OVERVIEW

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

AIMS AND CONTENT

LEARNING OUTCOMES

The unit 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 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;

- the ability to solve elementary exercises.

PREREQUISITES

Numerical sets, equations and inequalities, analytic geometry, trigonometrey.

TEACHING METHODS

Lecture classes and exercises classes.

SYLLABUS/CONTENT

Real numbers, the real plane, graphs and elementary functions. Operations on functions and their graphical interpretation. Monotonicity, composition and inversion. Supremum and infimum. Numerical sequences. Limits of functioins, infinitesimal and infinite functions. Continuous functions and their local and global properties. Derivatives, differentiation rules and elementary derivatives. Sign of derivatives and study of monotonicity and convexity. Theorems of Rolle, Lagrange e de L'Hopital. Study of the graph of functions. Taylor expansions and their applications.

RECOMMENDED READING/BIBLIOGRAPHY

M.Baronti, F. De Mari, R. van der Putten, I.Venturi - Calculus Problems - Springer International, 2016.

C. Canuto, A. Tabacco - Analisi Matematica 1 - Springer Italia, 2014.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

Lessons start when first semester starts.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written examination by tests with multiple answers. To participate to a written exam you must register on the specific Unige web site at least 7 days before the date of the exam.

ASSESSMENT METHODS

The test aim at verify the ability of students in performing short computations and simple deductive reasonings.

FURTHER INFORMATION

On the AulaWeb page of the course you can find the text of previous written examnations and lists of exercises.