35433 - Numerical Methods

Learning outcomes

At the end of the course, the student is aware of techniques for the solution of computational economics problems, involving basic numerical calculus, numerical linear algebra, differential and difference equations, dynamic optimization, basics of descriptive statistics. She/ He can face and solve such problems within a uniform, integrated computer algebra environment.

Course contents

Finite numbers and floating point arithmetic; error analysis; problem conditioning; method stability.

Brief introduction to data approximation via polynomial interpolation or least squares approach. Some results on numerical integration and Monte Carlo approach.

Numerical linear algebra: introduction to the direct methods of Gauss and Householder. Some results on matrix eigenvalues. Brief introduction to iterative methods for linear and non linear equations.

The course activities are supported by laboratory facilities, including the availability of the MATHEMATICA environment.

Readings/Bibliography

Any of the following books, available at the Bologna University Libraries:

Accuracy and Stability of Numerical Algorithms, N. Higham, SIAM 2002.

Numerical analysis: mathematics of scientific computing, D. Kincaid, E. W. Cheney, 2nd ed., Brooks and Cole, 199

Numerical Linear Algebra, D. Bau, N. Trefethen, SIAM 1998.

Afternotes on Numerical Analysis, G. W. Stewart, SIAM 1996.

Course notes (in italian) published by Pitagora, Bologna.

Further readings:

Numerical Computing with IEEE Floating Point Arithmetic, M. Overton, SIAM, 2001.

Computational Economics and Finance: Modeling and Analysis with Mathematica, H. R. Varian, Springer, 1996.

Mathematica for Microeconomics, J. R. Stinespring, Academic Press, 2002.

Teaching methods

1. Class lectures
2. Exercises and tests
3. Seminars
4. Description of software environments for scientific computing

Assessment methods

Written test on the course contents, aimed at verifying the achievement of the learning outcomes, above described. The test questions concern all the course topics: questions may be purely conceptual and theoretical, or they may imply a reasoning connected to the rapid performing of short exercises.
The grade obtained in the Numerical Methods module exam contributes to forming the arithmetic mean with the grade obtained in the Computer Programming module exam: such a mean represents the overall grade of the integrated course of Numerical Analysis.

Teaching tools

Text books available at the departmental libraries, course notes and material available at AMScampus.

Links to further information

https://www.unibo.it/sitoweb/giulia.spaletta/news

Office hours

See the website of Giulia Spaletta