Computer Simulation of Realistic Mathematical Models
What you'll learn
- How to create and interpret computer simulations of real-life mathematical models using open-source software
- How epidemics evolve
- How the prey-predator model (or Lotka-Volterra model) explains a variety of real-world phenomena
- How the parameters of the model affect results
- the basics of calculus could be enough, especially what derivatives and functions are.
In this course two mathematical models are analyzed: one is the so-called Lotka-Volterra model, which is also known as prey-predator model, and the other is the model of epidemics. We will analyze and solve these models using free and open-source software called Scilab (quite similar to Matlab). In particular, we will use a tool that is contained in Scilab called Xcos, which will help us construct the mathematical models.
The models presented in the course are very important in applied mathematics because they can explain a variety of phenomena. The Lotka-Volterra model derives its name from the mathematicians who first employed it to explain some real-life phenomena: Lotka used this model to explain the interaction between two molecules, so he was interested in chemical reactions, whereas Volterra was an Italian mathematician who used this model to explain why the number of sharks in the Adriatic Sea had increased substantially during the first world war with respect to the pre-war and the post-war periods.
The discovery about the greater percentage of sharks was made by Volterra's son-in-law, whose name was Umberto D’Ancona. D'Ancona was an Italian biologist who made this observation from the data he collected, and asked Volterra to analyze this problem mathematically, knowing that Volterra was a respected mathematician. Volterra took the challenge and decided to create a mathematical model, which is now known as the Lotka-Volterra model, or prey-predator model. This model focuses on the interaction between two populations: a population of prey versus a population of predators. In this case, the population of predators is represented by sharks, whereas the population of prey is represented by prey-fish.
Volterra understood that the reason why the number of sharks increased dramatically during the first world war was due to the less intense activity of fishing, which had interfered with the interaction between sharks and prey-fish.
We are going to see this more thoroughly in the course; besides, the prey-predator model can be used to explain other interesting phenomena that I will mention at the end of the first part of the course. After that, we are going to study epidemics and we will use the same concepts previously introduced with Scilab.
The mathematics that we need in the course are not difficult; you just need to know what derivatives and functions are, but we are not going into the mathematical details of how to solve a model. In fact, I want to focus more on the practical applications.
Who this course is for:
- Students who want to understand how to implement mathematical models using Scilab
- Students who want to understand how to construct a mathematical model
I obtained my PhD in "Mechanics and Advanced Engineering Sciences" in 2021.
I attained a Bachelor of Science and Master of Science in Mechanical engineering in 2015 and 2017 respectively, with honors from the University of Bologna.
I was the teaching tutor for the course of Mechanics of Machines from the academic year 2018 until the end of 2021 at the University of Bologna (branch of Forlì).
My passion for mathematics, physics and teaching has motivated me to lecture high school and university students.
My approach as a teacher is to prove to students that memory is less important for an engineer, mathematician, or physicist, than learning how to tackle a problem through logical reasoning. I believe that a teacher of scientific subjects should try to develop his students’ curiosity about the subject, rather than just concentrating on acquisition of knowledge, however important that may also be. Students should be encouraged to dig deeper and build on their knowledge by continually questioning it, rather than accepting everything at face value without a thorough understanding.
For enquiries (e.g. about tutoring, or advice related to the subjects spanned by my courses), you can either contact me on LinkedIn, or you can post questions in my courses' message boards, or you can also contact me via email or on my website.
You can also find the updated versions of my courses on my website.