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Calculus for the Life Sciences

Calculus for the Life Sciences

Marvin Bittinger, Neal Brand, John Quintanilla

Dec 2005, Hardback, 780 pages
ISBN13: 9780321279354
ISBN10: 0321279352
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Based on the best-selling Calculus and Its Applications by Marv Bittinger, this new text is appropriate for a two-semester calculus course for life science majors. With four new chapters and two new co-authors, Calculus for the Life Sciences continues the Bittinger reputation as one of the most student-oriented and clearly written Applied Calculus texts available. The exercises and examples have been substantially updated to include additional relevant life science applications and current topics.

Chapter 1 Functions and Graphs

1.1 Slope and Linear Functions

1.2 Polynomial Functions

1.3 Rational and Radical Functions

1.4 Trigonometric Functions

1.5 Trigonometric Functions and the Unit Circle

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Carbon Dioxide Concentrations

Chapter 2 Differentiation

2.1 Limits and Continuity: Numerically and Graphically

2.2 Limits: Algebraically

2.3 Average Rates of Change

2.4 Differentiation Using Limits of Difference Quotients

2.5 Differentiation Techniques: Introduction

2.6 Instantaneous Rates of Change

2.7 Differentiation Techniques: The Product and Quotient Rules

2.8 The Chain Rule

2.9 Higher-Order Derivatives

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Rate of Epidemic Spread: SARS

Chapter 3 Applications of Differentiation

3.1 Using the First Derivatives to Find Maximum and Minimum Values and Sketch Graphs

3.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs

3.3 Graph Sketching: Asymptotes and Rational Functions

3.4 Using Derivatives to Find Absolute Maximum and Minimum Values

3.5 Maximum-Minimum Problems

3.6 Approximation Techniques

3.7 Implicit Differentiation of Related Rates

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Polymorphism

Chapter 4 Exponential and Logarithmic Functions

4.1 Exponential Functions

4.2 Logarithmic Functions

4.3 Applications: The Uninhibited Growth Model, dP/dt = kP

4.4 Applications: Decay

4.5 The Derivatives of ax and logax

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Maximum Sustainable Harvest

Chapter 5 Integration

5.1 Integration

5.2 Riemann Sums and Definite Integrals

5.3 Fundamental Theorem of Calculus

5.4 Properties of Definite Integrals

5.5 Integration Techniques: Substitution

5.6 Integration Techniques: Integration by Parts

5.7 Integration Techniques: Tables and Technology

5.8 Volume

5.9 Improper Integrals

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Estimating Dinosaur Mass

Chapter 6 Matrices

6.1 Matrix Operations

6.2 Solving Linear Systems of Equations

6.3 Finding a Matrix Inverse and Determinant

6.4 Computing Eigenvalues and Eigenvectors

6.5 Solving Difference Equations

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Population Growth

Chapter 7 Functions of Several Variables

7.1 Functions of Several Variables

7.2 Partial Derivatives

7.3 Maximum-Minimum Problems

7.4 An Application: The Method of Least Squares

7.5 Multiple Integration

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Stocking Fish

Chapter 8 First-Order Differential Equations

8.1 Differential Equations and Initial-Value Problems

8.2 Linear First-Order Differential Equations

8.3 Stability of Autonomous Differential Equations

8.4 Separable Differential Equations

8.5 Numerical Solutions of Differential Equations

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Larvae and Forest Defoliation

