Calculus for the Life Sciences

Description

Table of Contents

New Textbook Features

 

·     Exercises and examples have been updated to reflect the latest data and to incorporate feedback received on the previous version of the text.

·         “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.

·         Updated Chapter Reviews

o    A list of important formulas and definitions has been added.

o    Review exercises now begin with Concept Check exercises—a series of true/false exercises designed to assess key ideas.

o    The answers for review exercises (at the back of the book) now include a table listing the examples within the chapter that are most similar to each review exercise.

·         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 reference specific review material in the text for targeted remediation.

·         The updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.

 

New MyMathLab Course

·         Exercise coverage–choose from hundreds of assignable exercises to help you craft just the right assignments

·         Diagnostic quizzes and Personalized Homework provide individualized remediation for any gaps in prerequisite skills.

·         Video program features example and section coverage.

·         Graphing calculator and Excel spreadsheet guidance for students.

·         Application exercises within MyMathLab are labeled by type of application.

 

 

• Chapter Reviews are structured to help students prepare for tests.
• NEW! A list of important formulas and definitions has been added.
• NEW! Review exercises now begin with Concept Check exercises—a series of true/false exercises designed to assess key ideas.
• NEW! The answers for review exercises (at the back of the book) now include a table listing the examples within the chapter that are most similar to each review exercise.
• Help for Gaps in Prerequisite Skills for students who need it.
• NEW! 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 reference specific review material in the text for targeted remediation.
• “For Review” boxes in the margin provide immediate review, or refer students back to appropriate sections as needed.
• Algebra Reference Chapter R appears at the beginning of the text, allowing students to brush up on their algebra skills.
• Diverse exercise sets show how math is used in the life sciences.
• Writing Exercises, denoted with an icon, provide students with an opportunity to write about important mathematical ideas.
• Technology Exercises, denoted with an icon, explore concepts using a graphing calculator or spreadsheet.
• Connection Exercises, denoted with an icon, integrate topics/concepts from different sections.
• Concept Check exercises in the Chapter reviews help students verify their understanding of important topics.

• Technology coverage allows you to include as much or as little use of technology as you prefer.
• NEW! The updated design makes it easier 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 life science applications.
• Graphing Calculator discussions are included in many examples, but are not essential for understanding the text. Figures depicting graphing calculator screens now feature the new TI MathPrint™ operating system.
• Graphing Calculator Manual and Excel Spreadsheet Manual provide step-by-step assistance for students and follow the order of topics within the course. Both are available for download within MyMathLab.

This edition features the same content as the traditional text in a convenient, three-hole-punched, loose-leaf version. Books a la Carte also offer a great value–this format costs significantly less than a new textbook. Before you purchase, check with your instructor or review your course syllabus to ensure that you select the correct ISBN. Several versions of Pearson’s MyLab & Mastering products exist for each title, including customized versions for individual schools, and registrations are not transferable. In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson’s MyLab & Mastering products.

 

Calculus for the Life Sciences features interesting, relevant applications that motivate students and highlight the utility of mathematics for the life sciences. This edition also features new ways to engage students with the material, such as Your Turn exercises.

New Textbook Features

·         Exercises and examples have been updated to reflect the latest data and to incorporate feedback received on the previous version of the text.

·        “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.

·         Updated Chapter Reviews

o    A list of important formulas and definitions has been added.

o    Review exercises now begin with Concept Check exercises—a series of true/false exercises designed to assess key ideas.

o    The answers for review exercises (at the back of the book) now include a table listing the examples within the chapter that are most similar to each review exercise.

·         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 reference specific review material in the text for targeted remediation.

·         The updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.

 

New MyMathLab Course

·         Exercise coverage—choose from hundreds of assignable exercises to help you craft just the right assignments

·         Diagnostic quizzes and Personalized Homework provide individualized remediation for any gaps in prerequisite skills.

·         Video program features example and section coverage.

·         Graphing calculator and Excel spreadsheet guidance for students.

·         Application exercises within MyMathLab are labeled by type of application.

 

New and Revised Content

Chapter 1

Changes in the presentation were made throughout to increase clarity, including adding some examples and rewriting others. In Section 1.1, a new example has been added which models the prevalence of cigarette smoking in the U.S., and then uses the model to make predictions. Section 1.2 has been revised, giving the formulas for the least squares line explicitly and making them more consistent with the formula for the correlation coefficient. In Section 1.4, an example on vaccination coverage, which illustrates how to derive a quadratic model, both by hand and with technology, has been added. In Section 1.5, material on identifying the degree of a polynomial has been rewritten as an example to better highlight the concept. An example on tuberculosis in the U.S., which illustrates how to derive a cubic model, has also been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as cancer, diabetes, gender ratio, energy consumption, meat consumption, the demand for nurses, organic farming, and ideal partner height have been added.

 

Chapter 2

In Section 2.1, a new example has been added, which covers the surplus of food, illustrating how to derive an exponential model, both by hand and with technology. In Section 2.4, an example using a trigonometric function to model the pressure on the eardrum has been included. A new Extended Application on Power Functions has been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as the bald eagle population, minority population growth, carbon monoxide emissions, wind energy, metabolic rate, physician demand, and music have been added.

