An Invitation to Mathematical Biology / by David G Costa, Paul J Schulte.

Format:

Book

Author/Creator:

Costa, David G., Author.

Schulte, Paul J., Author.

Language:

English

Subjects (All):

Biology.

Medical sciences.

Bioinformatics.

Biomathematics.

Population genetics.

System theory.

Biological Sciences.

Health Sciences.

Computational and Systems Biology.

Mathematical and Computational Biology.

Population Genetics.

Complex Systems.

Local Subjects:

Biological Sciences.

Health Sciences.

Computational and Systems Biology.

Mathematical and Computational Biology.

Population Genetics.

Complex Systems.

Physical Description:

1 online resource (IX, 124 p. 71 illus., 66 illus. in color.)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

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.

Contents:

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

3.4 Exercises

3.5 References- 4 Fixed Points, Stability, and Cobwebbing

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

9.6 Exercises

9.7 References- 10 Competition Models with Logistic Term

10.1Addition of Logistic Term to Competition Models

10.2 Predator-Prey-Prey Three Species Model

10.3Predator-Prey-Prey Model Solutions

10.4 Summary

10.5Exercises

10.6References- 11 Infectious Disease Models

11.1 Basic Compartment Modeling Approaches

11.2SI Model

11.3SI model with Growth in S

11.4 Applications using Mathematica

11.5 Applications using MATLAB

11.6 Summary

11.7 Exercises

11.8 References- 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

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.

ISBN:

3-031-40258-8