Description

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. The MyMathLab^® course for the text provides online homework supported by learning resources such as video tutorials, algebra help, and step-by-step examples.

Teaching and Learning Experience
This program will provide a better teaching and learning experience. Here’s how:

• Personalized help with MyMathLab: MyMathLab delivers proven results by personalizing the learning process.
• Motivation: Students constantly see the math applied to the life sciences.
• Built for student success: Proven pedagogy, robust exercise sets, and comprehensive end-of-chapter material help students succeed in the course.

Please note that the product you are purchasing does not include MyMathLab.

MyMathLab

Join over 11 million students benefiting from Pearson MyLabs.

This title can be supported by MyMathLab, an online homework and tutorial system designed to test and build your understanding. Would you like to use the power of MyMathLab to accelerate your learning? You need both an access card and a course ID to access MyMathLab.

These are the steps you need to take:

1. Make sure that your lecturer is already using the system

Ask your lecturer before purchasing a MyLab product as you will need a course ID from them before you can gain access to the system.

2. Check whether an access card has been included with the book at a reduced cost

If it has, it will be on the inside back cover of the book.

3. If you have a course ID but no access code, you can benefit from MyMathLab at a reduced price by purchasing a pack containing a copy of the book and an access code for MyMathLab (ISBN:9781292072050)

4. If your lecturer is using the MyLab and you would like to purchase the product...

Go to www.mymathlab.com to buy access to this interactive study programme.

For educator access, contact your Pearson representative. To find out who your Pearson representative is, visit www.pearsoned.co.uk/replocator

Features

Motivation: Students constantly see the math applied to the life sciences.

• A wide variety of life science applications reference real data from current sources. A complete list of these sources is at www.pearsonhighered.com/mathstatsresources.
  • Apply It (formerly called “Think About 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.
  • Index of Applications provides instructors and students with an overview of the types of applications throughout the book.
  • NEW! Application exercises within MyMathLab are now labeled by type of application.

Built for student success: Proven pedagogy, robust exercise sets, and comprehensive end-of-chapter material help students succeed in the course.

• Learning aids appear at key points to help students learn the key ideas.
  • NEW! “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.
  • Caution boxes warn students of common errors/misconceptions and Note boxes offer additional useful information. Both are highlighted for easy reference.
  • 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®&nbsp

New to this Edition

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 cohesivene

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. Functions

1.1 Lines and Linear Functions

1.2 The Least Squares Line

1.3 Properties of Functions

1.4 Quadratic Functions; Translation and Reflection

1.5 Polynomial and Rational Functions

   Chapter Review

   Extended Application: Using Extrapolation to Predict Life Expectancy

2. Exponential, Logarithmic, and Trigonometric Functions

2.1 Exponential Functions

2.2 Logarithmic Functions

2.3 Applications: Growth and Decay

2.4 Trigonometric Functions

   Chapter 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 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

4.6 Derivatives of Trigonometric Functions

   Chapter Review

   Extended Application: Managing Renewable Resources

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

 

6. Applications of the Derivative

6.1 Absolute Extrema

6.2 Applications of Extrema

6.3 Implicit Differentiation

6.4 Related Rates

6.5 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

   Chapter Review

   Extended Application: Estimating Depletion Dates for Minerals

8. Further Techniques and Applications of Integration

8.1 Numerical Integration

8.2 Integration by Parts

8.3 Volume and Average Value

8.4 Improper Integrals

   Chapter Review

   Extended Application: Flow Systems

 

9. Multivariable Calculus

9.1 Functions of Several Variables

9.2 Partial Derivatives

9.3 Maxima and Minima

9.4 Total Differentials and Approximations

9.5 Double Integrals

   Chapter Review

   Extended Application: Optimization for a Predator

10. Matrices

10.1 Solution of Linear Systems

10.2 Addition and Subtraction of Matrices

10.3 Multiplication of Matrices

10.4 Matrix Inverses

10.5 Eigenvalues and Eigenvectors

   Chapter Review

   Extended Application: Contagion

11. Differential Equations

11.1 Solutions of Elementary and Separable Differential Equations

11.2 Linear First-Order Differential Equations

11.3 Euler's Method

11.4 Linear Systems of Differential Equations

11.5 Non-Linear Systems of Differential Equations

11.6 Applications of Differential Equations

   Chapter Review

   Extended Application: Pollution of the Great Lakes

12. Probability

Author

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.