Calculus with Applications

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.  

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. 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