Lecture D1 (2022-02-10): Introduction to Numerical Simulation of Dynamical Systems, Part 1

In this video, we begin the discussion of using computer-based automation tools (in this case, spreadsheets) to generate numerical simulations of dynamical system behaviors over time (BOT). We start with a simplistic example of compound interest in a bank and show how the small-time scale behavior of any dynamical system can be approximated by a "bank account model" so long as each "compounding period" ("dt") is sufficiently small to assume that the variables are not changing much during that period. This is equivalent to the "secant approximation" of a derivative (where a derivative, which is strictly defined at a point, is approximated by the slope of a line connecting that point to a point just a little later in the trajectory). We close with an exercise where the exponential growth of bacteria is numerically simulated within a spreadsheet.