1st Edition
Mathematical Modeling the Life Sciences Numerical Recipes in Python and MATLAB®
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1. Introduction
1.1 What is a Model?
1.2 Projectile Motion
1.3 Problems
2. Mathematical Background
2.1 Mathematical Preliminaries
2.2 Linearization
2.3 Qualitative Analysis
2.4 Problems
2.5 Appendix: Planar Example
3. Introduction to the Numerical Methods
3.1 Introduction
3.2 Best Practices in Coding
3.3 Getting the Programs Running
3.4 Initial Programs
3.5 Problems
4. Ecology
4.1 Historical Background
4.2 Single Species Models
4.3 Competitive Exclusion
4.4 State of the Art and Caveats
4.5 Problems
5. Within-host Disease Models
5.1 Historical Background
5.2 Pathological: Tumor
5.3 Viral: Acute Infection
5.4 Chronic: Tuberculosis
5.5 Problems
5.6 Appendix
6. Between-Host Disease Models
6.1 Historical Background
6.2 Two Compartment Models
6.3 Classical SIR
6.4 Waning Antigens
6.5 Caveats and State of the Art
6.6 Problems
7. Microbiology
7.1 Historical Background
7.2 Bacterial Growth: Chemostat
7.3 Multiple State Model: Free/Attached
7.4 Cooperators, Cheaters, and Competitions
7.5 Problems
8. Circulation and Cardiac Physiology
8.1 Historical Background
8.2 Blood Circulation Models
8.3 Cardiac Physiology
8.4 Problems
9. Neuroscience
9.1 Historical Background
9.2 Action Potential
9.3 Fitzhugh-Nagumo
9.4 Problems
10. Genetics
10.1 Historical Background
10.2 Heredity
10.3 Problems
Biography
Nicholas G. Cogan is Professor of Mathematics at Florida State University. He began studying mathematical biology in undergraduate school and received his Ph.D. from the University of Utah under James P. Keener. He routinely works with microbiologists, environmental engineers, clinicians, and other scientists outside of mathematics. He has taught for twenty years at the undergraduate level and his research focuses on mathematical modeling in the life sciences. He is the author of over fifty articles using mathematics with biology.
