Calculus with Applications, Brief Version

Series
Pearson
Author
Margaret L. Lial / Raymond N. Greenwell / Nathan P. Ritchey  
Publisher
Pearson
Cover
Softcover
Edition
11
Language
English
Total pages
656
Pub.-date
December 2015
ISBN13
9780321979414
ISBN
0321979419
Related Titles


Product detail

Title no longer available

Description

For freshman/sophomore, 1-semester (1-2 quarter) courses covering applied calculus for students in business, economics, social sciences, or life sciences.

 

Calculus with Applications, Brief Version, Eleventh 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.

 

Also available with MyMathLab

The MyMathLab® course for the text provides online homework and additional learning resources for students, such as video tutorials, algebra help, step-by-step examples, and graphing calculator help. The course features many more assignable exercises than the previous edition.

 

Features

About the Textbook

  • A wide variety of applications reference real data from articles in newspapers, journals, and websites. Examples and exercises with recent data help students learn how the mathematics is applied to their field of study, immediately addressing the question, “Why are we learning this?” NEW! The authors have added or updated 137 (18.3%) of the application exercises throughout the text..
    • Apply It opens most sections with a provocative, real-world oriented question that is addressed in the exposition and exercises.
    • Applied exercises are grouped by type of application and highlighted for easy identification.
    • Extended Applications appear at the end of all chapters to stimulate student interest and foster in-depth learning. Directions for Group Projects in the Extended Applications provide an opportunity for cooperative learning.
    • Index of Applications provides instructors and students with an overview of the types of applications throughout the book.
    • Application exercises within MyMathLab are labeled by type of application.
  • Assessment and remediation features appear at key points to ensure that students keep up with the material, and provide plenty of pointers to help those who fall behind.
    • “Your Turn” exercises following selected examples provide students with an easy way to stop and check their understanding of the skill or concept being presented. Answers are provided at the end of the section’s exercises.
    • NEW! Warm-Up exercises were added to many exercise sets to provide an opportunity for students to refresh key prerequisite skills at “point of use.” Each exercise includes a note about where students can go for help if needed.
    • The Prerequisite Skills Diagnostic Test, just prior to Chapter R, gives students and instructors an opportunity to assess students’ skills on topics that are critical to success in this course. Answers refer to specific review material in the text for targeted remediation.
    • An Algebra Reference chapter appears at the beginning of the text, allowing students to brush up on their algebra skills.
    • “For Review” boxes in the margin provide immediate review, or refer students back to appropriate sections as needed.
    • “Help text” annotations, 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. Many more have been added in this edition.
    • Chapter Summaries include important concepts, rules, and formulas, helping students review what they have learned.
    • Caution notes warn students of common errors/misconceptions and Note boxes offer additional useful information. Both are highlighted for easy reference.
  • Diverse exercise sets show how math is used in students’ major courses of study—business, life science, and social sciences.
    • Connection Exercises integrate topics/concepts from different sections. These are denoted with an icon.
    • Writing Exercises provide students with an opportunity to write about important mathematical ideas. These are denoted with an icon.
    • Technology Exercises, denoted with an icon, explore concepts using a graphing calculator or spreadsheet.
    • Concept Check exercises in the Chapter Reviews help students verify their understanding of important topics.
    • Reference Tables for Exercises appear in the back of the book. These tables correlate homework exercises to a helpful example in the text.
  • Technology coverage keeps your classroom and students up-to-date with the latest software and technology options available on the market.
    • The design makes it easy to identify technology coverage so instructors can more easily highlight (or skip) the material.
    • Excel® Spreadsheets are included in examples and exercises where appropriate, allowing students to work problems that closely relate to real-life and business situations.
    • Graphing Calculator discussions are included in many examples, but are not essential for understanding the text. NEW! Graphing calculator screens have been updated to reflect the TI-84 Plus C, which features a higher-resolution color screen.
    • Technology Notes Material on graphing calculators or Microsoft Excel is clearly labeled to make it easier for instructors to use this material (or not).

 

Also available with MyMathLab

MyMathLab is the online homework, tutorial, and assessment program designed for this text to engage students and improve results. Within its structured environment, students learn, practice and apply what they learn, test their understanding, and take advantage of a personalized study plan that adapts to their needs.

