Unit NUMERICAL MODELS
- Course
- Mathematics
- Study-unit Code
- A005470
- Curriculum
- Generale
- Teacher
- Bruno Iannazzo
- Teachers
-
- Bruno Iannazzo
- Hours
- 47 ore - Bruno Iannazzo
- CFU
- 6
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/08
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- English (or Italian only if all students agree)
- Contents
- Selected topics of Numerical Linear Algebra with applications to Numerical Models (especially PDEs)
- Reference texts
- Teaching material provided by the teacher. Textbooks provided during the course also following the topics chosen by students.
- Educational objectives
- The aim of the course is to present advanced topics in numerical analysis and applications to mathematical modeling. The mathematical models will be explored and studied in detail. The student will learn about advanced methodologies in numerical analysis, up to touching on some techniques used in scientific research. The student will be able to appreciate the richness of mathematical modeling with the application of linear algebra techniques to problems in very different contexts (partial differential equations, applied probability, social network analysis).
- Prerequisites
- Linear Algebra, Multivariate Differential Calculus, Numerical Analysis (a basic knowledge of Functional Analysis may be helpful).
- Teaching methods
- Face-to-face Lectures and laboratory in Matlab/Octave.
- Other information
- Part of the course will be held by a foreign co-teacher.
- Learning verification modality
- Oral exam of approximately one hour. Optionally, the exam can be replaced by two parts: 1) exercises to be solved by groups of student working together (including the part taught by a foreign teacher); 2) a research project individual or collective, based on the study of a problem whose solution is unknown, the collection of existing material (including any numerical methods to be implemented) and the investigation of possible approaches to the solution. The purpose of the oral exam is to evaluate the understanding of the course topics and the mastery in their use. The purpose of the project is the (self-)evaluation of the aptitude to carry out research activities. For information on support services for students with disabilities and/or DSA visit the page http://www.unipg.it/disabilita-e-dsa
- Extended program
- Matrix analysis. Spectral theory. Elementwise positivity: Perron and Frobenius theory; definite positiveness. Perturbation and localization of roots of polynomials and eigenvalues. Numerical methods for parabolic and hyperbolic differential equations. The techniques will be applied to one or more mathematical models: partial differential equations, Markov chains, complex networks.