Calculus with Applications make mathematics relevant and accessible through timely applications, real data, examples, exercise sets and supplementary resources. You'll have ample opportunity to relate what you're learning to realistic career situations, while preparing for success in your career.
Table of Contents:
Preface
Prerequisite Skills Diagnostic Test
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 1 Review
Extended Application: Predicting 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 2 Review
Extended Application: Power Functions
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 4 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 5 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
6.4 Implicit Differentiation
6.5 Related Rates
6.6 Differentials: Linear Approximation
Chapter 6 Review
Extended Application: A Total 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 7 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 8 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 9 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 10 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 11 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 at 0
12.4 Infinite Series
12.5 Taylor Series at 0
12.6 Newton's Method
12.7 L'Hôpital's Rule
Chapter 12 Review
Extended Application: Living Assistance and Subsidized Housing
13. The Trigonometric Functions
13.1 Definitions of the Trigonometric Functions
13.2 Derivatives of Trigonometric Functions
13.3 Integrals of Trigonometric Functions
Chapter 13 Review
Extended Application: The Shortest Time and the Cheapest Path
Appendix
- Solutions to Prerequisite Skills Diagnostic Test
- Tables
Complete Instructor Answers
Credits
Index of Applications
Index
Sources
About the Author :
About our authors 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 led 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 4 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.
Katherine Ritchey earned a B.A. in Mathematics from the University of Notre Dame. She earned a Ph.D. in Mathematics from The Ohio State University, and her research interests include combinatorics and graph theory. While at OSU, she began her lifelong dream of teaching mathematics and was awarded several graduate student teaching awards. She is currently an Assistant Professor of Mathematics at the University of Mount Union in Ohio.
Blain A. Patterson earned a B.S. in Mathematics Education with a minor in Mathematics from Youngstown State University. He earned both a M.S. and Ph.D. in Mathematics Education from North Carolina State University. He is currently an Assistant Professor of Applied Mathematics at Virginia Military Institute. He has published articles in various mathematics and education journals on mathematics teacher education, learning disabilities, middle school mathematics education, and cryptography. Blain is currently a Project NExT Fellow (Brown '20) and an active member of MAA, SIAM, SIMIODE and AWM. When he is not thinking about mathematics, Blain enjoys spending time outdoors with his dogs and playing board games.
Sarah Ritchey Patterson earned a B.S. in Mathematics and Computer Science from Youngstown State University. She earned a Ph.D. in Mathematics from Duke University. Sarah is currently an assistant professor at the Virginia Military Institute. Her research interests include computational fluid dynamics, fluid-structure interaction problems, and mathematical modeling. Sarah actively advises undergraduate research projects and uses this perspective to enhance her teaching and the textbook.
