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Algebra  Trigonometry  Finite-Math  Discrete-Math  Calculus-1   Calculus-2  Business-Calculus  Statistics-1  Statistics-2  Advanced-Stats  Stats-for-Engineers  Physics-1  Physics-2

ALGEBRA, TRIGONOMETRY AND PRE-CALCULUS

THE BASICS
  1. Sets of Numbers: N,Z,Q,I,R
  2. Order of Operations
  3. Rules of Signs
  4. Multiplications and Divisions of Fractions
  5. Adding and Subtracting Fractions
  6. Rules of Exponents
  7. Roots
  8. Roots.Part II
  9. Polynomials
  10. Factoring
  11. Polynomial Division and Synthetic Division
  12. Intervals

 

EQUATIONS AND INEQUALITIES
  1. Linear Equations
  2. Quadratic Equations
  3. Solving Inequalities
  4. Inequalities with Absolute Values
  5. Polynomial and Rational Inequalities
  6. Radical Equations

 

DISTANCE, MIDPOINTS, STRAIGHT LINES
  1. Distance, Midpoint and Slope
  2. Straight Lines
  3. Parallel and Perpendicular Lines

 

FUNCTIONS
  1. Functions
  2. Domain of a Function
  3. More Domains
  4. Transformations
  5. Quadratic Functions
  6. Quadratic Functions. Part II
  7. Quadratic Functions. Part III
  8. Polynomial Functions
  9. Polynomial Functions Part II
  10. Polynomial Behavior Near Zeros
  11. The Fundamental Theorem of Algebra
  12. Graphing Rational Functions
  13. Domains, Holes and Asymptotes

 

EXPONENTIAL AND LOGARITHMIC FUNCTIONS
  1. Composition of Functions
  2. Inverse Functions
  3. Exponential Functions
  4. Exponential Equations
  5. Logarithms
  6. Properties of Logs
  7. Exponential Equations Part II
  8. Logarithmic Equations
  9. Compound Interest
  10. Exponential Growth and Decay

 

TRIGONOMETRY
  1. Right Triangle Trigonometry
  2. Trigonometric Functions of General Angles
  3. Trigonometric Identities
  4. Trigonometric Functions of Real Numbers
  5. Graphs of The Sine and Cosine
  6. Graphs of the Tangent and Cotangent
  7. Graphs of the Secant and Cosecant
  8. Transformations of Sine and Cosine
  9. Example of Transformations of the Sine
  10. The Inverse Sine Function
  11. The Inverse Cosine Function
  12. The Inverse Tangent Function
  13. The Inverse Cotangent Function
  14. The Inverse Secant Function
  15. The Inverse Cosecant Function
  16. Sum and Difference Formulas
  17. Double Angle Formulas
  18. Half Angle Formulas
  19. Product-to-Sum and Sum-to-Product Formulas
  20. The Law of Sines
  21. The Law of Sines: The Ambiguous Case
  22. The Law of Cosines

 

CONIC SECTIONS
  1. The Circle
  2. The Parabola
  3. The Ellipse
  4. The Hyperbola

 

POLAR COORDINATES
  1. Polar Coordinates
  2. Polar Equations and Graphs

 

COMPLEX NUMBERS
  1. Complex Numbers part I
  2. Complex Numbers part II

 

MATRICES AND SYTEMS OF EQUATIONS
  1. Method of Substitution
  2. Substitution: Larger Systems
  3. Substitution: Larger Dependent Systems
  4. Method of Elimination
  5. Matrix Methods. Part I
  6. Matrix Methods. Part II
  7. Determinants: Cramer's Rule
  8. Systems of Equations with the TI-83/84
  9. Matrix Algebra
  10. Inverse of a Square matrix

 