Chapter 9 Higher-Order and Systems of Differential Equations

9.1 Higher-Order Homogeneous Differential Equations

9.2 Higher-Order Nonhomogeneous Differential Equations

9.3 Systems of Linear Differential Equations

9.4 Matrices and Trajectories

9.5 Models of Population Biology

9.6 Numerical Methods

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Epidemics

Chapter 10 Probability

10.1 Probability

10.2 Multiplication Trees and Bayes’ Rule

10.3 The Binomial Distribution

10.4 Expected Value and Standard Deviation for Discrete Random Variables

10.5 Continuous Random Variables

10.6 Poisson Process

10.7 The Normal Distribution

Summary and Review

Test

EXTENDED LIFE SCIENCE CONNECTION: Axenic Cultures

Appendix A: Review of Basic Algebra

Appendix B: Functions

Tables

Integration Formulas

Areas for a Standard Normal Distribution

Answers

Index

  • Chapter Openers: Each chapter opener includes an application to motivate the chapter material. These applications also provide an intuitive introduction to a key calculus topic.
  • Section Objectives: As each new section begins, its objectives are clearly stated in the margin. These can be spotted easily by the student, and thus provide the answer to the typical question, “What material am I responsible for?"
  • Technology Connections: Though optional, the use of technology reinforces the concepts presented. For the topics which are computationally intensive (see Sections 3.7, 5.7, 8.5 and 9.6), technology greatly reduces the amount of effort required to solve exercises numerically. This feature illustrates the use of technology while students explore key ideas in calculus.
  • Variety of Exercises: The exercise sets include skill and drill exercises, detailed art pieces, and extra graphs. The various kinds of exercises include Technology Connections, Synthesis, Thinking and Writing, and Applications.
  • Summary and Review: At the end of each chapter is a summary and review. These are designed to provide students with all the material they need for successful review. Answers are at the back of the book, together with section references so that students can easily find the correct material to restudy if they have difficulty with a particular exercise.
  • Chapter Test: Each chapter ends with a chapter test that includes synthesis and technology questions. The answers, with section references to the chapter tests, are at the back of the book.
  • Extended Life Science Connections: The Extended Life Science Connections that conclude each chapter are designed to demonstrate the importance of mathematical concepts to modern scientific research in fields such as ecology, genetics, paleontology, and epidemiology. They present multiple exercises that build on each other to form a conceptual framework for studying the given application. Group study is promoted by integrating concepts presented throughout the text. References to the literature are often cited.

Marvin Bittinger For over thirty years Professor Marvin L. Bittinger has been teaching math at the university level. Since 1968 he has been employed as a professor of mathematics education at Indiana University - Purdue University at Indianapolis. Professor Bittinger has authored 159 publications on topics ranging from Basic Mathematics to Algebra and Trigonometry to Brief Calculus. He received his BA in Mathematics from Manchester College in 1963 and his PhD in Mathematics Education from Purdue University in 1968. Special honors include being Distinguished Visiting Professor at the United States Air Force Academy and being elected to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking, baseball, golf, and bowling and he enjoys membership in the Professional Bowler's Association and the Society for the Advancement of Baseball Research.

Professor Bittinger has also had the privilege of speaking at a recent mathematics convention giving a lecture entitled, Baseball and Mathematics. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and three grandchildren.

Neal Brand is the Departmental Chair and Professor of Mathematics at the University of North Texas in Denton, Texas, where he has taught since 1983. Before teaching at UNT, he taught at Ohio State University and Loyola University of Chicago, and he was employed as a scientist at McDonnell-Douglass Corporation. He received his BS in Mathematics from Purdue University in 1974, and his MS and PhD in Mathematics from Stanford University in 1976 and 1978 respectively. He has authored or co-authored 26 refereed articles that have appeared in the mathematical literature.

Dr. Brand is a member of the Mathematical Association of America and the American Mathematical Society. Outside of mathematics, his interests include woodworking and carpentry. He is a founding board member and current board president of Habitat for Humanity of Denton County. He lives in Denton, Texas with his wife Shari. He also has two grown daughters.

John A. Quintanilla is an Associate Professor of Mathematics at the University of North Texas in Denton, Texas, where he has taught since 1996. He received both his BS and MS in Mathematics from Stanford University in 1992, and he received his PhD in Civil of Engineering and Operations Research from Princeton University in 1997. He has authored or co-authored 18 refereed articles that have appeared in the scientific literature.

Dr. Quintanilla has been the recipient of multiple teaching awards. In 2004, he received the University of North Texas President's Council Teaching Award. In 2005, he was conferred the Distinguished College or University Teaching of Mathematics Award by the Texas Section of the Mathematical Association of America. Dr. Quintanilla is a member of the Mathematical Association of America and the Association of Christians in the Mathematical Sciences.

His outside interests include golf, volleyball, softball, and Bible study. He lives in Denton, Texas with his wife Sandra and their daughter Sarah.

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