In nearly every example of scientific computing, a mathematical model is used. In short, a model is an equation, set of equations or some algorithm that is assumed as a mathematical understanding of the underlying problem. Mathematical models range vastly from field to field and generally the details are only taught in the individual fields, so we’re not covering too much about models in this course, but here’s a few examples.
- In weather prediction, if the underlying physics is assumed, there is a large set of partial differential equations called the Navier-Stokes equations. Some approximation of these is used often with some statistical modeling for weather models.
- In the autonomous car example above, modeling of the car dynamics often consists of the physics of moving objects which link position, velocity, acceleration and force. There is also a lot of artificial intelligence (AI) for object detection.
- In the contagious disease models, there is usually some please of differential equations (the SIR model is a simple version) and some probability modelling. We will discuss both of these in this text.