My project focuses on the study and application of partial differential equations (PDEs), which are mathematical equations that involve multiple independent variables and their partial derivatives. PDEs are fundamental tools in describing and understanding various physical phenomena, ranging from heat conduction and fluid dynamics to electromagnetic fields and quantum mechanics. The project delves into both the theoretical aspects of PDEs, exploring their mathematical properties and solutions, as well as their practical applications across diverse scientific and engineering domains.
In the theoretical aspect, the project involves a type of PDEs (first order PDEs), comparison between ODEs and PDEs, and methods for solving PDEs, which includes direct integration and separation of variables. On the applied side, the project investigates how PDEs can be used to model and solve real-world problems. Examples include heat conduction, wave equation, Laplace equation, and more. Ultimately, the project contributes to advancing our comprehension of natural phenomena and enhancing our ability to address challenges in science and engineering.
