Lecture D1 - Introduction to Numerical Simulation of Dynamical Systems, Part 1 (2020-02-11)

In this lecture, we introduce basic numerical methods for simulating (or "integrating") dynamical systems models, like those specified by ordinary differential equations (ODE's) or System Dynamics Models formulated graphically as stock-and-flow diagrams. The lecture starts with a compound interest example (a model of how money grows in a "bank" -- with the bank balance playing the role of a stock and the interest generated over a year playing the role of a flow) and demonstrates how more general continuous dynamics (like the average population trajectory of bacterial growth) can be approximated like money growing in a bank via compound interest. All examples are done in a spreadsheet program, like Microsoft Excel, with hints of how the models will later be put into a formal System Dynamics Modeling tool like Vensim or Insight Maker in the form of stock-and-flow diagrams.