Introduction to floating point arithmetic. Numerical stability. Iterative methods for SEL: convergence analysis, stopping criteria. Conditioning. Solution of non-linear equations: Fixed point methods: convergence conditions, stopping criteria. Polynomial interpolation: Lagrange, Newton, Chebyshev polynomials, interpolation error. Curves adjustment. Numerical Integration: Newton-Cotes formulas, composite methods, Romberg method, Gaussian method. Differential equations: Mathematical models. The exponential matrix and solution of linear systems. Nonlinear ODE systems. Stability. Numerical integration of ODE: Taylor, Runge-Kutta, predictor-corrector, exponentials; convergence, A-stability, implementation. Computational methods for PDE. Stochastic simulation. Numerical integration of stochastic equations (EDEs): Euler, Milstein, Ito-Taylor. Types of approximation and convergence. Monte Carlo methods for EDEs. Computer simulation of EDEs. Applications.

#### Basic Information

**Mandatory: **

- Conte, S.D., de Boor, C. (1980). Elementary Numerical Analysis, an Algorithmic

Approach. McGraw-Hill. - Faire, D., & Burden, R. L. (2002). Numerical Methods . Brooks Cole.
- Griffiths D., & Higham, D. (2010). Numerical Methods for Ordinary Differential Equations. Springer.
- Higham D. (2004). An Introduction to Financial Option Valuation- Mathematics, Stochastics and Computation. Cambridge.
- Stoer, J. & Bulirsch, R. (2002). Introduction to Numerical Analysis. Springer.
- Sauer, T. (2011). Numerical Analysis. Pearson.