MATHEMATICAL ANALYSIS 1A

CODE	118126
ACADEMIC YEAR	2025/2026
CREDITS	6 cfu anno 1 INGEGNERIA BIOMEDICA 11878 (L-8 R) - GENOVA 6 cfu anno 1 INGEGNERIA ELETTRONICA E TECNOLOGIE DELL'INFORMAZIONE 11911 (L-8 R) - GENOVA
SCIENTIFIC DISCIPLINARY SECTOR	MAT/05
LANGUAGE	Italian
TEACHING LOCATION	GENOVA
SEMESTER	1° Semester

OVERVIEW

The aim of the course is to provide the basic elements of differential calculus for functions of one variable

AIMS AND CONTENT

LEARNING OUTCOMES

The course provides some basic concepts of mathematical analysis and the first elements of differential calculus for functions of one variable

AIMS AND LEARNING OUTCOMES

The main expected learning outcomes are

to master the mathematical notation
the knowledge of the properties of the main elementary functions
the ability to follow the logical concatenation of arguments
to master simple demonstration techniques
the ability to solve exercises, discussing the reasonableness of the results

PREREQUISITES

Numerical sets, equations and inequalities, analytical geometry, trigonometry.

TEACHING METHODS

Lecture classes and exercise classes.

As part of the innovation learning project novel tools will be used for the active learning of students. The goal is to increase students' skills via interactive, experience-based, learning methodologies (e-learning, teamwork, etc.) for enhanced participation, using an advanced level of communication that makes the student more aware and autonomous

SYLLABUS/CONTENT

Real numbers, the oriented real line. The Cartesian plane, graphs of elementary functions. Operations on functions and their graphical interpretation. Monotonicity. Composition and inversion. Powers, exponentials and logarithms. Supremum and infimunm. Numerical sequences: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global properties. Derivatives and derivation rules. Derivatives of elementary functions. Sign of derivatives in the study of monotonicity and convexity. The classical theorems of Rolle, Cauchy, Lagrange and de l'Hôpital. Study of the graph of functions. Taylor expansions and theoir applications.

TEACHERS AND EXAM BOARD

MARCO BARONTI

Ricevimento: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed on February 2025. The e - mail address is : marco.baronti@unige.it

FILIPPO DE MARI CASARETO DAL VERME

Ricevimento: Weekly office hours, typically 2-hours per week, will be communicated. Meetings upon E-mail requests will also be considered compatibly with the teacher's availability.

LESSONS

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of

Multiple choice test
Written exam

To enroll the exam you must register by the deadline on the website
https://servizionline.unige.it/studenti/esami/prenotazione

ASSESSMENT METHODS

Multiple choice tests. It is aimed to verify the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It is necessary to be successful in the multiple choice test in order to access the written exam

Written exam. This part includes open questions and exercises. It is aimed to verify the knowledge of the main tools of differential calculus. The written exam consists of exercises with several questions of different difficulty. The student must be able to solve the exercises correctly and to justify the necessary steps to obtain the final result, and to use the correct formalism.