The course consists of a detailed description of continuous and discrete dynamical systems. We shall combine the introduction to the general theory with the consideration of bifurcations and chaos, the most important subtopics. The analysis of appropriate mechanical, physical, economic and biological models is an essential part of almost every lecture of the course. To support the course numerical and computational toolbox will be used.
For further information see the academic catalog: IAM529 - Applied Nonlinear Dynamics
This course introduces time series methodology emphasizing the data analytic aspects related to financial applications. Topics that will be discussed are as follows: Univariate linear stochastic models: ARMA and ARIMA models building and forecasting using these models. Univariate non-linear stochastic models: Stochastic variance models, ARCH processes and other non-linear univariate models. Topics in the multivariate modeling of financial time series. Applications of these techniques to finance such as time series modeling of equity returns, trading day effects and volatility estimations will be discussed.
For further information see the academic catalog: IAM526 - Time Series Applied to Finance
Interpolation, Numerical Integration and Differentiation, Initial Value Problems for Ordinary Differential Equations, Boundary Value Problems for Ordinary Differential Equations, Partial Differential Equations, Fast Fourier Transform.
For further information see the academic catalog: IAM562 - Introduction to Scientific Computing II
Introduction, Systems of Linear Equations, Iterative Methods, Linear Least Squares, Eigenvalue Problems, Nonlinear Equations, Optimization; Coursework and Programming Projects.
For further information see the academic catalog: IAM561 - Introduction to Scientific Computing I
Unconstrained optimization: line search methods, steepest descent, Newton and quasi Newton methods, the conjugate gradient method constrained optimization: equality and inequality constraints, linear constraints and duality, linear programming, the simplex method, Lagrange multiplier algorithms, interior point methods, penalty methods, large scale optimization.
For further information see the academic catalog: IAM566 - Numerical Optimization