Description
Book Synopsis Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received bachelor's and master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often find their way into her books as applications, exercise sets, and feature sets. Her interest in archeology lead to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
Thomas W. Hungerford received his bachelor's degree from Holy Cross and his Ph.D. from the
Table of Contents
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 Consumers Often Need to Just Do the Math
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 Architectural Arches
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 Continuous Compounding
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 Matrix Operations and 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
10.4 Normal Distributions and Boxplots
10.5 Normal Approximation to the Binomial Distribution
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
12. Applications of the Derivative
12.1 Derivatives and Graphs
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 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
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
Appendix A. Graphing Calculators
Appendix B: Tables
Table 1: Formulas from Geometry
Table 2: Areas under the Normal Curve
Table 3: Integrals
Appendix C. Learning Objectives
Appendix D. Solutions to Prerequisite Skills Tests
Answers to Selected Exercises
Index of Companies, Products, and Agencies
Index of Applications
Subject Index