  • The MyMathLab® course for this text contains many assignable exercises with help features that can be customized to the needs of your students. NEW! At the request of MyMathLab users, we added more applications to this revision.
    • NEW! Setup & Solve exercises require students to specify how to set up a problem, then solve it. These exercises mirror what students will be asked to do on tests.
    • Application labels within exercise sets (e.g., “Business/Econ”) make it easy for instructors to find types of applications appropriate to students.
  • NEW! An Integrated Review version of the course contains pre-assigned diagnostic and remediation resources for key prerequisite skills. Skills Check Quizzes help diagnose gaps in skills prior to each chapter. MyMathLab then provides personalized help on only those skills that a student has not mastered.
  • Personalized Homework functionality allows instructors to create homework assignments based on the results of student assessments.
  • Tutorial videos for every section of the textbook cover important concepts and terms, and are easily accessible for students who miss lecture. NEW! Videos are available as full-length lectures and as shorter, assignable video clips that focus on a specific concept or example.
    • NEW! A Guide to Video-Based Assignments shows which exercises correspond to each video clip, making it easy to assess students after they watch an instructional video. This is perfect for flipped-classroom situations.
    • NEW! Tutorial videos involving graphing calculators are now included within MyMathLab exercises to augment videos showing "by hand" methods. If you require graphing calculator usage for the course, your students will find the instruction in these videos very helpful. (If you do not use calculators, you can hide these videos from students.) The videos were created by veteran math instructors at the University of Arkansas with technical assistance from the university's Global Campus.
  • NEW! Learning Catalytics is a “bring your own device” student engagement, assessment, and classroom intelligence system. Students use any modern web-enabled device they already have. With Learning Catalytics, you assess students in real time, using open-ended tasks to probe student understanding. It allows you to engage students by creating open-ended questions that ask for numerical, algebraic, textual, or graphical responses—or simple multiple-choice. Students who have access to MyMathLab have instant access to Learning Catalytics and can log in using their MyMathLab username and password. Learning Catalytics contains Pearson-created content for calculus that allows you to take advantage of this exciting technology immediately.
  • Interactive Figures illustrate key concepts and allow manipulation for use as teaching and learning tools. These include assignable exercises that require use of the figures.

 

New to this Edition

New and updated features

  • Warm-Up exercises were added to many exercise sets to provide an opportunity for students to refresh key prerequisite skills at “point of use.”
  • Graphing calculator screens have been updated to reflect the TI-84 Plus C, which features color and a much higher resolution screen. Additionally, the graphing calculator notes have been updated throughout.
  • More help text in the examples provide an additional aid for students with weaker algebra skills. These notes are set in small blue type next to the steps within worked-out examples.
  • More real data in examples and exercises include additional or updated data:
    • The authors have added or updated 137 (18.3%) of the application exercises throughout the text.
  • Updated exercises and examples are based on user feedback and other factors.
    • Of the 2720 exercises within the sections, 304 (11.2%) are new or updated.
    • Of the 320 examples in the text, 48 (15.0%) are new or updated.

 

Content Updates

  • Chapter R
    • Added new Your Turn exercises to ensure that there is a student assessment for each major concept.
    • Added more detail to R.2 on factoring perfect squares.
  • Chapter 1
    • Rewrote the part of 1.1 involving graphing lines, emphasizing different methods for graphing.
    • Rewrote 1.2 on supply, demand, break-even analysis, and equilibrium; giving formal definitions that match what students would see in business and economics courses. All of the business applications were revised, according to recommendations of reviewers, to be more in line with business texts. Also added a new Example 6 on finding a cost function.
    • Added color for pedagogical reasons to make content easier to follow.
  • Chapter 2
    • Updated introduction to 2.1, rewriting it as an example to make it easier for students to reference the necessary skills to identify nonlinear functions, determine the domain and range, and estimate values from a graph.
    • In 2.2, added another approach to graphing parabolas by splitting former Example 4 into two separate examples. The new Example 5 illustrates how to graph a parabola by first finding its characteristics (including orientation, intercepts, vertex, and axis of symmetry). The characteristics are highlighted in a box for easy reference.
    • Added quadratic regression to 2.2. Example 9 includes a by-hand method and a method using technology.
    • Rewrote Example 10 in 2.2, which illustrates translations and reflections of a graph, by breaking it into three parts. The first part is a basic transformation, and the ensuing parts build in complexity.
    • Added the definition of a real root to 2.3 and added a technology box to illustrate how to use a graphing calculator to approximate the roots of higher degree polynomials.
    • Added cubic regression to 2.3 (Example 5).
  • Chapter 3
    • Added Caution note to 3.1 and added a new solution method to Example 9.
    • Added new Example 2 to 3.3 using recent data.
    • Updated Example 4 in 3.3 to use clearer wording.
  • Chapter 4
    • Clarified the rules for differentiation in 4.1, 4.2, 4.3 and added a new Example 8.
    • Expanded Example 9 in 4.1 to include a new graph.
    • Updated Example 10 in 4.1 and Example 4 in 4.5.
  • Chapter 5
    • Added new examples to 5.2 (Example 3c) and 5.3 (Example 6b).
    • Expanded Example 6a in 5.4 to show the inflection point.
  • Chapter 6
    • Updated Example 3 in 6.1 to show an application of the concept.
    • Modified examples in 6.2 (Example 3), 6.4 (Example 2), and 6.6 (Example 1).
  • Chapter 7
    • Added annotations and comments to Example 10 in 7.1.
    • Simplified Examples 1, 2, 3, and 6 in 7.2 and added annotations and comments.
    • Added a “For Review” box to 7.3.
    • Enlarged all small integral signs throughout the chapter for added clarity.
    • Updated Example 7 in 7.4 and Example 5 in 7.5.
    • Added more explanation of the consumer surplus to 7.5.
  • Chapter 8
    • Added annotations to several examples in 8.1 to denote steps in integration by parts.
    • Revised the solutions to Examples 4 and 5 in 8.3, giving more detail and adding annotation to denote the steps in determining the accumulated amount of money flow.
  • Chapter 9
    • Rewrote and expanded Exercise 8 in 9.1, on the Cobb-Douglas Production Function, emphasizing the interpretation of the solutions.
    • Added 3 new exercises to 9.1 on exponential and logarithmic functions of several variables.
    • Revised the solution to Example 4 in 9.3, giving more detail.
    • Rewrote the solution to Example 3 in 9.4, illustrating how to find the extrema of a constrained function of one or more variables using a spreadsheet.

