Jones / Plank / Sleeman Differential Equations and Mathematical Biology, Second Edition

2. Auflage 2011
ISBN: 978-1-4200-8358-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 462 Seiten

Reihe: Chapman & Hall/CRC Mathematical & Computational Biology

Deepen students’ understanding of biological phenomena
Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material.

New to the Second Edition

- A section on spiral waves

- Recent developments in tumor biology

- More on the numerical solution of differential equations and numerical bifurcation analysis

- MATLAB® files available for download online

- Many additional examples and exercises

This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator–prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.

Zielgruppe

Undergraduate students in mathematics, biology, and the physical sciences; graduate students and researchers in mathematical biology.

Autoren/Hrsg.

Jones, D.S.

Plank, Michael

Sleeman, B.D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction

Population growth

Administration of drugs

Cell division

Differential equations with separable variables

Equations of homogeneous type

Linear differential equations of the first order

Numerical solution of first-order equations

Symbolic computation in MATLAB

Linear Ordinary Differential Equations with Constant Coefficients
Introduction

First-order linear differential equations

Linear equations of the second order

Finding the complementary function

Determining a particular integral

Forced oscillations

Differential equations of order n

Uniqueness

Systems of Linear Ordinary Differential Equations

First-order systems of equations with constant coefficients

Replacement of one differential equation by a system

The general system

The fundamental system

Matrix notation

Initial and boundary value problems

Solving the inhomogeneous differential equation

Numerical solution of linear boundary value problems

Modelling Biological Phenomena

Introduction

Heartbeat

Nerve impulse transmission

Chemical reactions
Predator–prey models

First-Order Systems of Ordinary Differential Equations

Existence and uniqueness

Epidemics

The phase plane and the Jacobian matrix

Local stability

Stability

Limit cycles

Forced oscillations

Numerical solution of systems of equations

Symbolic computation on first-order systems of equations and higher-order equations

Numerical solution of nonlinear boundary value problems

Appendix: existence theory

Mathematics of Heart Physiology

The local model

The threshold effect

The

Über Autor(innen)

D.S. Jones, FRS, FRSE is Professor Emeritus in the Department of Mathematics at the University of Dundee in Scotland.
M.J. Plank is a senior lecturer in the Department of Mathematics and Statistics at the University of Canterbury in Christchurch, New Zealand.
B.D. Sleeman, FRSE is Professor Emeritus in the Department of Applied Mathematics at the University of Leeds in the UK.