医学和生命科学中的数学问题（影印版）

　　 Mathematical Biology is the study of medicine and the life sciences that uses mathematical models to help predict and interpret what we observe. This book describes several major contributions that have been made to population biology and to physiology by such theoretical work.
　　 We have tried to keep the presentation brief to keep the price of the book as reasonable as possible, and to ensure that the topics are presented at a level that is accessible to a wide audience. Each topic could serve as a launching point for more advanced study, and suitable references are suggested to help with this. If the underlying mathematics is understood for these basic examples. then mathematical aspects of more advanced life science preblems will
　　be within reach.
　　

series preface
preface
introduction
1 the mathematics of populations: demographics
1.1. geometric population growth
1.1.1. growth of bacterial cultures
1.1.2. least-squares estimation of the growth rate
1.1.3. growth of human populations
1.1.4. infinitesimal sampling intervals and doubling times
1.2. geometric growth in a population stratified by age
1.2.1. fibonacei's rabbit population
1.2.2. euler's renewal equations
1.2.3. age structure in human populations
1.3. the limits of growth
1.3.1. verhulst's model
1.3.2. predator satiation
1.3.3. chaos
1.3.4. infinitesimal sampling intervals in
a limiting environment
1.4. age structure of populations near

　　Preface
　　 Mathematical Biology is the study of medicine and the life sciences that uses mathematical models to help predict and interpret what we observe. This book describes several major contributions that have been made to population biology and to physiology by such theoretical work.
　　 We have tried to keep the presentation brief to keep the price of the book as reasonable as possible, and to ensure that the topics are presented at a level that is accessible to a wide audience. Each topic could serve as a launching point for more advanced study, and suitable references are suggested to help with this. If the underlying mathematics is understood for these basic examples. then mathematical aspects of more advanced life science preblems will
　　be within reach.
　　 The techniques presented here range in mathematical difficulty up to calculus and matrix theory. The material is presented in general order of increasing mathematical difficulty. Some exercises deal with material in preceding sections, others are projects that extend preceding material.
　　 Our purpose in this book is not the systematic presentation of mathematical material, although there are important threads that run through several chapters. Instead, we hope to illustrate how mathematics can be used. In particular, our goal is to make available to students, having at least one term of calculus, topics in the life sciences and medicine that have benefited from
　　mathematical modeling and analysis. In addition to exposing students to current ideas, the material is intended to reinforce their mathematics education by presenting familiar mathematical topics from novel points of view. Finally,enabling students to think in terms of models early in their academic experience should motivate them to develop and apply modeling skills further.
　　 While hoping this interdisciplinary book will be useful to a wide variety of individuals, we believe that it can have special significance for the premedical student, who will find a mathematical introduction to a host of phenomena that axe central to the practice of medicine. These include genetics and epidemics as well as the functions of the heart, lungs, and kidneys. It is our hope that the mathematical study of these topics will give the student a depth of
　　understanding and insight that could not have been achieved through traditional, descriptive education in the medical sciences.
　　 The mix of topics, taken largely from population biology and from physiology, includes important phenomena that are within reach of the students described above. The population part of the book draws its material from the areas of demographics, genetics, epidemics, and biogeography, while the physiological part surveys cardiovascular, pulmonary, renal, and muscle physiology. The final chapter is intended to introduce students to models of nerve cells and some neural circuits as a basis for studying how the brain works. We are on the rise of a wave of understanding of brain function, and mathematical modeling can be useful in understanding this complex organ.
　　 We thank Anneli Lax for her early interest in the course that led to this book and for helpful discussion during the preparation of the lecture notes on which this book is based. Besides the authors, the course has been taught by Stephen Childress, H. Michael Lacker, and Daniel Tranchina, and we are indebted to them for their comments and advice.
　　 Frank C. Hoppensteadt
　　 Charles S. Pesk/n
　　 November, 1990