Table of Contents
R. Algebra Reference.
Polynomials.
Factoring.
Rational Expressions.
Equations.
Inequalities.
Exponents.
Radicals.
1. Linear Functions.
Slopes and Equations of Lines.
Linear Functions and Applications.
The Least Squares Line.
2. Systems of Linear Equations and Matrices.
Solution of Linear Systems by the Echelon Method.
Solution of Linear Systems by the Gauss-Jordan Method.
Addition and Subtraction of Matrices.
Multiplication of Matrices.
Matrix Inverses.
Input-Output Models.
3. Linear Programming: The Graphical Method.
Graphing Linear Inequalities.
Solving Linear Programming Problems Graphically.
Applications of Linear Programming.
4. Linear Programming: The Simplex Method.
Slack Variables and the Pivot.
Maximization Problems.
Minimization Problems; Duality.
Nonstandard Problems.
5. Mathematics of Finance.
Simple and Compound Interest.
Future Value of an Annuity.
Present Value of an Annuity; Amortization.
6. Logic.
Statements.
Truth Tables and Equivalent Statements.
The Conditional and Circuits.
More on the Conditional.
Analyzing Arguments and Proofs.
Analyzing Arguments with Quantifiers.
7. Sets and Probability.
Sets.
Applications of Venn Diagrams.
Introduction to Probability.
Basic Concepts of Probability.
Conditional Probability; Independent Events.
Bayes' Theorem.
8. Counting Principles; Further Probability Topics.
The Multiplication Principle; Permutations.
Combinations.
Probability Applications of Counting Principles.
Binomial Probability.
Probability Distributions; Expected Value.
9. Statistics.
Frequency Distributions; Measures of Central Tendency.
Measures of Variation.
The Normal Distribution.
Normal Approximation to the Binomial Distribution.
10. Nonlinear Functions.
Properties of Functions.
Quadratic Functions; Translation and Reflection.
Polynomial and Rational Functions.
Exponential Functions.
Logarithmic Functions.
Applications: Growth and Decay; Mathematics of Finance.
11. The Derivative.
Limits.
Continuity.
Rates of Change.
Definition of the Derivative.
Graphical Differentiation.
12. Calculating the Derivative.
Techniques for Finding Derivatives.
Derivatives of Products and Quotients.
The Chain Rule.
Derivatives of Exponential Functions.
Derivatives of Logarithmic Functions.
13. Graphs and the Derivative.
Increasing and Decreasing Functions.
Relative Extrema.
Higher Derivatives, Concavity, and the Second Derivative Test.
Curve Sketching.
14. Applications of the Derivative.
Absolute Extrema.
Applications of Extrema.
Further Business Applications: Economic Lot Size, Economic Order Quantity; Elasticity of Demand.
Implicit Differentiation.
Related Rates.
Differentials: Linear Approximation.
15. Integration.
Antiderivatives.
Substitution.
Area and the Definite Integral.
The Fundamental Theorem of Calculus.
The Area Between Two Curves.
Numerical Integration.
16. Further Techniques and Applications of Integration.
Integration by Parts.
Volume and Average Value.
Continuous Money Flow.
Improper Integrals.
Solutions of Elementary and Separable Differential Equations.
17. Multivariable Calculus.
Functions of Several Variables.
Partial Derivatives.
Maxima and Minima.
Lagrange Multipliers.
Total Differentials and Approximations.
Double Integrals.
18. Probability and Calculus.
Continuous Probability Models.
Expected Value and Variance of Continuous Random Variables.
Special Probability Density Functions.
Tables.
Table 1: Formulas from Geometry.
Table 2: Area Under a Normal Curve.
Table 3: Integrals.
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