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Contents
Prerequisite Skills Test
Calculus Readiness Test
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
Summary and Review
CASE STUDY 1. Energy Efficiency and Long-Term Cost Savings
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
Summary and Review
CASE STUDY 2. Using Extrapolation and Interpolation for Prediction
3. Functions and Graphs
3.1 Functions
3.2 Graphs of Functions
3.3 Applications of Linear Functions
3.4 Quadratic Functions and Applications
3.5 Polynomial Functions
3.6 Rational Functions
Summary and Review
CASE STUDY 3. Maximizing Profit
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
Summary and Review
CASE STUDY 4. Gapminder.org
5. Mathematics of Finance
5.1 Simple Interest and Discount
5.2 Compound Interest
5.3 Annuities, Future Value, and Sinking Funds
5.4 Annuities, Present Value, and Amortization
Summary and Review
CASE STUDY 5. Investing in Stocks and Using the Rule of 72
6. Systems of Linear Equations and Matrices
6.1 Systems of Two Linear Equations in Two Variables
6.2 Larger Systems of Linear Equations
6.3 Applications of Systems of Linear Equations
6.4 Basic Matrix Operations
6.5 Matrix Products and Inverses
6.6 Applications of Matrices
Summary and Review
CASE STUDY 6. Airline Route Maps
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
Summary and Review
CASE STUDY 7. Cooking with Linear Programming
8. Sets and Probability
8.1 Sets
8.2 Applications of Venn Diagrams and Contingency Tables
8.3 Introduction to Probability
8.4 Basic Concepts of Probability
8.5 Conditional Probability and Independent Events
8.6 Bayes' Formula
Summary and Review
CASE STUDY 8. Medical Diagnosis
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
Summary and Review
CASE STUDY 9. Quick Draw® from the New York State Lottery
10. Introduction to Statistics
10.1 Frequency Distributions
10.2 Measures of Center
10.3 Measures of Variation and Boxplots
10.4 Normal Distributions
Summary and Review
CASE STUDY 10. Standard Deviation as a Measure of Risk
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
Summary and Review
CASE STUDY 11. Price Elasticity of Demand
12. Applications of the Derivative
12.1 Local Extrema
12.2 The Second Derivative
12.3 Optimization Applications
12.4 Implicit Differentiation
12.5 Related Rates
12.6 Curve Sketching
Summary and Review
CASE STUDY 12. A Total Cost Model for a Training Program
13. Integral Calculus
13.1 Antiderivatives
13.2 Integration by Substitution
13.3 Integration by Parts
13.4 Area and the Definite Integral
13.5 The Fundamental Theorem of Calculus
13.6 Applications of Integrals
13.7 Differential Equations
Summary and Review
CASE STUDY 13. Bounded Population Growth
14. Multivariate Calculus
14.1 Functions of Several Variables
14.2 Partial Derivatives
14.3 Extrema of Functions of Several Variables
14.4 Lagrange Multipliers
Summary and Review
CASE STUDY 14. Global Warming and the Method of Least Squares
APPENDICES
A. Areas under the Normal Curve
B. Solutions to Prerequisite Skills Test and Calculus Readiness Test
C. Table of Integrals
Answers to Selected Exercises Index of Companies, Products, and Agencies Index of Applications Subject Index Photo Credits Reference Endpapers:
Algebra Review
Geometric Formulas
Finite Math Review
Calculus Review
