Mathematics
Quantifying Source Strength in Noisy Vector Fields
Overview
The project, explored computational mathematics using MATLAB to estimate the amplitude of a point source within a noisy environment. The objective was to apply numerical integration techniques to a vector field perturbed by normally distributed noise, to determine the strength of a point source, Q. The methodology involved the computation of 10,000 integrals to estimate the source amplitude while accounting for the influence of noise within the data.
Results
The MATLAB implementation yielded a histogram that adhered to a normal distribution, affirming the theoretical expectations underpinning the experiment. The resulting data pointed towards a mean value of approximately 2000 for the source strength, with a standard deviation of 25. This precision in the results was indicative of the robustness of the numerical methods applied. Additionally, the project output included a visual representation of the normalized vector field, featuring several closed curves that provided a qualitative understanding of the field's behavior. This graphical representation served as a confirmation of the underlying mathematical model and the computational approach used in the analysis. The coherent results not only demonstrate the viability of the numerical methods employed but also underscore the potential for applying such techniques to similar problems in fields that rely on precise measurements within noisy datasets.
Optimization of Production for Maximum Profit using Lagrange's Method
Overview
This project tackles a nonlinear optimization problem faced by a computer monitor manufacturer considering production constraints. It delves into determining the optimal quantities of two new monitor models to manufacture for maximizing profit, while accounting for the diminishing retail price with increased sales and the interdependence of sales between the two models. Employing Lagrange's multiplier method, the project addresses the complex dynamics of competitive pricing and limited production capacity, ensuring all produced units are sold. The study extends to explore optimal production strategies under fixed manufacturing limits, providing valuable insights into profit maximization in constrained production scenarios. (Pictures coming soon)
