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

ISBN-13: 9781475710977 / Angielski / Miękka / 2012 / 417 str.

Edward K. Yeargers; James V. Herod; Ronald W. Shonkweiler

Opis

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."

Recenzje

"A very well balanced combination of biology and mathematics. Mathematics students have an opportunity to learn enough biology to make good models, and biology students will see it as an opportunity to understand the dynamics of a biological system. It can serve as the source of many good models with possible applications in different areas of biological research."   -Gen. Physiol. Biophysics

"The title is a good description of this introductory textbook, which integrates quite nicely biology and mathematics... Each chapter ends with questions for discussion and references pointing to further reading... Intended for biology students with one year of calculus who want an introduction to mathematical modeling and for mathematics students with little knowledge of biology who want to become familiar with biological applications. The book succeeds at both intents. It is an excellent appetizer."   -Zentralblatt MATH

Spis treści

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.