Mathematical models course, Fall 2022, UNAL
This repository contains various mathematical models used to provide solutions to industrial and scientific problems. The tools used in these models vary from linear regression to numerical methods for differential equations using MatLab libraries. The mentioned problems are as follows:
- Introductory problems: Estimation of the number of restaurants in Colombia using linear regression and modeling of craft techniques to desingn the trajectory of a welding arm.
- Regression problems:Linear regression was used to obtain simple models (formulas) for estimating the price of a product, evaluating the vibration of a spring, and understanding the importance of this concept in the task of digit recognition.
- Pharmacokinetics: We developed two models to study the behavior of a medicine in the bloodstream. In the first one we made the assumption that the body is comformed by just one container and we modeled this situation using an ordinary differential equation. In the second model, we improved the first model assuming that the body is conformed by two containers (stomach and bloodstream) using a system of differential equations. Finally, we answered the same questions for both models and compared results.
- Forest conservation and diabetes diagnosis: We developed two models to study the problem of forest conservation and diagnosis of diabetes melitus. We made use of non-linear regressions and numerical methods to solve systems of differential equations. With those models, we answered questions related with the design of public policies to take care of the forest without affecting the economy of the population and we designed a clinical method to determine if a pacient has diabetes or not.