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ALGEBRA AND TRIGONOMETRY

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 the Cosine
  6. Graphs of the Tangent and the 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
  3. Quadratic Equations with Complex Solutions
MATRICES AND SYTEMS OF 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
  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. Permutations and Combinations
  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

  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. Implitit Differentiation
  10. Related Rates Part I
  11. Related Rates Part II
  12. Local Linear Approximations
  13. Error Propagation
  14. Derivatives of Log and Exponential Functions
  15. Logarithmic differentiation
  16. Derivatives of Trig and Inverse Trig Functions
  17. Indeterminate Forms
  18. L'Hopital's Rule Part I
  19. L'Hopital's Rule Part II
  20. Increasing and Decreasing Functions
  21. Maximum and Minimum
  22. Second Derivative Test
  23. Concavity and Inflection Points
  24. Absolute Maximum and Minimum


CALCULUS II

  1. Antiderivatives
  2. Integration by Substitution
  3. Area as a Limit
  4. The Definite Integral
  5. Definite Integrals by Substitution
  6. Integration by Parts
  7. Improper Integrals
  8. The Fundamental Theorem of Calculus
  9. Area Between Curves
  10. Area Between Curves. Part II
  11. Solids of Revolution. Method of Disks
  12. Solids of Revolution. Method of Washers
  13. Method of Washers. Integrating on Y
  14. Method of Shells
  15. Work Done by a Variable Force


CALCULUS FOR BUSINESS

BUSINESS CONCEPTS
  1. Demand-Revenue-Cost-Profit
  2. Equilibrium
  3. Break Even
  4. Break Even Ex1
  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. Implitit 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 STATS FOR BUSINESS AND ECONOMICS

  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. The Empirical Rule
  18. Tchebyshef's Rule
  19. Discrete vs Continuous
  20. Binomial Random Variables
  21. Binomial Tables
  22. The Poisson Distribution
  23. Hypergeometric Distribution
  24. Expected Value and Std Dev of Discrete Random Variables
  25. The Normal Distribution
  26. The Exponential Distribution
  27. The Normal Approximation to the Binomial
  28. Percentiles
  29. Boxplots
  30. Sampling Distributions
  31. 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


STATS 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
  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. ANOVA: Randomized Block
  4. ANOVA: Randomized Block. Part II
  5. Two-Way ANOVA. Part I
  6. Two-Way-ANOVA. Part II
  7. Two-Way-ANOVA. Part III
  8. Two-Way-ANOVA. Part IV
  9. 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. MR3. Measure of Good Fit. Residual Plots
  4. MR4. The Global Test
  5. MR5. Estimation and Prediction
  6. MR6. Interaction Models
  7. MR7. Higher Order Models

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)

  1. Measurements. Significant Figures. Conversions
  2. Vectors
  3. Motion Along-a Straight Line
  4. Motion with Constant Acceleration
  5. Free Falling Objects
  6. Free Fall. Part II
  7. Projectile Motion
  8. Projectile Motion II
  9. Newtons Laws
  10. Newtons Laws II
  11. Newtons Laws III

PHYSICS II (Without Calculus)

  1. Electric Charge. Coulomb Law
  2. Coulomb Law. Part II
  3. Electric-Field
  4. Electric-Field. Part II