Biology is a source of fascination for most scientists, whether their training is in the life sciences or not. In particular, there is a special satisfaction in discovering an understanding of biology in the context of another science like mathematics. Fortunately there are plenty of interesting (and fun) problems in biology, and virtually all scientific disciplines have become the richer for it. For example, two major journals, Mathematical Biosciences and Journal of Mathematical Biology, have tripled in size since their inceptions 20-25 years ago. The various sciences have a great deal to give to one another, but there are still too many fences separating them. In writing this book we have adopted the philosophy that mathematical biology is not merely the intrusion of one science into another, but has a unity of its own, in which both the biology and the math ematics should be equal and complete, and should flow smoothly into and out of one another. We have taught mathematical biology with this philosophy in mind and have seen profound changes in the outlooks of our science and engineering students: The attitude of "Oh no, another pendulum on a spring problem!," or "Yet one more LCD circuit!" completely disappeared in the face of applications of mathematics in biology. There is a timeliness in calculating a protocol for ad ministering a drug.
Content Level » Research
Author(s): Edward K. Yeargers, James V. Herod, Ronald W. Shonkweiler
Edition: Softcover reprint of the original 1st ed. 1996
Publisher: Birkhäuser
Year: 1996
Language: English
Pages: C+X, 417
Tags: Биологические дисциплины;Матметоды и моделирование в биологии;
Cover
An Introduction tothe Mathematics of Biology: with Computer Algebra Models
Copyright
© 1996 Springer Science+Business Media
ISBN 978-1-4757-1097-7
ISBN 978-1-4757-1095-3 (eBook)
DOI 10.1007/978-1-4757-1095-3
Contents
Preface
Chapter 1 Biology; Mathematics; and a Mathematical Biology Laboratory
Section 1.1 The Natural Linkage Between Mathematics and Biology
Section 1.2 The Use of Models in Biology
Section 1.3 What Can Be Derived from a Model and How Is It Analyzed?
References and Suggested Further Reading
Chapter 2 Some Mathematical Tools
Section 2.1 Linear Dependence
Section 2.2 Linear Regression, the Method of Least Squares
Section 2.3 Multiple Regression
Section 2.4 Modeling with Differential Equations
Section 2.5 Matrix Analysis
Section 2.6 Statistical· Data
Section 2.7 Probability
References and Suggested Further Reading
Chapter 3 Reproduction and the Drive for Survival
Section 3.1 The Darwinian Model of Evolution
Section 3.2 Cells
Section 3.3 Replication of Living Systems
Section 3.4 Population Growth and Its Limitations
Section 3.5 The Exponential Model for Growth and Decay
Section 3.6 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 4 Interactions Between Organisms and Their Environment
Section 4.1 How Population Growth Is Controlled
Section 4.2 Community Ecology
Section 4.3 Environmentally Limited Population Growth
Section 4.4 A Brief Look at Multiple Species Systems
Section 4.5 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 5 Age-Dependent Population Structures
Section 5.1 Aging and Death
Section 5.2 The Age-Structure of Populations
Section 5.3 Predicting the Age-Structure of a Population
Section 5.4 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 6 Random Movements in Space and Time
Section 6.1 Biological Membranes
Section 6.2 The Mathematics of Diffusion
Section 6.3 Interplacental Transfer of Oxygen: Biological and Biochemical Considerations
Section 6.4 Oxygen Diffusion Across the Placenta: Physical Considerations
Section 6.5 The Spread of Infectious Diseases
Section 6.6 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 7 The Biological Disposition of Drugs and Inorganic Toxins
Section 7.1 The Biological Importance of Lead
Section 7.2 Early Embryogenesis and Organ Formation
Section 7.3 Gas Exchange
Section 7.4 The Digestive System
Section 7.5 The Skin
Section 7.6 The Circulatory System
Section 7.7 Bones
Section 7.8 The Kidneys
Section 7.9 Clinical Effects of Lead
Section 7.10 A Mathematical Model for Lead in Mammals
Section 7.11 Pharmacokinetics
Section 7.12 Questions for Thought and Discussion
References and Suggested Funher Reading
Chapter 8 Neurophysiology
Section 8.1 Communication Between Parts of an Organism
Section 8.2 The Neuron
Section 8.3 The Action Potential
Section 8.4 Synapses-Interneuronal Connections
Section 8.5 A Model for the Conduction of Action Potentials
Section 8.6 The Fitzhugh-Nagumo Two-Variable Action Potential System
Section 8.7 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 9 The Biochemistry of Cells
Section 9.1 Atoms and Bonds in Biochemistry
Section 9.2 Biopolymers
Section 9.3 Molecular Information Transfer
Section 9.4 Enzymes and Their Function
Section 9.5 Rates of Chemical Reactions
Section 9.6 Enzyme Kinetics
Section 9.7 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 10 A Biomathematical Approach to HIV and AIDS
Section 10.1 Viruses
Section 10.2 The Immune System
Section 10.3 HIV and AIDS
Section 10.4 An HIV Infection Model
Section 10.5 A Model for a Mutating Virus
Section 10.6 Predicting the Onset of AIDS
Section 10.7 Questions for Thought and Discussion
References and Suggested Further Reading
Chapter 11 Genetics
Section 11.1 Asexual Cell Reproduction-Mitosis
Section 11.2 Sexual Reproduction-Meiosis and Fertilization
Section 11.3 Classical Genetics
Section 11.4 A Final Look at Darwinian Evolution
Section 11.5 The Hardy-Weinberg Principle
Section 11.6 The Fixation of a Beneficial Mutation
Section 11.7 Questions for Thought and Discussion
References and Suggested Further Reading
Index
