Mathematics for the Life Sciences

Calculus, Modeling, Probability, and Dynamical Systems

  • Glenn Ledder

Table of contents

  1. Front Matter
    Pages i-xx
  2. Calculus and Modeling

    1. Front Matter
      Pages 1-3
    2. Glenn Ledder
      Pages 5-81
    3. Glenn Ledder
      Pages 83-143
  3. Probability

    1. Front Matter
      Pages 145-147
    2. Glenn Ledder
      Pages 149-206
    3. Glenn Ledder
      Pages 207-257
  4. Dynamical Systems

    1. Front Matter
      Pages 259-260
    2. Glenn Ledder
      Pages 261-299
    3. Glenn Ledder
      Pages 301-326
    4. Glenn Ledder
      Pages 327-379
  5. Back Matter
    Pages 381-431

About this book

Introduction

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.

Keywords

calculus dynamical systems mathematical biology textbook mathematical modeling

Authors and affiliations

  • Glenn Ledder
    • 1
  1. 1.Department of MathematicsUniversity of Nebraska-LincolnLincolnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7276-6
  • Copyright Information Springer Science+Business Media, LLC 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7275-9
  • Online ISBN 978-1-4614-7276-6
  • Series Print ISSN 1867-5506
  • Series Online ISSN 1867-5514
  • About this book
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