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

To provide the fundamentals of differential calculus in one variable and the operational knowledge of some basic mathematical tools, while maintaining the necessary methodological rigor.

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

Transversal skills:

Literacy (basic level): Ability to communicate effectively in written and oral form, adaptation of one's communication to the context, use of sources and aids of various kind

PREREQUISITES

Numerical sets, equations and inequalities, analytical geometry in the plane, trigonometry.

TEACHING METHODS

Lecture classes and exercise classes.

For the transversal skills, a problems solving based approach will be used.

We advice working students and students with dysfunctionalities or disabilities or other special educational needs to contact the professor at the beginning of the course in order to devise an adequate teaching method and exams, which are in line with the learning outcomes as well as the individual learning skills.

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 their applications.

RECOMMENDED READING/BIBLIOGRAPHY

• C. Canuto, A. Tabacco, Analisi Matematica 1, 4a edizione, Springer-Verlag Italia, 2014,
• M. Baronti, F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, Springer International Publishing Switzerland, 2016

TEACHERS AND EXAM BOARD

Exam Board

MARCO BENINI (President)

LAURA CAPELLI (President Substitute)

LESSONS

LESSONS START

https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso

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 test: 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.