Advanced Engineering Mathematics

The course gives the background for simple analytical derivation and numerical calculations for stochastic processes in discrete and continuous time as well as the application of Finite Element Methods to the solution of partial Differential Equations arising from Structural Engineering, Heat Conductions, Geomatic Engineering and Electrical Transmission Lines and using appropriate software tools e.g. MATLAB.Objectives:

• To develop a fundamental understanding of state-of-the-art finite element formulations and procedures, to develop an appreciation for the strengths and limitations of modern finite element methods and related software, to reinforce knowledge in solid mechanics with particular emphasis on nonlinear and dynamic problems, and to learn to utilize finite element methods as a research tool. Topics include finite element fundamentals and Weighted residual and finite element methods for the solution of hyperbolic, parabolic and elliptical partial differential equations, with application to problems in science and engineering. Error estimates. Standard and discontinuous Galerkin methods.