Also available with MyMathLab

MyMathLab is an online homework, tutorial, and assessment program designed for this text to engage students and improve results. Within its structured environment, students learn, practice and apply what they learn, test their understanding, and take advantage of a personalized study plan that adapts to their needs.

  • Some resources were added or revised based on student usage of the previous edition of the MyMathLab course. For example, more exercises were added to those chapters and sections that are more widely assigned.
  • Hundreds of new exercises were added to the course to provide you with more options for assignments, including:
    • More application exercises throughout the text
    • Setup & Solve exercises that require students to specify how to set up a problem as well as to solve it
    • Exercises that take advantage of the enhanced graphing tool
  • An Integrated Review version of the course contains pre-assigned diagnostic and remediation resources for key prerequisite skills. Skills Check Quizzes help diagnose gaps in skills prior to each chapters. MyMathLab then provides personalized help on only those skills that a student has not mastered.
  • The videos for the course have increased in number, type, and quality:
    • New videos feature more applications and more challenging examples.
    • NEW! Tutorial videos involving graphing calculators are now included within MyMathLab exercises to augment videos showing "by hand" methods. If you require graphing calculator usage for the course, your students will find the instruction in these videos very helpful. (If you do not use calculators, you can hide these videos from students.) The videos were created by veteran math instructors at the University of Arkansas with technical assistance from the university's Global Campus.
    • Assignable, shorter video clips focus on a specific concept or example. These appear in addition to full-length lecture videos in MyMathLab.
    • MathTalk Videos help motivate students by pointing out relevant connections to their majors–especially business. The videos feature Andrea Young from Ripon College (WI), a dynamic math professor (and actor!). The videos can be used as lecture starters or as part of homework assignments (in regular or flipped classes). Assignable exercises that accompany the videos help make these videos a part of homework assignments.
    • A Guide to Video-Based Assignments shows which exercises correspond to each video, making it easy to assess students after they watch an instructional video. This is perfect for flipped-classroom situations.
  • Learning Catalytics is a “bring your own device” student engagement, assessment, and classroom intelligence system. Students use any modern web-enabled device they already have. With Learning Catalytics, you assess students in real time, using open-ended tasks to probe student understanding. It allows you to engage students by creating open-ended questions that ask for numerical, algebraic, textual, or graphical responses–or simple multiple-choice. Students who have access to MyMathLab have instant access to Learning Catalytics and can log in using their MyMathLab username and password. Learning Catalytics contains Pearson-created content for calculus that allows you to take advantage of this exciting technology immediately.
  • Interactive Figures no longer require a special plug-in. They have been re-programmed in HTML5.

 

 

 

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. 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 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 (new)

 

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 (new)

 

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

 

Tables

Table 1 Formulas of Geometry

Table 2 Integrals

 

Answers to Selected Exercises

Photo Acknowledgements

Index

Author

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.