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

Method of Elimination

Matrix Methods. Part I

Matrix Methods. Part II


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 

Four Basic Limits 

More Limits 

The Number e 

Continuity 

Derivatives Part I

Product and Quotient Rule 

The Chain Rule 

Implitit Differentiation 


APPLICATIONS OF DERIVATIVES
Related Rates Part I 
Related Rates Part II 

Increasing and Decreasing Functions 

Maximum and Minimum 

Second Derivative Test  

Concavity and Inflection Points 

Absolute Maximum and Minimum 


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

Antiderivatives 

Integration by Substitution 

The Definite Integral 

Definite Integrals by Substitution
Integration by Parts


STATS I AND STATS FOR BUSINESS AND ECONOMICS

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 
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 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

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© 2017 by Professor Serna