Computer Simulation of Realistic Mathematical Models

Computer Simulation of Realistic Mathematical Models paid course free. You will Learn How to model the interaction between prey and predators, as well as the evolution of epidemics

  • 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

Computer Simulation of Realistic Mathematical Models Course Requirements

  • the basics of calculus could be enough, especially what derivatives and functions are.

Computer Simulation of Realistic Mathematical Models Course Description

In this course, two mathematical models are analyzed: one is the so-called Lotka-Volterra model, also known as the prey-predator model, and the other is the epidemic model. We will use a free and open source software called Scilab (very similar to Matlab) to analyze and solve these models. In particular, we will use a tool called Xcos included in Scilab, which will help us build mathematical models. The models introduced in the course are very important in applied mathematics because they can explain various phenomena.

The Lotka-Volterra model got its name from mathematicians. They first used 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, and Volterra was one An Italian mathematician, he used this model to explain why the number of sharks in the Adriatic Sea during the First World War increased significantly compared to the pre-war and post-war periods. Volterra’s son-in-law Umberto D’Ancona (Umberto D’Ancona) found the highest percentage of sharks.

D`Ancona is an Italian biologist. He drew this observation from the data he collected and asked Volterra to analyze the problem mathematically, because he knew that Volterra was a subject. A respectable mathematician. Volterra accepted the challenge and decided to create a mathematical model, now called the Lotka-Volterra model, or prey-predator model.

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The model focuses on the interaction between two populations: the prey population and the predator population. In this case, the predator population is represented by sharks, and the prey population is represented by prey fish. Volterra understood that the reason for the sharp increase in the number of sharks during the First World War was that the sharks were less active.

Fishing interferes with the interaction between sharks and prey. We will learn more about this in the course; in addition, the prey-predator model can be used to explain other interesting phenomena that I will mention at the end of the first part of this course. After that, we will study epidemics and use the same concepts introduced in Scilab earlier. The mathematics we need in the course is not difficult; you only need to know what derivatives and functions are, but we will not go into the mathematical details of how to solve the model. In fact, I want to pay more attention to 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


Computer Simulation of Realistic Mathematical Models

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