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

✍ Scribed by Glenn Ledder (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 443
• Series: Springer Undergraduate Texts in Mathematics and Technology
• Edition: 1
• Category: Library

✦ Synopsis

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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.

✦ Table of Contents

Front Matter....Pages i-xx
Front Matter....Pages 1-3
A Brief Summary of Calculus....Pages 5-81
Mathematical Modeling....Pages 83-143
Front Matter....Pages 145-147
Probability Distributions....Pages 149-206
Working with Probability....Pages 207-257
Front Matter....Pages 259-260
Dynamics of Single Populations....Pages 261-299
Discrete Dynamical Systems....Pages 301-326
Continuous Dynamical Systems....Pages 327-379
Erratum to: Mathematics for the Life Sciences....Pages E1-E1
Back Matter....Pages 381-431

✦ Subjects

Mathematical and Computational Biology; Life Sciences, general; Dynamical Systems and Ergodic Theory