The major aim of this book is to present instances of interaction between two major disciplines, biology and
mathematics. The goal has been that of addressing a fairly wide audience. Biology students will find this text
useful as a summary of modern mathematical methods currently used in modelling, and furthermore, applied mathematics
students may benefit from examples of applications of mathematics to real-life problems. As little background as
possible has been assumed throughout the book: prerequisites are basic calculus so that undergraduate students,
as well as beginning graduate students, will find most of the material accessible.
Concepts basic in modelling are introduced in the early chapters and reappear throughout later material.
An emphasis is placed on mathematics as a means of unifying related concepts.
Mathematics is used as a means of obtaining an appreciation of problems that would be hard to understand through
verbal reasoning alone. Mathematics is used as a tool rather than as a formalism.
In analyzing models, the emphasis is on qualitative methods and graphical or geometric arguments, not on lengthy
calculations.
The models treated are deterministic and have deliberately been kept simple. In most cases, insight can be
acquired by mathematical analysis alone, without the need for extensive numerical simulation.
Biological applications discussed range from the subcellular molecular systems and cellular behavior to physiological
problems, population biology, and developmental biology. Previous biological familiarity is not assumed.
Problems follow each chapter and have different degrees of difficulty. Some are geared towards helping the
student practice mathematical techniques. Others guide the student through a modelling topic in which the formulation
and analysis of equations are carried out. Certain problems, based on models which have been published elsewhere,
are meant to promote an appreciation of the literature and encourage the use of library resources.
Table of Contents
PART 1: Discrete Process in Biology
Chapter 1: The Theory of Linear Difference Equations Applied to Population Growth
Chapter 2: Nonlinear Difference Equations
Chapter 3: Applications of Nonlinear Difference Equations to Population Biology
PART 2: Continuous Processes and Ordinary Differential Equations
Chapter 4: An Introduction to Continuous Models
Chapter 5: Phase-Plane Methods and Qualitative Solutions
Chapter 6: Applications of Continuous Models to Population Dynamics
Chapter 7: Models for Molecular Events
Chapter 8: Limit Cycles, Oscillations, and Excitable Systems
PART 3: Spatially Distributed Systems and Partial Differential Equation Models
Chapter 9: An Introduction to Partial Differential Equations and Diffusion in Biological Settings
Chapter 10: Partial Differential Equation Models in Biology
Chapter 11: Models for Development and Pattern Formation in Biological Systems
