• Finite Element Methods for Partial Differential Equations: Theory and Applications

    FEM for one dimensional problems. Variational formulation and weak solutions. FEM for elliptic equations. FEM spaces. Error analysis and adaptivity. Diffusion-convection equations. Time dependent problems. Iterative solution techniques and preconditioning.

    For further information see the academic catalog: IAM572

  • Programming Techniques in Applied Mathematics II

    Review of Programming and Toolboxes, Packages, Modules; Iterative Linear Algebra Problems; Root Finding Programs; Recursive Functions and Algorithms; Optimisation Algorithms; Data Fitting and Interpolation; Extrapolation; Numerical Integration; Numerical Solutions of Differential Equations: IVPs and BVPs; Selected Topics (algorithms and coding in different fields).

    For further information see the academic catalog: IAM592

  • Methods of Computational Finance

    Numerical Methods for Discrete Time Models: binomial method for options; discrete time optimal control problems. Reminders on Continuous Models: Ito process and its applications in stock market, Black-Scholes equation and its solution; Hedging, Volatility smile. Monte Carlo Method for Options: generating random numbers, transformation of random variables and generating normal variates; Monte Carlo integration; pricing by Monte Carlo integration; variance reduction techniques, quasi-random numbers and quasi-Monte Carlo method. Finite Difference Methods for Options: explicit and implicit finite difference schemes, Crank-Nicolson method; Free-Boundary Problems for American options. Finite Difference Methods for Control Problems: Markov Chain approximation method, elliptic Hamiltion-Jacobi-Bellman equations, computational methods.

    For further information see the academic catalog: IAM614