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Introduction to Mathematical Biology

S. I. Rubinow
Dover Publications
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Soheila Emamyari
, on

Biology is the science studying the structure, function, growth, evolution, distribution, and taxonomy of life and living organisms, from atoms to cells, from genes to proteins, and from populations to ecosystems. Considering the wide range of subjects and concepts related to it, there are many branches of biology, including the subject of this book, Mathematical Biology (or Biomathematics). In brief, it is the mathematical modeling and quantitative study of biological processes. Depending on what is aimed at and what is modeled, the techniques and methods used come from calculus, differential equations, probability theory, linear algebra, and graph theory. Moreover, some modern tools from dynamical systems, control theory, and neural networks have also been deployed in recent studies.

As its title indicates, the book under review is an introduction to some of the applications of some mathematical ideas to biology. It consists of five chapters. Each chapter ends with a number of serious exercises and problems, some of which explain a biological phenomenon; complete solutions of all exercises are included at the end of book. The first three chapters, entitled “Cell Growth,” “Enzyme Kinetics,” and “Tracers in Physiological Systems” discuss biological subjects. The final two chapters, entitled “Biological Fluid Dynamics” and “Diffusion in Biology,” deal with biophysical topics.

Although it is designed as a textbook for graduate students, biologists will also find the mathematics in this book useful in their work. Despite being an older book, it is still relevant enough to be recommended as a textbook for students, instructors and university libraries.

​Soheila Emamyari received her Ph.D. in Soft Condensed Matter fromthe Institute for Advanced Study in Basic Sciences in Iran. Her research interests include Soft Condensed Matter and Biophysics. She is now an instructor at the University of Zanjan, Iran, where she teaches fundamental physics. 


Chapter 1 Cell Growth
1.1 Exponential Growth or Decay
1.2 Determination of Growth or Decay Rates
1.3 The Method of Least Squares
1.4 Nutrient Uptake by a Cell
1.5 Inhomogeneous Differential Equations
1.6 Growth of a Microbial Colony
1.7 Growth in a Chemostat
1.8 Interacting Populations: Predator-Prey System
1.9 Mutation and Reversion in Bacterial Growth
Chapter 2 Enzyme Kinetics
2.1 The Michaelis-Menten Theory
2.2* Early Time Behavior of Enzymatic Reactions
2.3 Enzyme-Substrate-Inhibitor System
2.4 Cooperative Properties of Enzymes
2.5 The Cooperative Dimer
2.6 Allosteric Enzyme
2.7 Other Allosteric Theories
2.8 Hemoglobin
2.9 Graph Theory and Steady-State Enzyme Kinetics
2.10 Enzyme-Substrate-Modifier System
2.11 Enzyme-Substrate-Activator System
2.12 Aspartate Transcarbamylase
Chapter 3 Tracers in Physiological Systems
3.1 Compartment Systems
3.2 The One-Compartment System
3.3 Indicator-Dilution Theory
3.4 Continuous Infusion
3.5 The Two-Compartment System
3.6 Leaky Compartments and Closed Systems
3.7 The Method of Exponential Peeling
3.8 Creatinine Clearance: A Two-Compartment System
3.9 "The "Soaking Out" Experiment"
3.10 The Three-Compartment Catenary System
3.11* The n-Compartment System
Chapter 4 Biological Fluid Dynamics
4.1 The Equations of Motion of a Viscous Fluid
4.2 Poiseuille's Law
4.3 Properties of Blood
4.4 The Steady Flow of Blood through a Vessel
4.5 The Pulse Wave
4.6 The Swimming of Microorganisms
Chapter 5 Diffusion in Biology
5.1 Fick's Laws of Diffusion
5.2 The Fick Principle
5.3 The Unit One-Dimensional Source Solution
5.4 The Diffusion Constant
5.5 Olfactory Communication in Animals
5.6 Membrane Transport
5.7 Diffusion Through a Slab
5.8 Convective Transport: Ionic Flow in an Axon
5.9 The Gaussian Function
5.10 Ultracentrifugation
5.11 The Sedimentation Velocity Method
5.12* An Approximate Solution to the Lamm Equation
5.13 Sedimentation Equilibrium
5.14 Transcapillary Exchange
Solutions to Problems
Appendix A: Brief Review
"Appendix B: Determinants, Vectors, and Matrices"
Subject Index