Mathematics for the Life Sciences: Calculus, Modeling, Probability, and Dynamical Systems

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Springer Science & Business Media, Aug 29, 2013 - Mathematics - 431 pages
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Mathematics for the Life Sciences provides present and future biologists with the mathematical concepts and tools needed to understand and use mathematical models and read advanced mathematical biology books. It presents mathematics in biological contexts, focusing on the central mathematical ideas, and providing detailed explanations. The author assumes no mathematics background beyond algebra and precalculus. Calculus is presented as a one-chapter primer that is suitable for readers who have not studied the subject before, as well as readers who have taken a calculus course and need a review. This primer is followed by a novel chapter on mathematical modeling that begins with discussions of biological data and the basic principles of modeling. The remainder of the chapter introduces the reader to topics in mechanistic modeling (deriving models from biological assumptions) and empirical modeling (using data to parameterize and select models). The modeling chapter contains a thorough treatment of key ideas and techniques that are often neglected in mathematics books. It also provides the reader with a sophisticated viewpoint and the essential background needed to make full use of the remainder of the book, which includes two chapters on probability and its applications to inferential statistics and three chapters on discrete and continuous dynamical systems.

The biological content of the book is self-contained and includes many basic biology topics such as the genetic code, Mendelian genetics, population dynamics, predator-prey relationships, epidemiology, and immunology. The large number of problem sets include some drill problems along with a large number of case studies. The latter are divided into step-by-step problems and sorted into the appropriate section, allowing readers to gradually develop complete investigations from understanding the biological assumptions to a complete analysis.

 

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Contents

Part II Probability
145
Part III Dynamical Systems
259
Appendix A Additional Topics in Discrete Dynamical Systems
381
Appendix B The Definite Integral via Riemann Sums
407
Appendix C A RungeKutta Method for Numerical Solution of DifferentialEquations
409
Hints and Answers to Selected Problems
411
Index
428
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About the author (2013)

Glenn Ledder is an Associate Professor of Mathematics at the University of Nebraska.

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