An Invitation to Mathematical Biology

✍ Scribed by David G Costa, Paul J Schulte

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 129
• Edition: 1st ed. 2023
• Category: Library

✦ Synopsis

The textbook is designed to provide a "non-intimidating" entry to the field of mathematical biology. It is also useful for those wishing to teach an introductory course. Although there are many good mathematical biology texts available, most books are too advanced mathematically for most biology majors. Unlike undergraduate math majors, most biology major students possess a limited math background. Given that computational biology is a rapidly expanding field, more students should be encouraged to familiarize themselves with this powerful approach to understand complex biological phenomena. Ultimately, our goal with this undergraduate textbook is to provide an introduction to the interdisciplinary field of mathematical biology in a way that does not overly terrify an undergraduate biology major, thereby fostering a greater appreciation for the role of mathematics in biology

✦ Table of Contents

Preface
Contents
Chapter 1: Introduction
References
Chapter 2: Exponential Growth and Decay
2.1 Exponential Growth
2.2 Exponential Decay
2.3 Summary
2.4 Exercises
References
Chapter 3: Discrete Time Models
3.1 Solutions of the Discrete Logistic
3.2 Enhancements to the Discrete Logistic Function
3.3 Summary
3.4 Exercises
References
Chapter 4: Fixed Points, Stability, and Cobwebbing
4.1 Fixed Points and Cobwebbing
4.2 Linear Stability Analysis
4.3 Summary
4.4 Exercises
Reference
Chapter 5: Population Genetics Models
5.1 Two Phenotypes Case
5.2 Three Phenotypes Case
5.3 Summary
5.4 Exercises
References
Chapter 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
References
Chapter 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
References
Chapter 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
References
Chapter 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
9.6 Exercises
References
Chapter 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
References
Chapter 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
11.7 Exercises
References
Chapter 12: Organism Environment Interactions
12.1 Introduction to Energy Budgets
12.2 Radiation
12.3 Convection
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
Reference
Appendix 1: Brief Review of Differential Equations in Calculus
Geometric Interpretation of the IVP
Appendix 2: Numerical Methods for Solving ODEs
Appendix 3: Mathematica Tutorial
Appendix 4: MATLAB Introductory Tutorial
Appendix 5: Introduction to Python Programming
Index
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