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ELEMENTI DI MATEMATICA E STATISTICA - FISICA M - Z
Module ELEMENTI DI MATEMATICA E STATISTICA

Academic Year 2023/2024 - Teacher: PAOLO FALSAPERLA

Expected Learning Outcomes

The course aims to introduce the student to the basic concepts of calculus and the theory of functions of a real variable, with elements of analytical geometry. The student must be able to apply methods and basic concepts of probability and statistics to data analysis.

Course Structure

The course will take place through lectures with exercises

To students with disabilities and/or SLD:
To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and / or dispensatory measures, based on the didactic objectives and specific needs.
It is also possible to contact the referent teacher CInAP (Center for Active and Participatory Integration - Services for Disabilities and / or SLD) of our Department, Prof. Teresa Musumeci.

Required Prerequisites

Notions of algebra and basic geometry

Attendance of Lessons

Attendance is mandatory as required by the regulations. http://www.dsf.unict.it/corsi/l-29_sfa/regolamento-didattico

Detailed Course Content

Basic concepts of set theory (union, intersection, function, injective and surjective function). Rational and real numbers. Numerical sets, extremes and intervals. Real functions of real variable and their Cartesian representation. Composite and inverse functions. Equation of a line, parallelism, perpendicularity. Trigonometric functions, powers, exponentials, logarithms. Limit of a function, continuity, differentiability. Use of derivatives: monotonicity, convexity and limits. Determination of extremes.
Computation of concentration and dilution factors.
Fundamental concepts of statistics. Evaluation of statistical parameters. Linear regression. Use of logarithmic graphs. Distribution and probability density. Some significant distributions.

Textbook Information

[T] Teacher's notes

[MS] Marcellini, P., & Sbordone, C. (2002). Elementi di Analisi Matematica uno. Liguori Editore, ISBN: 8820733838.  

[E1] Marcellini, P., & Sbordone, C. (2013). Esercitazioni di Matematica. Vol 1 pt. 1. Liguori Editore, ISBN: 8820763510.  

[E2] Marcellini, P., & Sbordone, C. (2013). Esercitazioni di Matematica. Vol 1 pt. 2. Liguori Editore, ISBN: 8820752521.  

[G] Statistica, Lezioni ed esercizi, M.Garetto, freely available. https://www.dmi.unict.it/falsaperla/didattica/garetto_statistica.pdf

Course Planning

 SubjectsText References
1Sets, functions, calculus[T] [MS] [E1] [E2]
2Statistics[T] [G]
3Concentration and dilution factors[T]

Learning Assessment

Learning Assessment Procedures

Written and oral exam.
Information for students with disabilities and/or SLD:
To guarantee equal opportunities and in compliance with the laws in force, interested students can ask for a personal interview in order to plan any compensatory and / or dispensatory measures, based on the didactic objectives and specific needs.
It is also possible to contact the referent teacher CInAP (Center for Active and Participatory Integration - Services for Disabilities and / or SLD) of our Department, Prof. Teresa Musumeci.

Examples of frequently asked questions and / or exercises

Determination of the domain, symmetries and periodicity of functions.
Determination of the asymptotes of a function.
Calculation of derivatives, maximum and minimum, concavity and convexity of a function. 

Determination of simple statistical parameters (mean, median, mode, variance). Calculation of discrete probabilities.