Elementary Mathematical Modeling: A Dynamic Approach Book

1. INTRODUCTION TO MODELING. Introduction to Dynamical Systems. Examples of Modeling. Affine Dynamical Systems. Parameters. Financial Models. 2. ANALYSIS OF DYNAMICAL SYSTEMS. Introduction to Analysis. Equilibrium. Stability. Ratios and Proportional Change. Stable Distributions. Cycles. 3. FUNCTION APPROACH. Introduction to Function Approach. Linear Functions. Exponential Functions. Exponential Growth Decay. Translations of Exponential Functions. Curve Fitting. 4. HIGHER ORDER DYNAMICAL SYSTEMS. Introduction. Counting Sets. Introduction to Probability. The Gambler''s Ruin. Analyzing Higher Order Dynamical Systems. An Economic Model. Controlling an Economy. Exponential and Trigonometric Functions. 5. NONLINEAR DYNAMICAL SYSTEMS. Introduction. The Dynamics of Alcohol. Stability. Web Analysis. 6. POPULATION DYNAMICS. Introduction to Population Growth. The Logistic Model for Population Growth. Nonlinear Growth Rates. Graphical Approach to Harvesting. Analytic Approach to Harvesting. Economics of Harvesting. 7. GENETICS. Introduction to Population Genetics. Basics of Genetics. Mutation. Selection. Answers to Odd Exercises.