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Chapter R: Algebra Reference (shared with FM, CWA, and Brief)

R-1 Polynomials

R-2 Factoring

R-3 Rational Expressions

R-4 Equations

R-5 Inequalities

R-6 Exponents

R-7 Radicals

Chapter 1: Linear Functions (shared with FM, CWA, and Brief)

1-1 Slopes and Equations of Lines

1-2 Linear Functions and Applications

1-3 The Least Squares Line

Chapter Review

Extended Application: Using Extrapolation to Predict Life Expectancy

Chapter 2: Systems of Linear Equations and Matrices (FM)

2-1 Solution of Linear Systems by the Echelon Method

2-2 Solution of Linear Systems by the Gauss-Jordan Method

2-3 Addition and Subtraction of Matrices

2-4 Multiplication of Matrices

2-5 Matrix Inverses

2-6 Input-Output Models

Chapter Review

Extended Application: Contagion

Chapter 3: Linear Programming: The Graphical Method (FM)

3-1 Graphing Linear Inequalities

3-2 Solving Linear Programming Problems Graphically

3-3 Applications of Linear Programming

Chapter Review

Chapter 4: Linear Programming: The Simplex Method (FM)

4-1 Slack Variables and the Pivot

4-2 Maximization Problems

4-3 Minimization Problems; Duality

4-4 Nonstandard Problems

Chapter Review

Extended Application: Using Integer Programming in the Stock-Cutting Problem

Chapter 5: Mathematics of Finance (FM)

5-1 Simple and Compound Interest

5-2 Future Value of an Annuity

5-3 Present Value of an Annuity; Amortization

Chapter Review

Extended Application: Time, Money, and Polynomials

Chapter 6: Logic (FM)

6-1 Statements

6-2 Truth Tables and Equivalent Statements

6-3 The Conditional and Circuits

6-4 More on the Conditional

6-5 Analyzing Arguments and Proofs

6-6 Analyzing Arguments with Quantifiers

Chapter Review

Extended Application: Logic Puzzles

Chapter 7: Sets and Probability (FM)

7-1 Sets

7-2 Applications of Venn Diagrams

7-3 Introduction to Probability

7-4 Basic Concepts of Probability

7-5 Conditional Probability; Independent Events

7-6 Bayes' Theorem

Chapter Review

Extended Application: Medical Diagnosis

Chapter 8: Counting Principles: Further Probability Topics (FM)

8-1 The Multiplication Principle; Permutations

8-2 Combinations

8-3 Probability Applications of Counting Principles

8-4 Binomial Probability

8-5 Probability Distributions; Expected Value

Chapter Review

Extended Application: Optimal Inventory for a Service Truck

Chapter 9: Statistics (FM)

9-1 Frequency Distributions; Measures of Central Tendency

9-2 Measures of Variation

9-3 The Normal Distribution

9-4 Normal Approximation to the Binomial Distribution

Chapter Review

Extended Application: Statistics in the Law - The Castaneda Decision

Chapter 10: Nonlinear Functions (Chapter 2 of CWA)

10-1 Properties of Functions

10-2 Quadratic Functions; Translation and Reflection

10-3 Polynomial and Rational Functions

10-4 Exponential Functions

10-5 Logarithmic Functions

10-6 Applications: Growth and Decay; Mathematics of Finance

Chapter Review

Extended Application: Characteristics of the Monkeyface Prickleback

Chapter 11: The Derivative (Chapter 3 of CWA)

11-1 Limits

11-2 Continuity

11-3 Rates of Change

11-4 Definition of the Derivative

11-5 Graphical Differentiation

Chapter Review

Extended Application: A Model for Drugs Administered Intravenously (new)

Chapter 12: Calculating the Derivative (Chapter 4 of CWA)

12-1 Techniques for Finding Derivatives

12-2 Derivatives of Products and Quotients

12-3 The Chain Rule

12-4 Derivatives of Exponential Functions

12-5 Derivatives of Logarithmic Functions

Chapter Review

Extended Application: Electric Potential and Electric Field (new)

Chapter 13: Graphs and the Derivative (Chapter 5 of CWA)

13-1 Increasing and Decreasing Functions

13-2 Relative Extrema

13-3 Higher Derivatives, Concavity, and the Second Derivative Test

13-4 Curve Sketching

Chapter Review

Extended Application: A Drug Concentration Model for Orally Administered

Medications (new)

Chapter 14: Applications of the Derivative (Chapter 6 of CWA)

14-1 Absolute Extrema

14-2 Applications of Extrema

14-3 Further Business Applications: Economic Lot Size; Economic Order  Quantity; Elasticity of Demand

14-4 Implicit Differentiation

14-5 Related Rates

14-6 Differentials: Linear Approximation

Chapter Review

Extended Application: A Total Cost Model for a Training Program

Chapter 15: Integration (Chapter 7 of CWA)

15-1 Antiderivatives

15-2 Substitution

15-3 Area and the Definite Integral

15-4 The Fundamental Theorem of Calculus

15-5 The Area Between Two Curves

15-6 Numerical Integration

Chapter Review

Extended Application: Estimating Depletion Dates for Minerals

Chapter 16: Further Techniques and Applications of Integration (Chapter 8 of CWA)

16-1 Integration by Parts

16-2 Volume and Average Value

16-3 Continuous Money Flow

16-4 Improper Integrals

16-5 Solutions of Elementary and Separable Differential Equations (Section 10.1 of CWA)

Chapter Review

Extended Application: Estimating Learning Curves in Manufacturing with    Integrals

Chapter 17: Multivariable Calculus (Chapter 9 of CWA)

17-1 Functions of Several Variables

17-2 Partial Derivatives

17-3 Maxima and Minima

17-4 Lagrange Multipliers

17-5 Total Differentials and Approximations

17-6 Double Integrals

Chapter Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design

Chapter 18: Probability and Calculus (Chapter 11 of CWA)

18-1 Continuous Probability Models

18-2 Expected Value and Variance of Continuous Random Variables

18-3 Special Probability Density Functions

Chapter Review

Extended Application: Exponential Waiting Times

Tables

Table 1 Formulas of/from Geometry

Table 2 Area Under a Normal Curve

Table 3 Integrals

Answers to Selected Exercises

Photo Acknowledgements

Index