Iterative Algebra and Dynamic Modeling

Table of Contents

Chapter I: Polynomial Equations

1.1 Introduction

1.2 The Quadratic Formula

1.3 Solution By Iteration

1.4 Revisiting the Quadratic Formula

1.5 Babylonian Iteration

1.6 The Staircase Method

1.7 Quadratic Equations

1.8 Cubic Equations

1.9 Higher Order Equations

1.10 Analytic Geometry

1.11 Problems, Exercises, and Projects

Chapter II: Difference Equations

2.1 Introduction

2.2 A Banking Analogy

2.3 Radioactive Decay and Economic Equilibrium

2.4 Logistic Equations

2.5 Higher Order Equations

2.6 Problems, Exercises, and Projects

Chapter III: Refinement, Sloppiness, and Chaos

3.1 Introduction

3.2 Exponential Growth and Decay

3.3 The Logistic Equation Revisited

3.4 Iteration of Functions

3.5 Escape From Chaos

3.6 Restoring Order

3.7 Problems, Exercises, and Projects

Chapter IV: Complex Numbers, Polynomial Equations, and Fractals

4.1 Introduction

4.2 Does -1 Exist?

4.3 Quadratic Equations Revisited

4.4 Cubic Equations and Julia Sets

4.5 Iterative Geometry and Fractals

4.6 Problems, Exercises, and Projects

Chapter V: Algebraic Systems

5.1 Introduction

5.2 Linear Systems

5.3 Contraction Matrices

5.4 The Matrix Inverse

5.5 Input-Output Economics

5.6 Matrix Iteration

5.7 Synthesis

5.8 Problems, Exercises, and Projects

Chapter VI: Systems of Difference Equations

6.1 Introduction

6.2 Linear Systems

6.3 Nonlinear Systems

6.4 Higher Order Equations

6.5 Chaos Revisited

6.6 Multivariate Systems

6.7 Problems, Exercises, and Projects

Chapter VII: Stella Modeling

7.1 Introduction

7.2 Flows, Reservoirs, and Difference Equations

7.3 Systems

7.4 Iteration, Reservoirs, and Flows

7.5 Sub-models

7.6 Closed Systems, Thermodynamics, and Entropy

7.7 The Global System

7.8 Problems, Exercises, and Projects

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