Finite Mathematics and Calculus with Applications

by Lial, Margaret L.; Greenwell, Raymond N.; Ritchey, Nathan P.

• ISBN13: 9780321979407
• ISBN10: 0321979400
• Edition: 10th
• Format: Hardcover
• Copyright: 2016-01-05
• Publisher: Pearson

Summary

Finite Mathematics and Calculus with Applications, Tenth Edition by Lial, Greenwell, and Ritchey, is our most applied text to date, making the math relevant and accessible for students of business, life science, and social sciences. Current applications, many using real data, are incorporated in numerous forms throughout the book, preparing students for success in their professional careers. With this edition, students will find new ways to help them learn the material, such as Warm-Up Exercises and added “help text” within examples.

 

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Author Biography

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 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 Contents

R. 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. Systems of Linear Equations and Matrices

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

 

3. Linear Programming: The Graphical Method

3-1 Graphing Linear Inequalities

3-2 Solving Linear Programming Problems Graphically

3-3 Applications of Linear Programming

            Chapter Review

 

4. Linear Programming: The Simplex Method

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

 

5. Mathematics of Finance

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

 

6. Logic

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

 

7. Sets and Probability

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

 

8. Counting Principles: Further Probability Topics

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

 

9. Statistics

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

 

10. Nonlinear Functions

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

 

11. The Derivative

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

 

12. Calculating the Derivative

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

 

13. Graphs and the Derivative

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)

 

14. Applications of the Derivative

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

 

15. Integration

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

 

16. Further Techniques and Applications of Integration

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*

            Chapter Review

            Extended Application: Estimating Learning Curves in Manufacturing with Integrals

 

17. Multivariable Calculus

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

 

18. Probability and Calculus

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