500300 - Calculus and topics in Statistics (A-L)

courses

ID:

500300

Duration (hours):

48

CFU:

SSD:

ANALISI MATEMATICA

Year:

2025

Date/time interval

Secondo Semestre (02/03/2026 - 19/06/2026)

Course Objectives

Knowledge of the basic notions and tools in Calculus and Statistics. Proficiency in using these tools to understand and study the graph of a function. Proficiency in applying these tools to the study of experimental phenomena and to the correct interpretation of data.

Course Prerequisites

Basic mathematical notions provided by italian superior school.

Teaching Methods

The course is organized with lectures and exercises. The teachers will provide dedicated slides with the materials used in class on the KIRO platform of the course. For students with specific needs, who cannot attend the teaching activities in person and who have applied for inclusive teaching methods, it will be possible to organize, upon request, some dedicated online meetings, with flexible schedules depending on the needs.

Assessment Methods

Written exam (mandatory), consisting of two parts. The highest possible score for the module is 27/30 if it is not complemented by the oral exam. The first part is a preliminary screening section to be completed in a short time, featuring multiple-choice questions or questions where only the final answer is assessed. The second part includes standard exercises and lasts approximately 2 hours. The oral exam is optional and can only be taken after passing the written exam. The module “Mathematics with Elements of Statistics” (6 CFU) is part of the course “Mathematical and Physical Sciences” (12 CFU). Credits will only be officially awarded to students upon successful completion of both modules of the course (“Physics” and “Mathematics with Elements of Statistics”). Appropriate exam arrangements are available for students eligible under the categories of Specific Learning Disorders (DSA, in italian) and Special Educational Needs (BES, in italian).

Texts

M. Abate "Matematica e Statistica, le basi per le scienze della vita" McGraw-Hill D. Benedetto, M. Degli Esposti, C. Maffei "Matematica per le scienze della vita", terza edizione, Casa Editrice Ambrosiana V. Villani, G. Gentili "Matematica - Comprendere e interpretare fenomeni delle scienze della vita", quinta edizione, McGraw-Hill

Mathematics: Number sets. Percentages and concentrations. Real functions of real variable: graph, domain, range. Properties of functions: injective, surjective and bijective functions, even and odd functions, monotone functions. Relative and absolute maximizers and minimizers. Composition of functions. Inverse function. Operations on functions. Translations, dilations, reflections. Elementary functions: linear functions, absolute value, power functions, exponential and logarithmic functions, trigonometric functions. Notion of limit and its properties. Continuous functions. Definition of derivative. Tangent line. Derivatives of elementary functions. Derivation rules. Monotonicity criterion. Maximum and minimum problems. Convex functions. Study of the graph of a function. Models of population growth. Primitives and elementary integral calculus. Statistics: Mean value, geometric mean, median, and mode for a frequency distribution. Frequency histogram and frequency polygon. Cumulative frequency graph. Data dispersion: variance and standard deviation of a frequency distribution. Quartiles, interquartile range. Statistical distributions with emphasis on the normal distribution. Fundamental properties of the gaussian distribution. Central limit theorem and confidence intervals.

Course Language

Italian

More information

Student consultation by appointment. For more information, please refer to the course's KIRO page. For students with specific needs who are unable to attend in-person teaching activities and who have applied for inclusive teaching methods, it will be possible to arrange dedicated online meetings upon request, with flexible scheduling based on individual needs.