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E-raamat: Mathematical Biology

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The fast growing field of mathematical biology addresses biological questions using mathematical models from areas such as dynamical systems, probability, statistics, and discrete mathematics.

This book considers models that are described by systems of partial differential equations, and it focuses on modeling, rather than on numerical methods and simulations. The models studied are concerned with population dynamics, cancer, risk of plaque growth associated with high cholesterol, and wound healing. A rich variety of open problems demonstrates the exciting challenges and opportunities for research at the interface of mathematics and biology. This book primarily addresses students and researchers in mathematics who do not necessarily have any background in biology and who may have had little exposure to PDEs.
Preface vii
Chapter 1 Introductory biology
1(6)
Chapter 2 Introduction to modeling
7(8)
Chapter 3 Models of population dynamics
15(10)
3.1 Chemostat
15(3)
3.2 Infectious diseases
18(3)
3.3 A cancer model
21(4)
Chapter 4 Cancer and the immune system
25(8)
Chapter 5 Parameters estimation
33(8)
Chapter 6 Mathematical analysis inspired by cancer models
41(10)
Chapter 7 Mathematical model of atherosclerosis: Risk of high cholesterol
51(12)
Chapter 8 Mathematical analysis inspired by the atherosclerosis model
63(8)
Chapter 9 Mathematical models of chronic wounds
71(8)
Chapter 10 Mathematical analysis inspired by the chronic wound model
79(6)
Appendix: Introduction to PDEs
85(10)
A.1 Elliptic equations
85(3)
A.2 Parabolic equations
88(1)
A.3 Nonlinear equations and systems
89(2)
A.4 Free boundary problems
91(4)
Bibliography 95(4)
Index 99
Avner Friedman, Ohio State University, Columbus, OH.