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A Course in Mathematical Biology Quantitative Modeling with Mathematical and Computational Methods 1st Edition by Gerda de Vries, Thomas Hillen, Mark Lewis, Birgitt Schonfisch, Johannes Muller ISBN 0898716128 9780898716122

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A course in mathematical biology Quantitative modeling with mathematical and computational methods G. De Vries Digital Instant Download

Author(s): G. de Vries, T. Hillen, M. Lewis, J. Müller, B. Schönfisch
ISBN(s): 9780898716122, 0898716128
Edition: SIAM
File Details: PDF, 7.87 MB
Year: 2006
Language: english
SKU: EB-11739790 Category: Tags: , , , ,

A Course in Mathematical Biology: Quantitative Modeling with Mathematical and Computational Methods 1st Edition by Gerda de Vries, Thomas Hillen, Mark Lewis, Birgitt Schonfisch, Johannes Muller – Ebook PDF Instant Download/Delivery: 0898716128, 9780898716122
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Product details:

ISBN 10: 0898716128 
ISBN 13: 9780898716122
Author: Gerda de Vries, Thomas Hillen, Mark Lewis, Birgitt Schonfisch, Johannes Muller

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB®.

A Course in Mathematical Biology Quantitative Modeling with Mathematical and Computational Methods 1st Table of contents:

Chapter 1: Introduction to Mathematical Models in Biology
4. What Is a Mathematical Model?
5. The Role of Assumptions in Biological Modeling
6. Types of Biological Models: Continuous vs. Discrete
7. The Importance of Validation and Calibration in Models

Chapter 2: Basic Concepts in Mathematical Biology
8. Key Mathematical Tools: Calculus, Linear Algebra, and Differential Equations
9. Overview of Dynamical Systems
10. Stability and Bifurcation Theory
11. Time-Series Analysis in Biological Systems

Chapter 3: Population Dynamics
12. Modeling Population Growth: Exponential and Logistic Models
13. Predator-Prey Models: Lotka-Volterra Equations
14. Competition Models and Coexistence
15. Stochastic Models of Population Dynamics

Chapter 4: Epidemiology and Disease Modeling
16. Basic Epidemiological Models: SIR, SEIR, and Beyond
17. R0 and the Threshold Phenomenon in Epidemics
18. Modeling Vaccination Strategies and Disease Control
19. Computational Approaches to Epidemic Modeling

Chapter 5: Ecological Modeling
20. Ecosystem Dynamics and Species Interactions
21. Food Webs and Trophic Cascades
22. Spatial Models of Ecological Systems
23. The Role of Climate Change in Ecological Models

Chapter 6: Evolutionary Biology and Genetics
24. Modeling Evolution: Population Genetics Models
25. The Hardy-Weinberg Equilibrium and Its Application
26. Modeling Genetic Drift, Mutation, and Selection
27. Evolutionary Game Theory and its Applications

Chapter 7: Biochemical and Biophysical Systems
28. The Michaelis-Menten Kinetics and Enzyme Reactions
29. Feedback Loops in Biological Systems: Positive and Negative Feedback
30. Modeling Cellular Processes: Reaction-Diffusion Systems
31. Simulation of Metabolic Pathways

Chapter 8: Neural Networks and Computational Neuroscience
32. Introduction to Neural Modeling
33. Spiking Neuron Models and Synaptic Plasticity
34. Computational Techniques for Modeling Neural Networks
35. Applications of Neural Networks in Biological Systems

Chapter 9: Systems Biology and Networks
36. Introduction to Systems Biology
37. Modeling Gene Regulatory Networks
38. Network Topology and Dynamics
39. The Role of Computational Tools in Systems Biology

Chapter 10: Numerical Methods for Biological Models
40. Introduction to Numerical Methods
41. Solving Ordinary Differential Equations (ODEs) in Biological Models
42. Stability Analysis and Numerical Simulation Techniques
43. Finite Difference Methods for Partial Differential Equations (PDEs)
44. Agent-Based Models and Cellular Automata

Chapter 11: Applications and Case Studies in Mathematical Biology
45. Mathematical Modeling in Medicine and Public Health
46. Environmental Modeling: Climate, Conservation, and Sustainability
47. Case Study 1: Modeling Cancer Growth and Treatment
48. Case Study 2: Ecological Modeling of Invasive Species
49. Case Study 3: Epidemic Modeling and the COVID-19 Pandemic

Chapter 12: The Future of Mathematical Biology
50. Emerging Techniques and Technologies in Mathematical Biology
51. The Role of Machine Learning and Artificial Intelligence
52. Interdisciplinary Approaches to Solving Biological Problems

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