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

1 Biology, Mathematics, and a Mathematical Biology Laboratory.- 1.1 The Natural Linkage Between Mathematics and Biology.- 1.2 The Use of Models in Biology.- 1.3 What Can Be Derived from a Model and How Is It Analyzed?.- References and Suggested Further Reading.- 2 Some Mathematical Tools.- 2.1 Linear Dependence.- 2.2 Linear Regression, the Method of Least Squares.- 2.3 Multiple Regression.- 2.4 Modelig with qint Differential Equations.- 2.5 Matrix Analysis.- 2.6 Statistical Data.- 2.7 Probability.- References and Suggested Further Reading.- 3 Reproduction and the Drive for Survival.- 3.1 The Darwinian Model of Evolution.- 3.2 Cells.- 3.3 Replication of Living Systems.- 3.4 Population Growth and Its Limitations.- 3.5 The Exponential Model for Growth and Decay.- 3.6 Ouestions for Thou2ht and Discussion.- References and Suggested Further Reading.- 4 Interactions Between Organisms and Their Environment.- 4.1 How Population Growth is Controlled.- 4.2 Community Ecology.- 4.3 Environmentally Limited Population Growth.- 4.4 A Brief Look at Multiple Species Systems.- 4.5 Questions for Thought and Discussion.- References and Suggested Further Reading.- 5 Age-Dependent Population Structures.- 5.1 Aging and Death.- 5.2 The Age-Structure of Populations.- 5.3 Predicting the Age-Structure of a Population.- 5.4 Questions for Thought and Discussion.- References and Suggested Further Reading.- 6 Random Movements in Space and Time.- 6.1 BioloQical Membranes.- 6.2 The Mathematics of Diffusion.- 6.3 Interplacenlal Transfer of Oxygen: Biological and Biochemical Considerations.- 6.4 Oxygen Diffusion Across the Placenta: Physical Considerations.- 6.5 The Spread of Infectious Diseases.- 6.6 Questions for Thought and Discussion.- References and Suggested Further Reading.- 7 The Biological Disposition of Drugs and Inorganic Toxins.- 7.1 The Biological Importance of Lead.- 7.2 Early Embryogenesis and Organ Formation.- 7.3 Gas Exchange.- 7.4 The Digestive System.- 7.5 The Skin.- 7.6 The Circulatory System.- 7.7 Bones.- 7.8 The Kidneys.- 7.9 Clinical Effects of Lead.- 7.10 A Mathematical Model for Lead in Mammals.- 7.11 Pharmacokinetics.- 7.12 Questions for Thought and Discussion.- References and Suggested Further Reading.- 8 Neurophysiology.- 8.1 Communication Between Parts of an Organism.- 8.2 The Neuron.- 8.3 The Action Potential.- 8.4 Synapses-Interneuronal Connections.- 8.5 A Model for the Conduction of Action Potentials.- 8.6 The Fitzhugh-Nagumo Two-Variable Action Potential System.- 8.7 Questions for Thought and Discussion.- References and Suggested Further Reading.- 9 The Biochemistry of Cells.- 9.1 Atoms and Bonds in Biochemistry.- 9.2 Biopolymers.- 9.3 Molecular Information Transfer.- 9.4 Enzymes and Their Function.- 9.5 Rates of Chemical Reactions.- 9.6 Enzyme Kinetics.- 9.7 Questions for Thought and Discussion.- References and Suggested Further Reading.- 10 A Biomathematical Approach to HIV and AIDS.- 10.1 Viruses.- 10.2 The Immune System.- 10.3 HIV and AIDS.- 10.4 An HIV Infection Model.- 10.5 A Model for a Mutating Virus.- 10.6 Predicting the Onset of AIDS.- 10.7 Questions for Thought and Discussion.- References and Suggested Further Reading.- 11 Genetics.- 11.1 Asexual Cell Reproduction-Mitosis.- 11.2 Sexual Reproduction-Meiosis and Fertilization.- 11.3 Classical Genetics.- 11.4 A Final Look at Darwinian Evolution.- 11.5 The Hardy-Weinberg Principle.- 11.6 The Fixation of a Beneficial Mutation.- 11.7 Questions for Thought and Discussion.- References and Suggested Further Reading.