FINITE MATH

LOGIC
  1. Introduction to Logic
  2. Logic Exercises
  3. Bigger Truth Tables
  4. More on the Conditional. The Biconditional
  5. Logical Arguments
  6. Euler Diagrams
SETS
  1. Sets
  2. Applications of Sets
PROBABILITY AND STATISTICS
  1. Counting Methods
  2. Permutations of Non Distinct Objects
  3. Introduction to Probability
  4. Conditional Probabilities
  5. Independent Events
  6. Baye's Formula
  7. Deck of Cards Problems
  8. Probabilities. Ex-1
  9. Probabilities. Ex-2
  10. Probabilities. Ex-3
  11. Probabilities. Ex-4
  12. Mean, Median and Mode
  13. Standard Deviation
  14. Standard Deviation with the TI-30XIIS
  15. Std Dev with the TI-30XS Multiview
  16. Standard Deviation with the TI-83 or 84
  17. Discrete vs Continuous
  18. Binomial Random Variables
  19. Expected Value and Std Dev of Discrete Random Variables
  20. Binomial Tables
  21. The Normal Distribution
  22. The Normal Approximation to the Binomial
LINEAR EQUATIONS
  1. Linear Equations
  2. Distance, Midpoint and Slope
  3. Straight Lines
  4. Parallel and Perpendicular Lines
SYSTEMS OF LINEAR EQUATIONS
  1. Systems of Equations. Substitution
  2. Substitution: Larger Systems
  3. Substitution: Larger Dependent Systems
  4. Method of Elimination
  5. Matrix Methods. Part I
  6. Matrix Methods. Part II
LINEAR PROGRAMMING
  1. Graphing Linear Inequalities (2 var)
  2. Systems of Linear Inequalities
  3. Linear Programming Part I
  4. Linear Programming Part II

 

DISCRETE MATH

NUMBER SYSTEMS
  1. The Binary Number System

 

SETS AND LOGIC
  1. Sets
  2. Introduction to Logic
  3. Logic Exercises
  4. Bigger Truth Tables
  5. More on the Conditional. The Biconditional
  6. Logical Arguments
  7. Euler Diagrams

 

PERMUTATIONS AND COMBINATIONS
  1. Counting Methods
  2. Permutations of Non Distinct Objects

 

PROBABILITY
  1. Introduction to Probability
  2. Conditional Probabilities
  3. Independent Events
  4. Baye's Formula

 

STATISTICS
  1. Expected Value and Std Dev of Discrete Random Variables

 

CALCULUS I

LIMITS AND CONTINUITY
  1. Notion of Limit
  2. Four Basic Limits
  3. More Limits
  4. The Number e
  5. Continuity

 

THE DERIVATIVE
  1. Derivatives Part I
  2. Product and Quotient Rule
  3. The Chain Rule
  4. Related Rates Part I
  5. Related Rates Part II
  6. Local Linear Approximations
  7. Error Propagation

 

DERIVATIVE OF LOG, EXPONENTIAL AND INVERSE TRIG
  1. Implitit Differentiation
  2. Derivatives of Log and Exponential Functions
  3. Logarithmic differentiation
  4. Derivatives of Trig and Inverse Trig Functions
  5. Indeterminate Forms
  6. L'Hopital's Rule Part I
  7. L'Hopital's Rule Part II

 

GRAPHING AND APPLICATIONS
  1. Increasing and Decreasing Functions
  2. Maximum and Minimum
  3. Second Derivative Test
  4. Concavity and Inflection Points
  5. Absolute Maximum and Minimum

 

CALCULUS II

THE INTEGRAL
  1. Antiderivatives
  2. The Fundamental Theorem of Calculus
  3. Integration by Substitution
  4. Area as a Limit
  5. The Definite Integral
  6. Definite Integrals by Substitution
TECHNIQUES OF INTEGRATION
  1. Integration by Parts
  2. Trigonometric Integrals. Part I
  3. Trigonometric Integrals. Part II
  4. Trigonometric Integrals. Part III
  5. Trigonometric Integrals. Part IV
  6. Trigonometric Integrals. Part V
  7. Trigonometric Integrals. Part VI
  8. Trigonometric Integrals. Part VII
  9. Integrals Involving a Quadratic Expression
  10. Trigonometric-Substitutions
  11. Partial Fractions I
  12. Partial Fractions II
  13. Partial Fractions III
  14. Partial Fractions IV
  15. Improper Integrals
  16. Numerical Integration
APPLICATIONS OF INTEGRALS
  1. Area Between Curves
  2. Area Between Curves. Part II
  3. Solids of Revolution. Method of Disks
  4. Solids of Revolution. Method of Washers
  5. Method of Washers. Integrating on Y
  6. Method of Shells
  7. Work Done by a Variable Force

