# Numerical analysis with laboratory (2015/2016)

Course code
4S02755
Credits
12
Coordinator
Leonard Peter Bos
MAT/08 - NUMERICAL ANALYSIS
Language of instruction
Italian
Teaching is organised as follows:
Activity Credits Period Academic staff Timetable
teoria 9 I semestre Leonard Peter Bos
laboratorio 3 I semestre Elena Gaburro

### Lesson timetable

I semestre
Activity Day Time Type Place Note
teoria Monday 4:30 PM - 6:30 PM lesson Lecture Hall E from Oct 12, 2015  to Jan 29, 2016
teoria Wednesday 10:30 AM - 11:30 AM lesson Lecture Hall A from Nov 3, 2015  to Jan 29, 2016
teoria Thursday 5:30 PM - 6:30 PM lesson Lecture Hall E from Oct 8, 2015  to Jan 29, 2016
teoria Friday 3:30 PM - 5:30 PM lesson Lecture Hall E from Nov 3, 2015  to Jan 29, 2016
laboratorio Monday 9:30 AM - 12:30 PM laboratorio Laboratory Alfa from Oct 19, 2015  to Jan 29, 2016
laboratorio Wednesday 11:30 AM - 2:30 PM laboratorio Laboratory Alfa from Oct 14, 2015  to Jan 29, 2016

### Learning outcomes

Module: Laboratory
-------

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.

### Syllabus

Module: Theory
-------

* 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)

### Assessment methods and criteria

There will be an exam consisting of two parts. The first will be written in the Laboratory and consist of 2 or 3 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.