Differential equations and mathematical biology.
2nd ed.

*(English)*Zbl 1298.92003
Chapman & Hall/CRC Mathematical and Computational Biology Series. Boca Raton, FL: CRC Press (ISBN 978-1-4200-8357-6/hbk). xvii, 444 p. (2010).

Publisher’s description: Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, this book 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:

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 PoincarĂ© 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.

For reviews of the first edition see [Zbl 0504.92002; Zbl 1020.92001]

New to the Second Edition:

- {\(\bullet\)}
- A section on spiral waves.
- {\(\bullet\)}
- Recent developments in tumor biology.
- {\(\bullet\)}
- More on the numerical solution of differential equations and numerical bifurcation analysis.
- {\(\bullet\)}
- MATLAB files available for download online.
- {\(\bullet\)}
- 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 PoincarĂ© 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.

For reviews of the first edition see [Zbl 0504.92002; Zbl 1020.92001]

##### MSC:

92-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to biology |

34-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations |

35-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to partial differential equations |

92C40 | Biochemistry, molecular biology |

92C20 | Neural biology |

92D25 | Population dynamics (general) |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |