Freedom
Estimating-the-Sample-Size
Hypothesis Testing Part I
Hypothesis Testing Part II
Hypothesis Testing Part III. The t Test
Pvalues with the t Table
Confidence Intervals about the Variance
Hypothesis Test about a Population Variance
STATS II
INFERENCES BASED ON TWO SAMPLES
Two-Sample Z-Interval
Two-Sample Z-Test
Two-Sample t-Interval
Two-Sample t-Test
Two-Proportion Z-Interval
Two-Proportion Z-Test
Paired-Samples Z-Interval
Paired-Samples Z-Test
Paired-Samples t-Intervals
Paired-Samples t-Test
Confidence Interval for two Variances
C.I for two Variances. Part2
Hypothesis Test for two Variances
ANOVA: COMPARING THE MEANS OF MORE THAN TWO SAMPLES
ANOVA Part I
ANOVA Part II
Multiple Comparisons of Means
ANOVA: Randomized Block
ANOVA: Randomized Block. Part II
Two-Way ANOVA. Part I
Two-Way-ANOVA. Part II
Two-Way-ANOVA. Part III
Two-Way-ANOVA. Part IV
Two-Way-ANOVA. Part V
SIMPLE LINEAR REGRESSION AND CORRELATION
Simple Linear Regression
Simple Linear Regression Part II
The Coefficient of Correlation
Coeff of Corr with the TI-30XS Multiview
The Pearson's Test For Correlation
CATEGORICAL DATA ANALYSIS
Chi Square Goodness of Fit (One-Way Tables)
Chi Square Test for Independence (Two-Way Tables)
X2 Test for Normal Distribution
NON-PARAMETRIC TESTS
The Sign Test
The Wilcoxon Rank Sum Test
The Wilcoxon Rank Sum Test. Part II
The Wilcoxon Signed Rank Test
The Kruskal-Wallis Test
The Friedman's Test
The Spearman's Test For Correlation
ADVANCED STATS
MULTIPLE REGRESSION
Multiple Regression. Part 1
Multiple Regression. Part 2
Measure of Good Fit. Residual Plots
The Global Test
Multiple Regression Estimation and Prediction
Multiple Regression Interaction Models
Multiple Regression Higher Order Models
Multiple Regression Dummy Variables
Multiple Regression Dummy Variables. Part II
STATS FOR ENGINEERS
Densities vs Distributions
Expected Value
Expected Value Example
Variance
Joint Probabilities
Joint Cumulative Distr. Functions
Marginal Distributions