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.