An Introduction to the Mathematics of Biology: with Computer Algebra Models

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