Teaching code

4S004792

Academic staff

Giacomo Albi, Marco Caliari

Coordinator

Giacomo Albi

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/08 - NUMERICAL ANALYSIS

Period

Semester 2 dal Mar 3, 2025 al Jun 13, 2025.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The course will discuss, from both the analytic and computational points of view, the principal basic numerical methods for the solution of nonlinear equations, linear systems, polynomial data fitting and numerical quadrature. The course has a Laboratory component where the methods studied will be implemented using the MATLAB programming platform (using either the official Matlab from Mathworks or else the open source version GNU OCTAVE). At the end of the course the student will be expected to demonstrate that s/he has attained a level of competence in the computational and computer aspects of the course subject, as well as the ability to recognize which algorithms are appropriate for basic problems of numerical analysis.

Prerequisites and basic notions

Linear algebra, differential calculus in one variable, integral calculus.

Program

The course will discuss the following topics:
* Methods for finding zeros of functions (bisection, secant, Newton and its variants)
* Floating point numbers and error theory
* Methods for solving linear systems (conditioning, Gaussian elimination, LU factorization, Cholesky factorization, matrix norms)
* Polynomial interpolation and piecewise linear interpolation
* Quadrature rules, simple and composite (Rectangle Rule, Trapezoidal Rule, Simpson’s Rule, Romberg extrapolation)
It is expected that there will be a tutor with the Laboratory sessions.

Bibliography

Didactic methods

The teaching will be delivered in 52 classroom hours, of which 20 in the computer lab.

Learning assessment procedures

The purpose of the exam is to see if the student is able to recall and reproduce the theory of basic Numerical Analysis and knows how to use Computer resources for possible further investigation. Moreover, the student must show that s/he knows how to program in the specific software introduced during the course. The exam will consist of two parts. The first part will be held in a Laboratory where the student will be given two hours to individually implement the numerical methods necessary for the solution of the assigned questions. The questions will be based on the entire course material. A pass will be given for a mark of 18/30 or higher. To be admitted to the second part of the test, oral, it is necessary to have passed the written part in the same examination session. The oral examination involves a discussion of the topics covered during the theory lecture hours. If the oral examination is not passed or taken, the grade for the written is cancelled at the end of the session. The final grade is given by the average of the grades of the two tests.

Evaluation criteria

To pass the exam you will have to demonstrate:
* knowing and understanding the fundamentals of machine numbers
* knowing and understanding the fundamental methods of numerical solving of nonlinear equations
* knowing and understanding the fundamental direct methods of numerical solving of systems linear
* know and understand the methods for polynomial approximation
* know and understand the classical methods of numerical quadrature
* have an adequate capacity for analysis and synthesis and abstraction
* know how to apply this knowledge to solve problems and exercises, knowing how to argue his reasoning with mathematical rigor.

Criteria for the composition of the final grade

The final grade is the average of the scores for the laboratory and the oral exam.

Exam language

italiano

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