Discrete Dynamical Modeling

Abstract

Chapter 1: Introduction to dynamic modeling 1. Modeling drugs in the bloodstream 2. Terminology 3. Equilibrium values 4. Dynamic economic applications 5. Applications of dynamics using spreadsheets Chapter 2: First order dynamical systems 1. Solutions to linear dynamical systems with applications 2. Solutions to an affine dynamical system 3. An introduction to genetics 4. Solution to affine dynamical systems with applications 5. Applications to finance Chapter 3: Introduction to probability 1. The multiplication to probability 2. Introduction to probability 3. Multistage tasks 4. An introduction to Markov chains Chapter 4: Nonhomogeneous dynamical systems 1. Exponential terms 2. Exponential terms, a special case 3. Fractal geometry 4. Polynomial terms 5. Polynomial terms, a special case Chapter 5: Higher order linear dynamical systems 183 1. An introduction to second order linear equations 2. Multiple roots 3. The gambler's ruin 4. Sex-linked genes 5. Stability for second order affine equations 6. Modeling a vibrating string 7. Second order nonhomogeneous equations 8. Gambler's ruin revisited 9. A model of a national economy 10. Dynamical systems with order greater than two 11. Solutions involving trigonometric functions Chapter 6: Introduction to nonlinear dynamical systems 1. A model of population growth 2. Using linearization to study stability 3. Harvesting strategies 4. More linearization Chapter 7: Vectors and matrices 1. Introduction to vectors and matrices 2. Rules of linear algebra 3. Gauss-Jordan elimination 4. Determinants 5. Inverse matrices Chapter 8: Dynamical systems of several equations 1. Introduction to dynamical systems of several equations 2. Characteristic values 3. First order dynamical systems of several equations 4. Regular Markov chains 5. Absorbing Markov chains 6. Applications of absorbing Markov chains 7. Long term behavior of solutions 8. The heat equation 9. Bibliography