A Primer on Mathematical Models in Biology

About this book

A Primer on Mathematical Models in Biology grew out of a course that the highly respected applied mathematician Lee Segel taught at the Weizmann Institute. A Primer on Mathematical Models in Biology represents the unique perspective on mathematical biology of Segel and his co-author Leah Edelstein-Keshet (author of the popular SIAM book, Mathematical Models in Biology). It introduces differential equations, biological applications, and simulations, with emphasis on molecular events (biochemistry and enzyme kinetics), excitable systems (neural signals), and small protein and genetic circuits. The exposition combines clear and useful mathematical methods with plenty of applications to illustrate the power of such tools, along with many exercises in reasoning, modelling, and simulation. The reader will also find suggestions for further study and appendices containing useful background material. These features make A Primer on Mathematical Models in Biology ideal for students at the advanced undergraduate or graduate level in both biology and mathematics who wish to experience the application of mathematical techniques to the biological sciences.

Contents

List of figures
List of tables
Acknowledgments
Preface
1. Introduction
2. Introduction to biochemical kinetics
3. Review of linear differential equations
4. Introduction to nondimensionalization and scaling
5. Qualitative behavior of simple differential equation models
6. Developing a model from the ground up: case study of the spread of an infection
7. Phase plane analysis
8. Quasi steady state and enzyme-mediated biochemical kinetics
9. Multiple subunit enzymes and proteins: cooperativity
10. Dynamic behavior of neuronal membranes
11: Excitable systems and the FitzHugh–Nagumo equations
12. Biochemical modules
13. Discrete networks of genes and cells
14. For further study
15: Extended exercises and projects
Appendix A. The Taylor approximation and Taylor series
Appendix B. Complex numbers
Appendix C. A review of basic theory of electricity
Appendix D. Proofs of Boolean algebra rules
Appendix E. XPP files for models in this book
Bibliography
Index

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