Partial Differential Equations (PDEs) are mathematical expressions that incorporate numerous variables, including spatial and temporal dimensions, alongside their respective partial derivatives. These equations are indispensable for mathematical modeling, providing descriptions of how diverse physical phenomena, like heat diffusion, fluid motion, and electromagnetic interactions, evolve across both time and space.
Scientific computing plays a pivotal role in mathematical modeling and the study of PDEs. It involves the use of computational algorithms and numerical methods to solve complex mathematical models, represented by PDEs, which may have no analytical solutions. Through advanced simulations and numerical approximations, scientists and engineers can gain valuable insights into real-world phenomena, making scientific computing an essential bridge between mathematical theory and practical applications.
The summer school is designed to provide undergraduate students with a comprehensive introduction to the fascinating topic of mathematical modeling involving PDEs and the diverse techniques employed for their numerical solutions.
The initial portion of the summer school will comprise a series of lectures and hands-on practical sessions covering selected topics in PDEs, mathematical modeling with PDEs, and numerical methods for the solution of PDEs.
The second week will center around group projects for modeling a concrete real-world problem, fostering a deeper understanding of how PDEs are used to model real-world phenomena and how various discretization methods can be applied to obtain numerical solutions.
Possible topic areas for the modeling and simulation projects of the second week include
We have a flyer (white background) and a poster (beige background) in PDF format.