Calculus with Applications

Marge Lial 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, is now affiliated with American River College.   Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced 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 in1983, 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 is currently (2002-2005) 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 currently a Professor of Mathematics and Chair of the Department of Mathematics and Statistics at Youngstown State 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. A father of four children, Nate enthusiastically coaches soccer and softball. He also loves music, playing several instruments, and is a tenor in the Shenango Valley Chorale. More information about Nate Ritchey can be found at: http://www.as.ysu.edu/~nate/.

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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 Review

Extended Application: A Model for Drugs Administered Intravenously

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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

 

Chapter 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