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

1. Front Matter

   Pages i-x

   PDF

2. Biology, Mathematics, and a Mathematical Biology Laboratory

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 1-8

3. Some Mathematical Tools

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 9-76

4. Reproduction and the Drive for Survival

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 77-97

5. Interactions Between Organisms and Their Environment

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 98-131

6. Age-Dependent Population Structures

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 132-153

7. Random Movements in Space and Time

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 154-193

8. The Biological Disposition of Drugs and Inorganic Toxins

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 194-233

9. Neurophysiology

   • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

   Pages 234-263

10. The Biochemistry of Cells

    • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

    Pages 264-318

11. A Biomathematical Approach to HIV and AIDS

    • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

    Pages 319-368

12. Genetics

    • Edward K. Yeargers, Ronald W. Shonkwiler, James V. Herod

    Pages 369-409

13. Back Matter

    Pages 411-417

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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.

• algebra
• calculus
• chemistry
• computer algebra
• differential equation
• equation
• function
• genetics
• kinetics
• linear regression
• Mathematica
• mathematical biology
• mathematics
• philosophy
• variable

"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

• School of Biology, Georgia Institute of Technology, Atlanta, USA

  Edward K. Yeargers

• School of Mathematics, Georgia Institute of Technology, Atlanta, USA

  Ronald W. Shonkwiler, James V. Herod

Policies and ethics