ID:
504710
Duration (hours):
46
CFU:
6
SSD:
ANALISI NUMERICA
Year:
2025
Overview
Date/time interval
Primo Semestre (29/09/2025 - 16/01/2026)
Syllabus
Course Objectives
Being aware of the content and meaning of the basic theoretical results related tonumerical methods. Having understood elementary concepts regarding: a) Numerical solution of ordinary differential equations b) Solution of linear systems of equations c) solution of Nonlinear equations by the bisection and Newton's methods d) Lagrange interpolation e) Least squares method for data fitting f) Interpolatory quadrature formulas. Knowing how to reproduce with awareness the main demonstrative phases of theory construction and immplement the algorithm in MATLAB language.
Being able to frame and numerically solve some standard problems on the topics of the course
Being able to frame and numerically solve some standard problems on the topics of the course
Course Prerequisites
Differential and integral calculus for real functions; complex numbers; linear algebra; computer programming experience.
Teaching Methods
Lessons and computer lab practice
Assessment Methods
The exam will be written. Each student will be offered a couple of questions on topics developed in the classes and has one hour to answer.
There are two levels of exam:
1) Basic exam: it consists in a two questions and/or exercises (one easy and one medium difficulty), intended to verify the knowledge of numerical algorithms and the capability of applying them, without the need for a deep understanding. The maximum grade is 24/30.
2) Advanced exam: it consists in a couple questions (one medium difficulty and one theoretical-oriented), intended to verify comprehension of the subjects and not just a mere application of ready-to-use formulas. The answers must be articulated with a certain mathematical precision. The maximum grade is 30/30 cum laude.
Oral exam is not compulsory. However, students who got a positive grade in the written part (i.e., at least 18/30) might choose to take an oral exam. The oral exam covers the topics presented during the lessons and the MATLAB codes developed during the lab sessions. The oral exam can change the grade in any direction: a poor oral part might end up in a failed exam. For students that chose the basic written exam, the maximum grade obtainable can never exceed 24/30.
There are two levels of exam:
1) Basic exam: it consists in a two questions and/or exercises (one easy and one medium difficulty), intended to verify the knowledge of numerical algorithms and the capability of applying them, without the need for a deep understanding. The maximum grade is 24/30.
2) Advanced exam: it consists in a couple questions (one medium difficulty and one theoretical-oriented), intended to verify comprehension of the subjects and not just a mere application of ready-to-use formulas. The answers must be articulated with a certain mathematical precision. The maximum grade is 30/30 cum laude.
Oral exam is not compulsory. However, students who got a positive grade in the written part (i.e., at least 18/30) might choose to take an oral exam. The oral exam covers the topics presented during the lessons and the MATLAB codes developed during the lab sessions. The oral exam can change the grade in any direction: a poor oral part might end up in a failed exam. For students that chose the basic written exam, the maximum grade obtainable can never exceed 24/30.
Texts
Teacher' slides. For more material see: A. Quarteroni, R. Sacco, F. Saleri . Numerical Mathematics-2nd edition. Springer Series: Texts in Applied Mathematics, Vol. 37 (2007).
Contents
* Numerical solution of ordinary differential equations.
*Solution of linear systems of equations: direct and iterative methods.
*Nonlinear equations: bisection and Newton's methods. Convergence, order of convergence, stopping criteria.
*Lagrange interpolation: interpolation error, piecewise Lagrange interpolation, order of approximation.
*Least squares method for data fitting: linear regression and various examples.
*Interpolatory quadrature formulas in 1D: midpoint, trapezoidal, Simpson and error analysis. Gaussian formulae.
*Solution of linear systems of equations: direct and iterative methods.
*Nonlinear equations: bisection and Newton's methods. Convergence, order of convergence, stopping criteria.
*Lagrange interpolation: interpolation error, piecewise Lagrange interpolation, order of approximation.
*Least squares method for data fitting: linear regression and various examples.
*Interpolatory quadrature formulas in 1D: midpoint, trapezoidal, Simpson and error analysis. Gaussian formulae.
Course Language
English
More information
Additional information can be found on the web page:
https://mate.unipv.it/sangalli/numerical_methods_eng_sciences.html
https://mate.unipv.it/sangalli/numerical_methods_eng_sciences.html
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