35433 - Numerical Methods

Course Unit Page

  • Teacher Giulia Spaletta

  • Credits 6

  • SSD MAT/08

  • Teaching Mode Traditional lectures

  • Language English

  • Campus of Bologna

  • Degree Programme Second cycle degree programme (LM) in Quantitative Finance (cod. 8854)

  • Course Timetable from Sep 22, 2021 to Oct 29, 2021

SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education

Academic Year 2021/2022

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

Representation of numbers and operations with a prefixed precision; floating point case. Error analysis. Conditioning of a problem. Stability of an algorithm. Accuracy of the result.

Basics of data approximation via interpolation or fitting. Some results on numerical integration.

Introduction to the numerical integration of differential equations.

Mention to the need for iterative algorithms to solve nonlinear equations. Mention to the possibility of a direct solution process in the linear case, using the Gauss method as an example.

The course activities are supported by laboratory facilities (obviously, complying with COVID-19 indications and the like), 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 UniBO Virtuale platform; lectures are not recorded. 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 Philadelphia, Pennsylvania, USA, 2002.

Numerical analysis: mathematics of scientific computing, D. Kincaid, E. W. Cheney, 3rd ed., American Mathematical Society, Providence, Rhode Island, USA, 2009.

Numerical Linear Algebra, D. Bau, N. Trefethen, SIAM, Philadelphia, Pennsylvania, USA, 1997.

Afternotes on Numerical Analysis, G. W. Stewart, SIAM, Philadelphia, Pennsylvania, USA, 1996.

Course notes (in italian) published by Pitagora: Analisi Numerica, G.Spaletta, Pitagora, Bologna, 2004.

Further Readings:

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

Computational Economics and Finance: Modeling and Analysis with Mathematica, H. R. Varian editor, Springer Telos, New York, USA, 1996.

Mathematica for Microeconomics, J. R. Stinespring, Academic Press, San Diego, California, USA, 2002.

Teaching methods

1. Class lectures (obviously, complying with COVID-19 indications and the like)
2. Exercises in class and home assignments
3. Seminars
4. Description of a software environment 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. Students with specific learning disorders, special educational needs or disabilities can make use of all their compensatory and dispensatory aiding tools.

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 Numerical Analysis integrated course.

In the event of COVID-19 indications and the like, the assessment method may have to vary: in this case, students will be notified in advance and, in any case, during the lectures; in this case, moreover, the assessment procedures will be published in the teacher's NEWS and in the note contained in each exam enrolling list in Almaesami.

Teaching tools

Course notes and material to study and exercise available at the Virtuale platform (https://virtuale.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