 

INFINITE SERIES
  1. Infinite Sequences
  2. Infinite Sequences. Part II
  3. Infinite Sequences. Part III
  4. Infinite Series 1
  5. Infinite Series 2. Telescoping
  6. Harmonic Series
  7. The-Divergence-Test

 

CALCULUS FOR BUSINESS

BUSINESS CONCEPTS
  1. Demand-Revenue-Cost-Profit
  2. Equilibrium
  3. Break Even
  4. Break Even Example
  5. Optimal Selling Price Example
  6. Property Tax Bill Example
LIMITS AND DERIVATIVES
  1. Notion of Limit
  2. Four Basic Limits
  3. More Limits
  4. The Number e
  5. Continuity
  6. Derivatives Part I
  7. Product and Quotient Rule
  8. The Chain Rule
  9. Implicit Differentiation
APPLICATIONS OF DERIVATIVES
  1. Related Rates Part I
  2. Related Rates Part II
  3. Increasing and Decreasing Functions
  4. Maximum and Minimum
  5. Second Derivative Test
  6. Concavity and Inflection Points
  7. Absolute Maximum and Minimum

 

EXPONENTIAL AND LOGARITHMIC FUNCTIONS
  1. Composition of Functions
  2. Inverse Functions
  3. Exponential Functions
  4. Exponential Equations
  5. Logarithms
  6. Properties of Logs
  7. Exponential Equations Part II
  8. Logarithmic Equations
  9. Compound Interest
  10. Exponential Growth and Decay
  11. Derivatives of Log and Exponential Functions

 

INTEGRATION
  1. Antiderivatives
  2. Integration by Substitution
  3. The Definite Integral
  4. Definite Integrals by Substitution
  5. Integration by Parts

 

STATS I AND BUSINESS STATS

  1. Counting Methods
  2. Introduction to Probability
  3. Conditional Probabilities
  4. Independent Events
  5. Baye's Formula
  6. Deck of Cards Problems
  7. Probabilities. Ex-1
  8. Probabilities. Ex-2
  9. Probabilities. Ex-3
  10. Probabilities. Ex-4
  11. Mean, Median and Mode
  12. Standard Deviation
  13. Standard Deviation with the TI-30XIIS
  14. Std Dev with the TI-30XS Multiview
  15. Standard Deviation with the TI-83 or 84
  16. Bar Graphs vs Histograms
  17. Steps to Construct a Histogram
  18. The Empirical Rule
  19. Chebyshef's Rule
  20. Discrete vs Continuous
  21. Binomial Random Variables
  22. Binomial Tables
  23. The Poisson Distribution
  24. Hypergeometric Distribution
  25. Expected Value and Std Dev of Discrete Random Variables
  26. The Uniform Distribution
  27. The Normal Distribution
  28. The Exponential Distribution
  29. The Normal Approximation to the Binomial
  30. Percentiles
  31. Boxplots
  32. Sampling Distributions
  33. Central Limit Theorem

 

INFERENCES BASED ON A SINGLE SAMPLE

 

  1. Confidence Intervals Part I
  2. Confidence Intervals Part II
  3. Degrees of Freedom
  4. Estimating-the-Sample-Size
  5. Hypothesis Testing Part I
  6. Hypothesis Testing Part II
  7. Hypothesis Testing Part III. The t Test
  8. Pvalues with the t Table
  9. Confidence Intervals about the Variance
  10. Hypothesis Test about a Population Variance

 

STATISTICS II

 

