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Calculus with Applications, Brief Version, 12th edition

Published by Pearson (January 7, 2021) © 2022

  • Margaret L. Lial American River College
  • Raymond N. Greenwell Hofstra University
  • Nathan P. Ritchey Edinboro University of PA , Youngstown State University

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For 1-semester/1-2 quarter courses covering applied calculus for business, economics, social sciences or life sciences.

An applied presentation that makes math meaningful

Calculus with Applications, Brief Version, 12th Edition prepares students for career success with applications throughout. Known for real data in their examples and exercises, the authors make mathematics relevant in the exposition, examples, exercise sets and supplementary resources. Students have ample opportunity to relate what they're learning to career situations through the Apply It question at the beginning of sections, the applied examples and exercises, and the Extended Application at the end of each chapter. 

Hallmark features of this title

  • An Apply It question typically at the start of a section poses a real-world question that is then answered within the examples or exercises. 
  • Extended Applications at the end of each chapter provide in-depth applied exercises that can be completed individually or as a group project.
  • Your Turn Exercises follow selected examples and enable students to check their understanding. Answers are provided at the end of the section's exercises. 
  • Chapter Review Exercises include Concept Check exercises and a set of Practice and Exploration exercises, useful for exam prep.
  • For Review boxes in the margins give students just-in-time help with skills that may need refreshing.
  • Tech Notes: Material on graphing calculators and Microsoft® Excel® is clearly labeled.

New and updated features of this title

  • Enhanced Assignments are editable, assignable, section-level assignments that address gaps in prerequisite skills with personalized prerequisite review, help keep skills fresh with spaced practice of key concepts, and provide opportunities to work exercises without learning aids so that students can check their understanding.
  • More "help text" annotations have been added to examples. These notes, set in small blue type, appear next to the steps within worked-out examples and provide an additional aid for students with weaker algebra skills. 
  • Approximately 12% of the exercises are new or updated, improving data and applications. This includes nearly 300 new exercises written for the 12th Edition. 
  • New Concept Check exercises added to the beginning of the exercises in every section ensure that students understand basic concepts before proceeding. 
  • All answers in the Annotated Instructor's Edition are now located in one place at the back, saving time and page-flipping to find answers, and are also available to download as PDF. 

Features of MyLab Math for the 12th Edition

  • A built-in Integrated Review option offers pre-assigned diagnostic and remediation resources for key prerequisite skills. 
  • All  MyLab  Math exercises have been reviewed and edited as needed by coauthor Geoffrey Krader for improved quality and fidelity to the text.
  • Hundreds of new exercises have been added to the course, including more application exercises throughout the text, Setup & Solve exercises that require students to specify how to set up a problem as well as how to solve it, and exercises added to chapters and sections that were more widely assigned, based on data from the previous edition. 
  • An expanded suite of interactive figures: Created in GeoGebra, these figures illustrate key concepts and can be manipulated by users. They can be used in lectures or independently by students. 
  • Student's Solutions Manual available within MyLab Math provides detailed solutions to all odd-numbered text exercises and sample chapter tests with answers.
  • Graphing Calculator and Excel Manuals are available within MyLab Math under Video & Resource Library > Learning Tools as well as at bit.ly/3kSaDDT. 

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

Appendix

  1. Solutions to Prerequisite Skills Diagnostic Test
  2. Tables

Answers to Selected Exercises
Credits
Index of Applications
Index
Sources

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. 

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