Vector Calculus and Applications
This module is an introduction to vector calculus and its applications especially fluid dynamics. It lays down some basic principles using a number of simplifying assumptions. It examines how one can use vector formalism and calculus together to describe and solve many problems in two and three dimensions. For example, the rules that govern the flow of fluids and the motion of solids can be described using vector calculus, with resulting laws of motion described by partial differential equations rather than ordinary differential equations. The emphasis will be on inviscid, incompressible flows: viscous flow is the subject of later modules. Applications include the design of aeroplanes, car body shapes and the flows of liquids and gases through pipes. These problems raise important questions, such as: How is flight possible? How can one minimise drag? How do vortices form? What is pressure and how does it interact with the flow? Physical applications include meteorology (fluid dynamics applied to weather forecasting and events such as tornadoes and hurricanes) and oceanography (fluid dynamics applied to ocean currents, tides and waves). This module is a prerequisite for a number of more specialist modules in the third year.
Please note that all modules are subject to change, please get in touch if you have any questions about this module.