Computational Mathematics

Recommended Prerequisites

Linear Algebra and Vectorial Calculus and preferably a basic course in Numerical Analysis.

Teaching Methods

Lectures have an expository character, being up to the professor the choice of the most appropriate way to do it and the degree of participation of the students. As an integral part of the learning process, it may be recommended or required the solution of exercises, course projects (possibly with a computational component) or oral presentations.

Learning Outcomes

The goal of this course is to provide a general knowledge of Numerical Analysis and Optimization at an advanced level. It is intended that the students become familiar with the main basic techniques and results of this area of Mathematics, or at least attain enough familiarity with some of  them to be able to acquire others by themselves that may later prove to be useful.

Work Placement(s)

No

Syllabus

A brief review of the principles of numerical computation and numerical solution of systems of linear equations.

Multidimensional numerical interpolation and integration.

A brief introduction to systems of nonlinear equations and minimization of unconstrained functions.

Numerical solution of ordinary differential equations.

A brief introduction to the numerical solutions of PDEs.

Head Lecturer(s)

José Augusto Mendes Ferreira

Assessment Methods

Assessment
Resolution Problems: 25.0%
Exam: 75.0%

Bibliography

G. Dahlquist and Å. Björck, Numerical Methods in Scientific Computing, SIAM, Philadelphia, 2008.

M.T. Heath, Scientific Computing: An Introductory Survey, 2nd edition, McGraw-Hill, New York, 2002.

A. Quarteroni, R. Sacco, and F. Saleri, Numerical Mathematics, 2nd edition, Springer-Verlag, New York, 2007.