Calculus for The Life Sciences

Book Cover

Calculus for The Life Sciences

By Sebastian J. Schreiber, Karl Smith, Wayne Getz

SINGLE-TERM
$69  USD | $99  CAN
MULTI-TERM
$119  USD | $155  CAN

The gateway to the exciting interface of mathematics and biology. In this highly anticipated first edition, the authors present the basic canons of first-year calculus through real-life biological problems. The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, analytical techniques, and numerical methods and to help students understand how, when, and why calculus can be used to model biological phenomena.

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Topics are motivated where possible by significant biological applications

Topics are motivated where possible by significant biological applications, several of which appear in no other introductory calculus texts. Examples involve real-world data and whenever possible, these examples motivate and develop formal definitions, procedures, and theorems. Significant applications includes CO2 buildup at the Mauna Loa observatory in Hawaii, scaling of metabolic rates with body size, optimal exploitation of resources in patchy environments, insect developmental rates and degree days, rapid decline of populations, velocities of stooping peregrine falcons, drug infusion and accumulation rates, measurement of cardiac output, in vivo HIV dynamics, mechanism of memory formation, and the spread of disease in human populations.

Each chapter includes one or more projects that can be used for individual or group work

Each chapter includes one or more projects that can be used for individual or group work. These projects are diverse in scope, ranging from a study of enzyme kinetics to the heart rates in mammals to disease outbreaks.

Bifurcation diagrams and life history tables

Bifurcation diagrams and life history tables, two topics that are often not covered in other calculus books, are introduced. Bifurcation diagrams for univariate differential equations are a conceptually rich yet accessible topic. They provide an opportunity to illustrate that small parameter changes can have large dynamical effects. Life history tables provide students with an introduction to age structured populations and net reproductive number R0 of a population or a disease.

Concepts are presented visually, numerically, algebraically, and verbally

Throughout the book, concepts are presented visually, numerically, algebraically, and verbally. Presenting these different perspectives enhances and reinforces students’ understanding and appreciation for the main ideas.

Problems described as Historical Quest appear throughout the text

Problems described as Historical Quest appear throughout the text. These problems are not just historical notes to help students see mathematics and biology as living and breathing disciplines, but they are designed to involve the student in the quest of pursuing some great ideas in the history of science.

Sebastian J. Schreiber received his B.A. in mathematics from Boston University in 1989 and his Ph.D. in mathematics from the University of California, Berkeley in 1995. He is currently Professor of Ecology and Evolution at the University of California, Davis. Previously, he was an associate professor of mathematics at the College of William and Mary, where he was the 2005 recipient of the Simon Prize for Excellence in the Teaching of Mathematics, and Western Washington University. Professor Schreiber’s research on stochastic processes, nonlinear dynamics, and applications to ecology, evolution, and epidemiology has been supported by grants from the U.S. National Science Foundation, the U.S. National Oceanic and Atmospheric Administration, the Bureau for Land Management, and the U.S. Fisheries and Wildlife Service. He is the author or co-author of over seventy scientific papers in peer-reviewed mathematics and biology journals, including papers co-authored with undergraduate students. Professor Schreiber is currently on the editorial boards of the following research journals: Discrete and Continuous Dynamical Systems B, Ecology, Journal of Biological Dynamics, Journal of Mathematical Biology, Mathematical Medicine and Biology, and Theoretical Ecology.

Karl J. Smith received his B.A. and M.A. in 1967 in mathematics form UCLA. He moved to northern California in 1968 to teach at Santa Rosa Junior College, where he taught until his retirement in 1993. Along the way, he served as department chair, and he received a Ph.D. in 1979 in mathematics education at Southeastern University. A past president of the American Mathematical Association of Two-Year Colleges, Professor Smith is active nationally in mathematics education. He was founding editor of Western AMATYC News, a chairperson of the Committee on Mathematics Excellence, and a NSF grant reviewer. He was a recipient in 1979 of an Outstanding Young Men of America Award, in 1980 of an Outstanding Educator Award, and in 1989 of an Outstanding Teacher Award. Professor Smith is the author of over 60 successful textbooks. Over two million students have learned mathematics from his textbooks.

Wayne M. Getz received his undergraduate and Ph.D. (1976) degrees in applied mathematics from the University of the Witwatersrand, South Africa. In 1979 he emigrated to the United States to take a faculty position at the University of California, Berkeley, where he is currently the A. Starker Leopold Professor of Wildlife Ecology and Biomathematician in Agricultural Experiments Station. Professor Getz has a D.Sc. from the University of Cape Town, South Africa and has honorary appointments in the Mammal Research Institute at the University of Pretoria and in the School of Mathematical Sciences at the University of KwaZulu-Natal, both in South Africa, and he is a founder and trustee of the South African Centre for Epidemiological Modeling and Analysis. Recognition for his research in biomathematics and its application to various areas of physiology, behavior, ecology, and evolution includes an Alexander von Humboldt US Senior Scientist Research Award in 1992, and election to the American Association for the Advancement of Science (1995), the California Academy of Sciences (2000), and the Royal Society of South Africa (2003). He was appointed as a Chancellor’s Professor at UC Berkeley from 1998 to 2001. Professor Getz has served as a consultant to both government and industry, and his research over the past thirty years has been funded by various government institutions and private foundations. Professor Getz has published a book titled Population Harvestingin the Princeton Monographs in Population Biology series, edited other books and volumes, and is an author or coauthor on more than 250 scientific papers in over fifty different peer-reviewed applied mathematics and biology journals.

Chapter 1: Modeling with Functions
Chapter 2: Limits and Derivatives
Chapter 3: Derivative Rules and Tools
Chapter 4: Applications of Differentiations
Chapter 5: Integration
Chapter 6: Differential Equations
Chapter 7: Probabilistic: Applications of Integration
Chapter 8: Multivariable Extensions