# Calculus for the Life Sciences: A Modeling Approach Volume 1

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James Cornette, Iowa State University

Ralph Ackerman, Iowa State University

Pub Date:

ISBN 13: 9781467976664

Publisher: Independent

Language: English

## Conditions of Use

Attribution-NonCommercial-NoDerivs

CC BY-NC-ND

## Table of Contents

- 1 Mathematical Models of Biological Processes
- 2 Functions
- 3 The Derivative
- 4 Continuity and the Power Chain Rule
- 5 Derivatives of the Exponential and Logarithm Functions
- 6 Derivatives of Products, Quotients, and Compositions
- 7 Derivatives of Trigonometric Functions
- 8 Applications of Derivatives
- 9 The Mean Value Theorem and Taylor's Polynomials
- 10 Partial Derivatives and the Diffusion Equation
- 11 The Integral
- 12 The Fundamental Theorem of Calculus
- 13 Applications of the Fundamental Theorem of Calculus

## About the Book

Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.

## About the Contributors

### Authors

**James L. Cornette** taught university level mathematics for 45 years as a graduate student at the University of Texas and a faculty member at Iowa State University. His research includes point set topology, genetics, biomolecular structure, viral dynamics, and paleontology, and has been published in Fundamenta Mathematica, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, Heredity, Journal of Mathematical Biology, Journal of Molecular Biology, and the biochemistry, the geology, and the paleontology sections of the Proceedings of the National Academy of Sciences, USA. Dr. Cornette received an Iowa State University Outstanding Teacher Award in 1973, was a Fulbright lecturer at the Universiti Kebangsaan Malaysia in 1973-74, worked in the Laboratory of Mathematical Biology in the National Cancer Institute, NIH in 1985-1987, and and was named University Professor at Iowa State University in 1998. He retired in 2000 and began graduate study at the University of Kansas where he earned a master's degree in Geology (Paleontology) in 2002. Presently he is a volunteer in the Earth Sciences Division of the Denver Museum of Nature and Science.

**Ralph A. Ackerman** is a professor in the Department of Ecology, Evolution and Organismal Biology at Iowa State University. He has been a faculty member since 1981 where his research focuses on describing and understanding the environmental physiology of vertebrate embryos, especially reptile and bird embryos. His approach is typically interdisciplinary and employs both theoretical and experimental techniques to generate and test hypotheses. He currently examines water exchange by reptile eggs during incubation and temperature dependent sex determination in reptiles.