Introduction to Mathematical Modeling Using Discrete Dynamical Systems
1. MATHEMATICAL MODELING AND DYNAMICAL SYSTEMS. Modeling Reality. Discrete Dynamical Systems. 2. LINEAR EQUATIONS AND MODELS. Some Linear Models. Linear Equations and Their Solutions. Homogenous Equations and Their Applications. Solutions of Non-Homogenous Equations. Applications of Non-Homogenous Equations. Dynamics of Linear Equations. Empirical Models and Linear Regression. 3. NONLINEAR EQUATIONS AND MODELS. Some Nonlinear Models. Autonomous Equations and Their Dynamics. Cobwebbing, Derivatives and Dynamics. Some Mathematical Applications. Periodic Points and Cycles. Parameterized Families. Bifurcation and Period-Doubling. Chaos. 4. MODELING WITH LINEAR SYSTEMS. Some Linear Systems Models. Linear Systems and Their Dynamics. Some Vector and Matrix Arithmetic. Stability and Eigenvalues. Repeated Real Eigenvalues. Complex Numbers and Their Arithmetic. Complex Eigenvalues. Non-Homogenous Systems. 5. MODELING WITH NONLINEAR SYSTEMS. Nonlinear Systems and Their Dynamics. Linearization and Local Dynamics. Bifurcation and Chaos. Fractals. Appendix. Answers to Odd-Numbered Exercises. Bibliography. Index.