Author | Yeargers, Edward K. author |
---|---|
Title | An Introduction to the Mathematics of Biology: with Computer Algebra Models [electronic resource] / by Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1996 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-1095-3 |
Descript | X, 417 p. 40 illus. online resource |
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 SynapsesโInterneuronal 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 ReproductionโMitosis -- 11.2 Sexual ReproductionโMeiosis 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