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Discrete Mathematical Modeling for Biology - overview of contents

(Link to lecture notes: Math 113 A)
 
surfplotPart 1. Linear Discrete Models
 
Chapter 1. Growth of a Population
1. Mathematical Modeling
2. Linearization
3. The Logistic Growth Model
4. Immigration
 
Chapter 2. The Fibonacci Rabbits 
1. Mathematical Modeling
2. The Fibonacci Sequence
3. Linear Difference Equations
4. Nonautonomous Linear Equation
 
Chapter 3. Linear Equations -Algebra 
1. Linear Equations
2. Matrix Inversion
3. Gaussian Elimination
 
Chapter 4. Interacting Population Models
1. Plant Growth
2. Red Blood Cell Production
3. Drug Uptake I
4. Drug Uptake II
5. Exercises
 
Chapter 5. Markov Chains
1. Discrete Markov Processes and Markov Chains
2. Regular Markov Chains
3. DNA Mutation
4. Ion-Gate Channel Openings
5. Mendelian Genetics
6. Selective Breeding
 
Part 2. Nonlinear Discrete Models
 
Chapter 6. Single Population Models
1. Graphical Method
2. Fixed Points and Their Stability.
3. Cycles
4. Basic Bifurcation Types
5. Single Nonlinear Difference Equations
 
Chapter 7. Nonlinear Discrete Systems 
1. Predator-Prey
2. Parasitoidy
3. Plant-Herbivore Interaction
4. Epidemic Diseases
5. Viral Dynamics
 
Chapter 8. Molecular and Cellular Biology
1. Glucose-Insulin Kinetics
2. Metabolic Pathways
3. Immunology
 
Chapter 9. Genetics
1. Hardy-Weinberg Stability Theorem
2. Gene Frequencies 33
3. Mutation
4. Inbreeding
 
Part 3. Probabilistic and Empirical Models
 
Chapter 10. Methods for Best Selected Models
1. Models, Data and Transformation
2. Search Techniques
3. Linear Programming
 
Chapter 11. Interpolation and Smoothing
1. Higher Degree Polynomials
2. Smoothing
 
Chapter 12. Spline Models
1. Linear Splines
2. Cubic Splines
 
Chapter 13. Models by Distributions 
1. Counts
2. Gauassian
3. Duration