 

Chapter 3

In Section 3.1, the introduction of limits was completely revised. The opening discussion and example were transformed into a series of examples that progress through different limit scenarios: a function defined at the limit, a function undefined at that limit (a “hole” in the graph), a function defined at the limit but with a different value than the limit (a piecewise function), and then finally, attempting to find a limit when one does not exist. New figures were added to illustrate the different scenarios. In Section 3.2, the definition and examples of continuity have been revised using a simple process to test for continuity. A medical devise cost analysis has been added as an example. In Section 3.3, an example calculating the rate of change of the number of households with landlines has been added. The opening discussion of Section 3.5, showing how to sketch the graph of the derivative given the graph of the original function, was rewritten as an example. An Extended Application on the modeling of drugs administered intravenously has been added. Throughout the chapter, real life exercises have been updated and new exercises on topics such as Alzheimer’s disease, body mass index, and immigration have been added.

 

Chapter 4

The introduction to the chain rule was rewritten as an example in Section 4.3. In Section 4.4, a new example illustrates the use of a logistic function to develop a model for the weight of cactus wrens. In the Chapter Review, a list of important formulas and definitions has been included. An Extended Application on managing renewable resources has been added. Throughout the chapter, real life exercises have been updated and new exercises on

 

topics such as tree growth, genetics, insect competition, whooping cranes, cholesterol, involutional psychosis, radioactive iron, radioactive albumin, heat index, Jukes-Cantor distance, eardrum pressure, online learning, and minority populations have been added.

 

Chapter 5

Twenty-six new exercises were added throughout Chapter 5, 9 of them applications based on scientific sources, such as three on foraging and two on cohesiveness, which involves the spacing between fish in a school or birds in a flock. There are now more trigonometric exercises in the chapter along with an additional example involving trigonometry.

 

Chapter 6

Throughout Chapter 6, 13 new exercises and 3 examples were added. Five of the new applications are based on scientific sources, such as the one on cancer cells and one on honeycombs in Section 6.2 on Applications of the Derivative. In addition, there are now more trigonometric exercises in the chapter.

 

Chapter 7

The antiderivatives of the trigonometric functions have been moved to the first section so they can now be applied throughout the chapter.  In addition, 6 exercises were added, some involving trigonometry and others involving integration using real data (such as those related to energy usage). The examples were improved by adding 2 new examples involving trigonometry and updating 6 involving real data.

 

Chapter 8

An example using tables to find trigonometric integrals has been included in Section 8.2. New graphics help illustrate the calculation of the volume of a solid of revolution in Section 8.3. Throughout the chapter, real life exercises have been updated.

 

Chapter 9

In Chapter 9, 7 of the new applications are based on scientific sources and 15 new exercises were added, such as those on zooplankton growth, hypoxia (when the lungs receive inadequate oxygen) and Body Shape Index. In addition, there are many more trigonometric exercises throughout the chapter. The Extended Application has been revised to include an additional question involving technology as well as a group project option. Finally, material was added justifying the second derivative test for functions of two variables.

 

Chapter 10

In Section 10.1, a brief summary of solutions of two equations in two variables has been added. An alternate method for fraction-free Gauss Jordan has been added to the first example.  Section 10.5 has been revised, with the beginning discussion rewritten as examples on insect population growth, determinant calculations, and eigenvalue and corresponding eigenvector calculations. New exercises on finding the determinant of a matrix have also been included in this section. Throughout the chapter, real life exercises have been updated and new exercises on topics such as cancer, motorcycle helmets, calorie expenditure, basketball, and baseball have been added.

 

 

 

Chapter 11

The chapter opener was changed relate to an exercise involving diseases in mouse populations. Material on equilibrium points and stability was added to Section 11.1. In addition, 13 new exercises were added, 6 of them applications based on scientific sources. One of the new exercises compares the three population growth models discussed in the chapter: exponential, limited growth, and logistic. There are now more trigonometric exercises throughout the chapter. Finally, exercises were updated and an example, a Your Turn exercise, a For Review box, and a Technology Note were added.

 

Chapter 12

In Section 12.1, an example on endangered species has been added to illustrate set operations. In Section 12.2, an exam on student health has been included to show how Venn diagrams can be used to determine probabilities. In Section 12.3, the beginning discussion has been rewritten as an example of conditional probability. Examples on environmental inspections and on playing cards, both illustrating the product rule, have been added. The solution to the example on sensitivity and specificity has been rewritten for clarity. Challenging problems from actuarial exams have been included as exercises throughout this chapter as well.

 

Chapter 13

New material was added on the Poisson random variable and its connection to the exponential random variable. In addition, new material was added on a random sample, its mean, and the Central Limit Theorem. To support the new material as well as to better align with the existing content, 4 new examples were added, and 20 new exercises were added, of which 4 are applications based on scientific sources, such as the ones on plant growth and on the Hodgkin-Huxley model for excitable nerve cells.

 

Chapter 14

Chapter 14 in the last edition was available online for those who chose to cover discrete dynamical systems. With an increased attention on this topic, the chapter has been heavily revised and supplemented to make for a robust topic in this course. In addition to a new chapter opener, 12 new exercises were added to the section 14.1, 6 to section 14.2, and 13 to section 14.3. Your Turn exercises and examples were added throughout the chapter. A Chapter Review was added with 30 exercises, 2 of them applications based on scientific sources. Finally, an Extended Application was added based on modeling the growth and decline of polio, as well as other life science situations that can be modeled by discrete dynamical systems.

 

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 currently 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.  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/.

 

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 find 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.

 

 

 

Additional information

Dimensions	1.50 × 8.55 × 11.05 in
Imprint	Pearson
Format	gen
ISBN-13	09780321964434
ISBN-10	0321964438
Author	Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Subjects	mathematics, higher education, applied math, Calculus, Applied & Advanced Math, Calculus for Life Sciences