Chapter 1 Algebra and Equations
1.1 The Real Numbers
1.2 Polynomials
1.3 Factoring
1.4 Rational Expressions
1.5 Exponents and Radicals
1.6 First-Degree Equations
1.7 Quadratic Equations
Case 1: Consumers Often Defy Common Sense
Chapter 2 Graphs, Lines, and Inequalities
2.1 Graphs
2.2 Equations of Lines
2.3 Linear Models
2.4 Linear Inequalities
2.5 Polynomial and Rational Inequalities
Case 2: Using Extrapolation to Predict Life Expectancy
Chapter 3 Functions and Graphs
3.1 Functions
3.2 Graphs of Functions
3.3 Applications of Linear Functions
3.4 Quadratic Functions
3.5 Applications of Quadratic Functions
3.6 Polynomial Functions
3.7 Rational Functions
Case 3: Architectural Arches
Chapter 4 Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Applications of Exponential Functions
4.3 Logarithmic Functions
4.4 Logarithmic and Exponential Equations
Case 4: Characteristics of the Monkeyface Prickleback
Chapter 5 Mathematics of Finance
5.1 Simple Interest and Discount
5.2 Compound Interest
5.3 Future Value of an Annuity and Sinking Funds
5.4 Present Value of an Annuity and Amortization
Case 5: Time, Money, and Polynomials
Chapter 6 Systems of Linear Equations and Matrices
6.1 Systems of Linear Equations
6.2 The Gauss-Jordan Method
6.3 Basic Matrix Operations
6.4 Matrix Products and Inverses
6.5 Applications of Matrices
Case 6: Matrix Operations and Airline Route Maps
Chapter 7 Linear Programming
7.1 Graphing Linear Inequalities in Two Variables
7.2 Linear Programming: The Graphical Method
7.3 Applications of Linear Programming
7.4 The Simplex Method: Maximization
7.5 Maximization Applications
7.6 The Simplex Method: Duality and Minimization
7.7 The Simplex Method: Nonstandard Problems
Case 7: Cooking with Linear Programming
Chapter 8 Sets and Probability
8.1 Sets
8.2 Applications of Venn Diagrams
8.3 Introduction to Probability
8.4 Basic Concepts of Probability
8.5 Conditional Probability and Independent Events
8.6 Bayes’ Formula
Case 8: Medical Diagnosis
Chapter 9 Counting, Probability Distributions, and Further Topics in Probability
9.1 Probability Distributions and Expected Value
9.2 The Multiplication Principle, Permutations, and Combinations
9.3 Applications of Counting
9.4 Binomial Probability
9.5 Markov Chains
9.6 Decision Making
Case 9: Optimal Inventory for a Service Truck
Chapter 10 Introduction to Statistics
10.1 Frequency Distributions and Measures of Central Tendency
10.2 Measures of Variation
10.3 Normal Distributions
10.4 Normal Approximation to the Binomial Distribution
Case 10: Statistics in the Law—The Castaneda Decision
Chapter 11 Differential Calculus
11.1 Limits
11.2 One-sided Limits and Limits Involving Infinity
11.3 Rates of Change
11.4 Tangent Lines and Derivatives
11.5 Techniques for Finding Derivatives
11.6 Derivatives of Products and Quotients
11.7 The Chain Rule
11.8 Derivatives of Exponential and Logarithmic Functions
11.9 Continuity and Differentiability
Case 11: Price Elasticity of Demand
Chapter 12 Applications of the Derivative
12.1 Derivatives and Graphs
12.2 The Second Derivative
12.3 Optimization Applications
12.4 Curve Sketching
Case 12: A Total Cost Model for a Training Program
Chapter 13 Integral Calculus
13.1 Antiderivatives
13.2 Integration by Substitution
13.3 Area and the Definite Integral
13.4 The Fundamental Theorem of Calculus
13.5 Applications of Integrals
13.6 Tables of Integrals (Optional)
13.7 Differential Equations
Case 13: Bounded Population Growth
Chapter 14 Multivariate Calculus
14.1 Functions of Several Variables
14.2 Partial Derivatives
14.3 Extrema of Functions of Several Variables
Case 14: Global Warming and the Method of Least Squares