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 module 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

Basic school skills about numerical sets, equations and inequalities, analytical geometry, trigonometry.

TEACHING METHODS

Lecture classes and exercise classes.

Students having disabilities or Specific Learning Disorders can request suitable aids for the examinations. Such aids will be defined according to specific needs, together with the Referent for the Polytechnic School of the Committe for the inclusion of Students with Disabilites and with SLD. Students in such conditions are invited to get in touch (via e-mail) with the Teacher a sufficient time before the examination, inserting in copy the Referent for the Polytechninc School

1) for Electrical Engineering prof. Silvana Dellepiane - silvana.dellepiane@unige.it

2) for Chemical Engineering or Civil, Construction and Environmental Engineering prof. Federico Scarpa - federico.scarpa@unige.it

(https://unige.it/en/commissioni/comitatoperlinclusionedeglistudenticondisabilita.html), without sending any document about their disabilites.

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 infimum. 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 their applications.

RECOMMENDED READING/BIBLIOGRAPHY

Specific guidelines on the reference bibliography will be provided by the professor at the beginning of the course.

In general, lecture notes and the materials available for download from the course webpage are sufficient for exam preparation.

More specifically, the following materials may be useful:

• Professor Maurizio Romeo's theory handouts, available for free download from the course's AulaWeb page;
• Worksheets containing links to webpages with various solved exercises, available for free download from the course's AulaWeb page;
• C. Canuto, A. Tabacco, Analisi Matematica 1, 4th edition, Springer-Verlag Italia, 2014;
• M. Baronti, M., F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, Springer International Publishing Switzerland, 2016.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Class schedule at https://corsi.unige.it/corsi/11879/studenti-orario

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. 



FURTHER INFORMATION

Ask the professor for other information not included in the teaching schedule