Environmental Math

1. Introduction

• 1.1 Our heritage and the environment
• 1.2 New subject, new approach
• 1.3 A broader view of mathematics and modeling
• 1.4 The visual
• 1.5 The qualitative
• 1.6 The computational
• 1.7 "Decay" and the tank model
• 1.8 Energy as a central concept
• 1.9 Overview of a Five-stage modeling process

2. Systems

• 2.1 Introduction
• 2.2 Closed and Open Systems
• 2.3 Taxonomy
• 2.4 Local, Global
• 2.5 Stability
• 2.6 Feedback Loops
• 2.7 Self-organization and Self-maintenance
• 2.8 Unintended Consequences
• 2.9 A Question of Scale
• 2.10 System Invariants
• 2.11 Energy

3. Modeling

• 3.1 What Is a Model . . . ?
• 3.2 Formulation and Interpretation
• 3.3 The Representation of Data
• 3.4 Units
• 3.5 Mexican Free-tail Bats

4. Modeling with Tanks

• 4.1 Introduction
• 4.2 Tanks
• 4.3 Five-stage Modeling
• 4.4 Model #1 Tank Fed by Constant-Flow Source
• 4.5 A Small Detour -- Steady State
• 4.6 Model #2 Small Storage Fed from a Large Reserve Storage
• 4.7 The Dynamical System Approach

5. Energy Diagrams

• 5.1 Introduction
• 5.2 The Basic Diagrams
• 5.3 Modeling
• 5.4 Pre-Columbus Culture

6. Economics as If Energy Matters

• 6.1 Introduction
• 6.2 Economics, Externals and Nature
• 6.3 Costs - Energy vs Dollars
• 6.4 How Much Is Nature Worth?
• 6.5 Money, Time and Energy
• 6.6 Embodied Energy

7 Energy Principles

• 7.1 What Is Energy?
• 7.2 Work and Power
• 7.3 Thermal Energy
• 7.4 Conservation of Energy
• 7.5 Entropy and the Degradation of Energy
• 7.6 Efficiency
• 7.7 Kinetic and Potential Energy
• 7.8 More on Energy and Power
• 7.9 The Maximum Power Principle
• 7.10 Autocatalytic (Self-organizing) Unit

8. Modeling with Work Gates

• 8.1 The Work Gate -- Energy Interaction
• 8.2 Model #3 Autocatalytic System with Storage Tank Input
• 8.3 Model #4 Autocatalytic System with Replenishable Tank Source
• 8.4 Model #5 Compound Interest, and the J-Curve
• 8.5 Model #6 Autocatalytic System with "Magic" Tank Source & Quadratic Drain
• 8.6 Model #7 Autocatalytic System with Renewable Source
• 8.7 Model #8 Two Sources: Renewable & Nonrenewable
• 8.8 Energy and Money Flows in an Economy

9. Embodied Energy, Efficiency and Emergy