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Mathematical models in biology an introduction 1st Edition by Elizabeth S Allman, John A Rhodes ISBN 0521819806 9780521819800

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Mathematical models in biology an introduction 1st Edition Elizabeth S. Allman Digital Instant Download

Author(s): Elizabeth S. Allman, John A. Rhodes
ISBN(s): 9780521819800, 0521819806
Edition: 1
File Details: PDF, 2.11 MB
Year: 2003
Language: english
SKU: EB-1076010 Category: Tags: ,

Mathematical models in biology an introduction 1st Edition by Elizabeth S Allman, John A Rhodes – Ebook PDF Instant Download/Delivery: 0521819806, 9780521819800
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ISBN 10: 0521819806 
ISBN 13: 9780521819800
Author: Elizabeth S Allman, John A Rhodes

This introductory textbook on mathematical biology focuses on discrete models across a variety of biological subdisciplines. Biological topics treated include linear and non-linear models of populations, Markov models of molecular evolution, phylogenetic tree construction, genetics, and infectious disease models. The coverage of models of molecular evolution and phylogenetic tree construction from DNA sequence data is unique among books at this level. Computer investigations with MATLAB are incorporated throughout, in both exercises and more extensive projects, to give readers hands-on experience with the mathematical models developed. MATLAB programs accompany the text. Mathematical tools, such as matrix algebra, eigenvector analysis, and basic probability, are motivated by biological models and given self-contained developments, so that mathematical prerequisites are minimal.

Mathematical models in biology an introduction 1st Table of contents:

1. Dynamic Modeling with Difference Equations
1.1. The Malthusian Model
1.2. Nonlinear Models
1.3. Analyzing Nonlinear Models
1.4. Variations on the Logistic Model
1.5. Comments on Discrete and Continuous Models
2. Linear Models of Structured Populations
2.1. Linear Models and Matrix Algebra
2.2. Projection Matrices for Structured Models
2.3. Eigenvectors and Eigenvalues
2.4. Computing Eigenvectors and Eigenvalues
3. Nonlinear Models of Interactions
3.1. A Simple Predator–Prey Model
3.2. Equilibria of Multipopulation Models
3.3. Linearization and Stability
3.4. Positive and Negative Interactions
4. Modeling Molecular Evolution
4.1. Background on DNA
4.2. An Introduction to Probability
4.3. Conditional Probabilities
4.4. Matrix Models of Base Substitution
4.5. Phylogenetic Distances
5. Constructing Phylogenetic Trees
5.1. Phylogenetic Trees
5.2. Tree Construction: Distance Methods – Basics
5.3. Tree Construction: Distance Methods – Neighbor Joining
5.4. Tree Construction: Maximum Parsimony
5.5. Other Methods
5.6. Applications and Further Reading
6. Genetics
6.1. Mendelian Genetics
6.2. Probability Distributions in Genetics
6.3. Linkage
6.4. Gene Frequency in Populations
7. Infectious Disease Modeling
7.1. Elementary Epidemic Models
7.2. Threshold Values and Critical Parameters
7.3. Variations on a Theme
7.4. Multiple Populations and Differentiated Infectivity
8. Curve Fitting and Biological Modeling
8.1. Fitting Curves to Data
8.2. The Method of Least Squares
8.3. Polynomial Curve Fitting
A. Basic Analysis of Numerical Data
A.1. The Meaning of a Measurement
A.2. Understanding Variable Data – Histograms and Distributions
A.3. Mean, Median, and Mode
A.4. The Spread of Data
A.5. Populations and Samples
A.6. Practice
B. For Further Reading

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