The teaching is organized as follows:

Learning outcomes

Module: Laboratory
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Implementation in Matlab and/or GNU Octave of the main algorithms of Numerical Analysis.

Module: Theory
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The basics of Numerical Analysis.

Program

Module: Theory
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* Analysis of errors: Overflow, Underflow, Cancellation
* Nonlinear equations: the Bisection Method, Fixed Point Iterations, Newton's Method, the Secant Method, Polynomials, Horner's Rule
* Linear Systems: Direct Methods, the LU Decomposition and Pivoting, Forward and Back Substitution; Iterative Methods, Jacobi Iteration, Gauss-Seidel and SOR. Iterative Improvement, the Gradient Method, Conjugate Gradient, over and under determined systems
* Eigenvalues and Eigenvectors: the Power Method, the Inverse Power Method, the QR algorithm
* Interpolation and Approximation fo Functions and Data: Polynomial interpolation, the Newton and Lagrange forms. Splines. Least Squares and the SVD.
* Numerical Integration and Derivatives: Simple formulas for the estimation of a derivative with relative error, numerical quadrature, interpolatory formulas, composite formulas, Gaussian Quadrature, Adaptive Quadrature.
* Numerical Solution of ODE's (time permitting)

Examination Methods

There will be an exam consisting of two parts. The first will be written in the Laboratory and consist of several questions to be solved using Matlab (or Octave) with appropriate brief description.

These questions will be very similar to the exercises given in the Laboratory and hence attending the Laboratory and completing the assigned exercises is strongly reccomended.

Student will be permitted to bring notes, handouts and their solutions to the exercises to the written exam.

The second part will be an oral exam based on the more theoretical aspects of the course. Students will be admitted to the oral exam only after having passed the written exam.