Essential Mathematical Biology / Edition 1

Essential Mathematical Biology / Edition 1

by Nicholas Britton, N. F. Britton
     
 

ISBN-10: 185233536X

ISBN-13: 9781852335366

Pub. Date: 04/08/2003

Publisher: Springer London

Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for

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Overview

Essential Mathematical Biology is a self-contained introduction to the fast-growing field of mathematical biology. Written for students with a mathematical background, it sets the subject in its historical context and then guides the reader towards questions of current research interest, providing a comprehensive overview of the field and a solid foundation for interdisciplinary research in the biological sciences. A broad range of topics is covered including: Population dynamics, Infectious diseases, Population genetics and evolution, Dispersal, Molecular and cellular biology, Pattern formation, and Cancer modelling. This book will appeal to 3rd and 4th year undergraduate students studying mathematical biology. A background in calculus and differential equations is assumed, although the main results required are collected in the appendices. A dedicated website at www.springer.co.uk/britton/ accompanies the book and provides further exercises, more detailed solutions to exercises in the book, and links to other useful sites.

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Product Details

ISBN-13:
9781852335366
Publisher:
Springer London
Publication date:
04/08/2003
Series:
Springer Undergraduate Mathematics Series
Edition description:
1st ed. 2003. Corr. 2nd printing
Pages:
335
Sales rank:
776,501
Product dimensions:
0.73(w) x 7.00(h) x 10.00(d)

Table of Contents

1. Single Species Population Dynamics.- 2. Population Dynamics of Interacting Species.- 3. Infectious Diseases.- 4. Population Genetics and Evolution.- 5. Biological Motion.- 6. Molecular and Cellular Biology.- 7. Pattern Formation.- 8. Tumour Modelling.- Further Reading.- A. Some Techniques for Difference Equations.- A.1 First-order Equations.- A.1.1 Graphical Analysis.- A.1.2 Linearisation.- A.2 Bifurcations and Chaos for First-order Equations.- A.2.1 Saddle-node Bifurcations.- A.2.2 Transcritical Bifurcations.- A.2.3 Pitchfork Bifurcations.- A.2.4 Period-doubling or Flip Bifurcations.- A.3 Systems of Linear Equations: Jury Conditions.- A.4 Systems of Nonlinear Difference Equations.- A.4.1 Linearisation of Systems.- A.4.2 Bifurcation for Systems.- B. Some Techniques for Ordinary Differential Equations.- B.1 First-order Ordinary Differential Equations.- B.1.1 Geometric Analysis.- B.1.2 Integration.- B.1.3 Linearisation.- B.2 Second-order Ordinary Differential Equations.- B.2.1 Geometric Analysis (Phase Plane).- B.2.2 Linearisation.- B.2.3 Poincaré-Bendixson Theory.- B.3 Some Results and Techniques for rath Order Systems.- B.3.1 Linearisation.- B.3.2 Lyapunov Functions.- B.3.3 Some Miscellaneous Facts.- B.4 Bifurcation Theory for Ordinary Differential Equations.- B.4.1 Bifurcations with Eigenvalue Zero.- B.4.2 Hopf Bifurcations.- C. Some Techniques for Partial Differential Equations.- C.1 First-order Partial Differential Equations and Characteristics.- C.2 Some Results and Techniques for the Diffusion Equation.- C.2.1 The Fundamental Solution.- C.2.2 Connection with Probabilities.- C.2.3 Other Coordinate Systems.- C.3 Some Spectral Theory for Laplace’s Equation.- C.4 Separation of Variables in Partial Differential Equations.- C.5 Systems of Diffusion Equations with Linear Kinetics.- C.6 Separating the Spatial Variables from Each Other.- D. Non-negative Matrices.- D.1 Perron-Frobenius Theory.- E. Hints for Exercises.

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