INFERENCES BASED ON TWO SAMPLES
  1. Two-Sample Z-Interval
  2. Two-Sample Z-Test
  3. Two-Sample t-Interval
  4. Two-Sample t-Test
  5. Two-Proportion Z-Interval
  6. Two-Proportion Z-Test
  7. Paired-Samples Z-Interval
  8. Paired-Samples Z-Test
  9. Paired-Samples t-Intervals
  10. Paired-Samples t-Test
  11. Confidence Interval for two Variances. Part 1
  12. C.I for two Variances. Part2
  13. Hypothesis Test for two Variances

 

ANOVA: COMPARING THE MEANS OF MORE THAN TWO SAMPLES
  1. ANOVA Part I
  2. ANOVA Part II
  3. Multiple Comparisons of Means
  4. ANOVA: Randomized Block
  5. ANOVA: Randomized Block. Part II
  6. Two-Way ANOVA. Part I
  7. Two-Way-ANOVA. Part II
  8. Two-Way-ANOVA. Part III
  9. Two-Way-ANOVA. Part IV
  10. Two-Way-ANOVA. Part V
SIMPLE LINEAR REGRESSION AND CORRELATION
  1. Simple Linear Regression
  2. Simple Linear Regression Part II
  3. The Coefficient of Correlation
  4. Coeff of Corr with the TI-30XS Multiview
  5. The Pearson's Test For Correlation

 

CATEGORICAL DATA ANALYSIS
  1. X2 Goodness of Fit (One-Way Tables)
  2. X2 Test for Independence (Two-Way Tables)
  3. X2 Test for Normal Distribution

 

NON-PARAMETRIC TESTS
  1. The Sign Test
  2. The Wilcoxon Rank Sum Test
  3. The Wilcoxon Rank Sum Test. Part II
  4. The Wilcoxon Signed Rank Test
  5. The Kruskal-Wallis Test
  6. The Friedman's Test
  7. The Spearman's Test For Correlation

 

ADVANCED STATS

MULTIPLE REGRESSION
  1. Multiple Regression. Part 1
  2. Multiple Regression. Part 2
  3. R2 as Measure of Good Fit. Residual Plots
  4. The Global Test
  5. Estimation and Prediction
  6. Interaction Models
  7. Higher Order Models
  8. Dummy Variables
  9. Dummy Variables. Part II

 

STATS FOR ENGINEERS

  1. Densities vs Distributions
  2. Expected Value
  3. Expected Value Example
  4. Variance
  5. Joint Probabilities
  6. Joint Cumulative Distr. Functions
  7. Marginal Distributions

 

PHYSICS I (Without Calculus)

 

MOTION IN ONE DIMENSION
  1. Measurements. Conversions
  2. Motion Along-a Straight Line
  3. Motion with Constant Acceleration
  4. Free Falling Objects
  5. Free Fall. Part II

 

MOTION IN TWO DIMENSIONS
  1. Vectors
  2. Projectile Motion
  3. Projectile Motion II

 

NEWTON'S LAWS OF MOTION
  1. Newtons Laws
  2. Newtons Laws II
  3. Newtons Laws III
  4. Force of Friction

 

CIRCULAR MOTION. GRAVITATION
  1. Uniform Circular Motion
  2. Law of Universal Gravitation

 

WORK AND ENERGY
  1. Work and Energy
  2. Work-Energy Principle
  3. Potential Energy
  4. Conservation of Mechanical Energy
  5. Energy Problems

 

LINEAR MOMENTUM
  1. Linear Momentum
  2. Conservation of Momentum
  3. Collisions and Impulse
  4. Elastic and Inelastic Collisions
  5. Center of Mass

 

ROTATIONAL MOTION
  1. Rotational Motion
  2. Rotational Motion. Problems.
  3. Rotational Motion. Problems. Part 2
  4. Rotational Motion. Problems. Part 3
  5. Torque

 

PHYSICS II (Without Calculus)

 

ELECTRIC CHARGE AND ELECTRIC FIELD
  1. Electric Charge. Coulomb Law
  2. Coulomb Law. Part II
  3. Electric-Field. Part I
  4. Electric-Field. Part II