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.

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

Basics on iterative methods for differential equations.

Brief introduction to direct methods for linear equations, using the Gauss method as an example. Mention to iterative methods for nonlinear equations, including the linear case.

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

Readings/Bibliography

The material developed in class, useful for exam preparation, is made available to students enrolled in the course through the IOL platform.
Any other material/text on fundamentals of Numerical Calculus/Analysis is obviously also useful, both for the exam preparation and for an in-depth study: the following (not compulsory) books are recommended because (besides being excellent texts) they are available at the UniBo 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.

It is an open-book test; mobile phones and internet connection are prohibited.

The test total time, including, in particular, its illustration by the teacher, does not generally exceed 90 minutes (120 minutes maximum).

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

Course notes and material available at the IOL platform (https://iol.unibo.it) and text books available at the departmental libraries.

Links to further information

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

Office hours

See the website of Giulia Spaletta