An invitation to mathematical biology

lt;b>David G Costa is a mathematician interested in Partial Differential Equations (PDEs), Ordinary Differential Equations (ODEs) and the Calculus of Variations. In particular, he is interested in the use of so-called variational and topological techniques to study qualitatively and visualization of phenomena in PDEs and ODEs. Such phenomena are present in various areas of sciences, including physics, biology, and chemistry, among others. He teaches a variety of courses at the undergraduate level (including Calculus, Linear Algebra, ODEs, PDEs, and Introductory Real Analysis), and graduate level (including PDEs, and Real Analysis), as well as a course in Biomathematics jointly offered by the Department of Mathematical Sciences and School of Life Sciences.
Paul J Schulte is a plant physiologist interested in biophysical approaches to studying internal processes in plants. These commonly involve applications of mathematical approaches as realized through computational solutions. Plants are dependent on water for survival and their ability to acquire water from the soil and transport it throughout the plant is determined in part by the hydraulic properties of the plant's tissues. Most of his work considers transport processes such as water flow in the xylem tissues or sugar flow in the phloem tissues. He teaches a variety of courses such as Plant Physiology, Plant Anatomy, Introduction to Biological Modeling, and Biomathematics jointly offered in the School of Life Sciences and Department of Mathematical Sciences.

lt;p>Preface

1 Introduction

2 Exponential Growth and Decay

2.1 Exponential Growth

2.2 Exponential Decay

2.3 Summary

2.4 Exercises

2.5 References

3 Discrete Time Models

3.1 Solutions of the discrete logistic

3.2 Enhancements to the Discrete Logistic Function

3.3 Summary

3.5 References

4.1 Fixed Points and Cobwebbing

4.2 Linear Stability Analysis

4.3 Summary

4.4 Exercises

4.5 References

5 Population Genetics Models

5.1 Two Phenotypes Case

5.2 Three Phenotypes Case

5.3 Summary

5.4 Exercises

5.5 References

6 Chaotic Systems

6.1 Robert May's Model

6.2 Solving the Model

6.3 Model Fixed Points

6.4 Summary

6.5 Exercises

6.6 References

7 Continuous Time Models

7.1 The Continuous Logistic Equation

7.2 Equilibrium States and their Stability

7.3 Continuous Logistic Equation with Harvesting

7.4 Summary

7.5 Exercises

7.6 References

8 Organism-Organism Interaction Models

8.1 Interaction Models Introduction

8.2 Competition

8.3 Predator-Prey

8.4 Mutualism

8.5 Summary

8.6 Exercises

8.7 References

 9 Host-Parasitoid Models

9.1 Beddington Model

9.2 Some Solutions of the Beddington Model

9.3 MATLAB Solution for the Host-Parasitoid Model

9.4 Python Solution for the Host-Parasitoid Model

9.5 Summary

9.7 References

 10 Competition Models with Logistic Term

10.1 Addition of Logistic Term to Competition Models

10.2 Predator-Prey-Prey Three Species Model

10.3 Predator-Prey-Prey Model Solutions

10.4 Summary.

10.5 Exercises

10.6 References

 11 Infectious Disease Models

11.1 Basic Compartment Modeling Approaches

11.2 SI Model

11.3 SI model with Growth in S

11.4 Applications using Mathematica

11.5 Applications using MATLAB

11.6 Summary.

11.8 References

12 Organism Environment Interactions

12.1 Introduction to Energy Budgets

12.2 Radiation

12.4 Transpiration

12.5 Total Energy Budget

12.6 Solving the Budget: Newton's Method for Root Finding

12.7 Experimenting with the Leaf Energy Budget

12.8 Summary

12.9 Exercises

12.10 References

13 Appendix 1: Brief Review of Differential Equations in Calculus

14 Appendix 2: Numerical Solutions of ODEs

15 Appendix 3: Tutorial on Mathematica

16 Appendix 4: Tutorial on MATLAB

17 Appendix 5: Tutorial on Python Programming

Index