- Raymond N. Greenwell |
- Nathan P. Ritchey |
- Margaret L. Lial |
Title overview
For freshman/sophomore, 1-2 semester or 2-3 quarter courses covering calculus for students in life sciences.
Motivate with relevant applications
Calculus for the Life Sciences features interesting, relevant applications that motivate students. A review chapter at the start of the text helps students brush up on algebra skills. The utility of mathematics for the life sciences is highlighted through constant, consistent applications throughout. Proven pedagogy, robust exercise sets, and comprehensive end-of-chapter material help students succeed.
The 2nd Edition includes new features such as Your Turn exercises. Exercises and examples have been updated to reflect recent data and incorporate user feedback; a list of important formulas and definitions has been added; revised review exercises now include Concept Check exercises; and much more.
Hallmark features of this title
- 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.
- Exercise sets show how math is used in the life sciences: Writing Exercises encourage students to write about important mathematical ideas; Technology Exercises explore concepts using a graphing calculator or spreadsheet; Connection Exercises integrate topics/concepts from different sections; Concept Check exercises in the Chapter reviews help students verify their understanding of important topics.
- 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 MyLab Math.
New to this edition
- Exercises and examples have been updated to reflect the latest data and to incorporate feedback received on the previous version of the text.
- NewYour Turn exercises following selected examples give students an easy way to stop and check their understanding. Answers are provided at the end of the section’s exercises.
- A list of important formulas and definitions has been added.
- Revised review exercises now begin with Concept Check exercises, a series of true/false exercises designed to assess key ideas. The answers for review exercises 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.
- An updated design makes it easier to identify technology coverage so instructors can more easily highlight (or skip) the material.
Key features
Features of MyLab Math for the 2nd Edition
- Exercise coverage: Instructors canchoose 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 MyLab Math are labeled by application type.
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 Eigenvectorsx
- 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
- 12.1 Sets
- 12.2 Introduction to Probability
- 12.3 Conditional Probability; Independent Events; Bayes’ Theorem
- 12.4 Discrete Random Variables; Applications to Decision Making
- Chapter Review
- Extended Application: Medical Diagnosis
- 13. Probability and Calculus
- 13.1 Continuous Probability Models
- 13.2 Expected Value and Variance of Continuous Random Variables.
- 13.3 Special Probability Density Functions
- Chapter Review
- Extended Application: Exponential Waiting Times
- 14. Discrete Dynamical Systems
- 14.1 Sequences
- 14.2 Equilibrium Points
- 14.3 Determining Stability
- Chapter Review
- Extended Application: Mathematical Modeling in a Dynamic World
-
Special Topics (available online):
Sequences and Series
- Geometric Sequences
- Annuities: An Application of Sequences
- Taylor Polynomials
- Infinite Series
- Taylor Series
- Newton’s Method
- L’Hôpital’s Rule
Markov Chains
Author bios
About our authors
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 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/.
The late Marge Lial 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.