Dynamical Systems for Biological Modeling

An Introduction
1. Auflage 2015
ISBN: 978-1-4200-6641-8
Verlag: CRC Press

Buch, Englisch, 492 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 862 g

Reihe: Advances in Applied Mathematics

Dynamical Systems for Biological Modeling: An Introduction prepares both biology and mathematics students with the understanding and techniques necessary to undertake basic modeling of biological systems. It achieves this through the development and analysis of dynamical systems.

The approach emphasizes qualitative ideas rather than explicit computations. Some technical details are necessary, but a qualitative approach emphasizing ideas is essential for understanding. The modeling approach helps students focus on essentials rather than extensive mathematical details, which is helpful for students whose primary interests are in sciences other than mathematics need or want.

The book discusses a variety of biological modeling topics, including population biology, epidemiology, immunology, intraspecies competition, harvesting, predator-prey systems, structured populations, and more.

The authors also include examples of problems with solutions and some exercises which follow the examples quite closely. In addition, problems are included which go beyond the examples, both in mathematical analysis and in the development of mathematical models for biological problems, in order to encourage deeper understanding and an eagerness to use mathematics in learning about biology.

Zielgruppe

Undergraduate

Autoren/Hrsg.

Brauer, Fred

Kribs, Christopher

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik

Inhaltsverzeichnis

ELEMENTARY TOPICS. Introduction to Biological Modeling. Difference Equations (Discrete Dynamical Systems). First-Order Differential Equations (Continuous Dynamical Systems). Nonlinear Differential Equations. MORE ADVANCED TOPICS. Systems of Differential Equations. Topics in Modeling Systems of Populations. Systems with Sustained Oscillations and Singularities. APPENDICES. An Introduction to the Use of MapleTM. Taylor’s Theorem and Linearization. Location of Roots of Polynomial Equations. Stability of Equilibrium of Difference Equations. Answers to Selected Exercises. Bibliography.

Über Autor(innen)

Fred Brauer, PhD, University of British Columbia, Vancouver, Canada

Christopher Kribs, PhD, University of Texas at Arlington, USA