Description
Book SynopsisMarge 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 found 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.
Raymond N. Greenwell earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in Applied Mathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in 1983, where he currently is Professor of Mathematics.
Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He has served as governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club's Inner City Outings program.
Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is former chair of the Department of Mathematics and Statistics at Youngstown State University and is currently serving as the dean of the College of Science and Health Professions at Edinboro University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations.
In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's People Who Make a Difference Award, the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program.
Table of ContentsR. Algebra Reference
R-1 Polynomials
R-2 Factoring
R-3 Rational Expressions
R-4 Equations
R-5 Inequalities
R-6 Exponents
R-7 Radicals
1. Linear Functions
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
2. Nonlinear Functions
2-1 Properties of Functions
2-2 Quadratic Functions; Translation and Reflection
2-3 Polynomial and Rational Functions
2-4 Exponential Functions
2-5 Logarithmic Functions
2-6 Applications: Growth and Decay; Mathematics of Finance
Chapter Review
Extended Application: Characteristics of the Monkeyface Prickleback
3. The Derivative
3-1 Limits
3-2 Continuity
3-3 Rates of Change
3-4 Definition of the Derivative
3-5 Graphical Differentiation
Chapter 3 Review
Extended Application: A Model for Drugs Administered Intravenously
4. Calculating the Derivative
4-1 Techniques for Finding Derivatives
4-2 Derivatives of Products and Quotients
4-3 The Chain Rule
4-4 Derivatives of Exponential Functions
4-5 Derivatives of Logarithmic Functions
Chapter Review
Extended Application: Electric Potential and Electric Field
5. Graphs and the Derivative
5-1 Increasing and Decreasing Functions
5-2 Relative Extrema
5-3 Higher Derivatives, Concavity, and the Second Derivative Test
5-4 Curve Sketching
Chapter Review
Extended Application: A Drug Concentration Model for Orally Administered
Medications
6. Applications of the Derivative
6-1 Absolute Extrema
6-2 Applications of Extrema
6-3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand
6-4 Implicit Differentiation
6-5 Related Rates
6-6 Differentials: Linear Approximation
Chapter Review
Extended Application: A Total Cost Model for a Training Program
7. Integration
7-1 Antiderivatives
7-2 Substitution
7-3 Area and the Definite Integral
7-4 The Fundamental Theorem of Calculus
7-5 The Area Between Two Curves
7-6 Numerical Integration
Chapter Review
Extended Application: Estimating Depletion Dates for Minerals
8. Further Techniques and Applications of Integration
8-1 Integration by Parts
8-2 Volume and Average Value
8-3 Continuous Money Flow
8-4 Improper Integrals
Chapter Review
Extended Application: Estimating Learning Curves in Manufacturing with Integrals
9. Multivariable Calculus
9-1 Functions of Several Variables
9-2 Partial Derivatives
9-3 Maxima and Minima
9-4 Lagrange Multipliers
9-5 Total Differentials and Approximations
9-6 Double Integrals
Chapter Review
Extended Application: Using Multivariable Fitting to Create a Response Surface Design
10. Differential Equations
10-1 Solutions of Elementary and Separable Differential Equations
10-2 Linear First-Order Differential Equations
10-3 Euler's Method
10-4 Applications of Differential Equations
Chapter Review
Extended Application: Pollution of the Great Lakes
11. Probability and Calculus
11-1 Continuous Probability Models
11-2 Expected Value and Variance of Continuous Random Variables
11-3 Special Probability Density Functions
Chapter Review
Extended Application: Exponential Waiting Times
12. Sequences and Series
12-1 Geometric Sequences
12-2 Annuities: An Application of Sequences
12-3 Taylor Polynomials
12-4 Infinite Series
12-5 Taylor Series
12-6 Newton's Method
12-7 L'Hospital's Rule
Chapter Review
13. The Trigonometric Functions
13-1 Definitions of the Trigonometric Functions
13-2 Derivatives of Trigonometric Functions
13-3 Integrals of Trigonometric Functions
Chapter Review
Extended Application: The Shortest Time and the Cheapest Path
Tables
Table 1 Formulas of Geometry
Table 2 Area Under a Normal Curve
Table 3 Integrals
Table 4 Integrals Involving Trigonometric Functions
Answers to Selected Exercises
Photo Acknowledgements
Index
