Scientific Computing

Introduction to partial differential equation problems and their importance in the applications. Non-dimensionalization and scaling procedures. Discretization of ordinary derivative equations: one-step methods with specific focus on Runge Kutta methods. Analysis and Matlab implementation. Partial derivative equations: theoretical properties and finite difference discretization in 1D and nD for elliptic and parabolic equations. Convection-diffusion-reaction problems with transport / dominant reaction. Introduction to inverse problems. Introduction to machine learning and the use of neural networks on selected examples. Each topic is treated theoretically along with its computer implementation in Matlab.