This module will provide a solid background in the mathematical description of fluid dynamics. They will cover the derivation of the conservation laws (mass, momentum, energy) that describe the dynamics of fluids and their application to a remarkable range of phenomena including water waves, sound propagation, atmospheric dynamics and aerodynamics. The focus will be on deriving approximate expressions using known mathematical techniques that yield analytic solutions.
This module introduces the basic concepts of Partial Differential Equations by concrete Examples. PDEs are used to describe a wide variety of phenomena such as sound, heat, diffusion, electrostatistics, electrodynamics, fluid dynamics, electricity, gravitation and quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs. Partial differential Equations are used in modelling of multidimensional systems.
This course will permit the users to work in industry. Environmental modelling is also tackled using PDEs. Climate change, Chemical reactions, competitions between species, modelling of dynamics of infectious diseases, among others are described using PDEs.