OVERVIEW

Numerical Calculus is a part of Applied Mathematics. The course provides students with the algorithms and mathematical tools to solve, in practice, some of the most common mathematical problems, such as computing the solution of even medium-sized linear systems, approximating the zeros of a function, interpolating sets of points using polynomials. Particular attention is paid to issues related to the solution of these problems through the use of a computer.

AIMS AND CONTENT

LEARNING OUTCOMES

Knowledge and understanding of fundamental concepts and elements of numerical analysis. Particular emphasis is given to understanding the numerical aspects of problem solving, such as conditioning and stability, and to understanding the concept of approximate solution as a means of solving real problems.

AIMS AND LEARNING OUTCOMES

The purpose of the "Calcolo Numerico" course is to illustrate to the student a different point of view on mathematics, much more applied, providing the main tools to be able to calculate, in practice, the solution of some of the most common mathematical problems, such as the computaion of zeros of a function, polynomial interpolation and the solution of linear systems. The topics presented illustrate how mathematics, generally considered a set of abstract concepts, shows to be a useful tool for solving problems deriving from the observation of real phenomena or from laboratory analyses.

At the end of the course the student will have acquired theoretical knowledge concerning the various solution methods presented, with particular attention to the study of the stability of the algorithms, to the conditioning of the problems and to the techniques of approximation of the solutions through iterative methods. Specifically, the student will be able to: • know the main algorithms for solving some of the most frequent mathematical problems (linear systems, zeros of function, interpolation) • deduce the conditioning properties of problems • choose the most suitable solution algorithm, according to the stability study • reason critically on the results provided by an algorithm to identify any critical issues due to the use of a computer.

Furthermore, thanks to innovative teaching techniques, the student will acquire personal competence (identify one's own abilities, concentrate, manage complexity, reflect critically, make decisions, work independently, manage stress) and the ability to "learn to learn " (organizing and evaluating one's own learning).

PREREQUISITES

Basic mathematical knowledge, which is the normal cultural baggage of a student who has finished the cycle of higher education, such as equations, inequalities, analytic geometry, the concept of function, is necessary to effectively address the teaching contents.

TEACHING METHODS

The course consists of 4 CFU, corresponding to 16 frontal lessons (2 hours each for a total of 32 hours) carried out by the teacher in the classroom. The exposed theory is applied to various examples, through the resolution of exercises.

Thanks to his own personal work, the student will have to acquire the knowledge and concepts underlying Numerical Calculus and be able to solve exercises. Personal preparation is completed by the quizzes available on Aulaweb, to be answered outside class hours and repeatable several times. This tool, innovative compared to traditional teaching, is a valid aid in developing the ability to solve exercises independently and within pre-set time limits, thus developing personal competence. The quizzes are also a valid tool for self-assessment (ability to learn to learn), as they allow you to test your level of preparation whenever you feel the need.

SYLLABUS/CONTENT

Content:

• Vectors and matrices
• Vectro and matrix norm
• Linear systems
• Condition number
• Overdetermined systems
• Regression
• Errors, sensitivity and stability
• Zeros of a function
• Polynomial Interpolation

RECOMMENDED READING/BIBLIOGRAPHY

The theory exposed during the course is illustrated, with examples, on the slides, written by the teacher, available on Aulaweb.

As a valid help in understanding how to carry out exercises similar to the written exam, the following book is recommended:

Claudia Fassino: "Esercizi svolti di Calcolo Numerico", Societa` Editrice Esculapio, 

available in paper version or online on the editrice-esclapio.com website

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

From February 2025

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written and an oral part. The writte part consists of exercises related to the theory, similar to the examples illustrated in class. The written test must be carried out before the oral exam and must be taken in the same session in which the student intends to take the oral exam.

To access the written exam, the student must have obtained a pass in all the quizzes on Aulaweb. This eligibility does not expire. To access the oral exam, students must have passed the written exam with a minimum mark of 18/30 and the mark obtained will be used in the final assessment.

There will be 2 exam sessions available for the winter session (mid-January-February) and 3 exam sessions for the summer session (June, July and September). Extraordinary exam sessions will not be granted outside the periods indicated in the study course regulations, with the exception of non-course students.

Students with DSA, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods which, in compliance with the teaching objectives, take into account the learning methods individuals and provide suitable compensatory instruments.

ASSESSMENT METHODS

Details on how to prepare  the exam and on the degree of detail of each topic will be given during the lessons. The written exam will verify the effective acquisition of the basic knowledge of Numerical Calculus: the exercises will allow assessing the ability to apply theoretical concepts to specific problems. The oral exam will mainly focus on the topics covered during the lectures and will aim to evaluate not only if the student has reached an adequate level of knowledge, but if he/she has acquired the ability to explain mathematical concepts (definitions, theorems and proofs) in clearly and in correct terminology.

Exam schedule

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.