The aim of this course is to provide the basic elements of differential calculus for functions of one variable.
The unit provides some basic concepts of mathematical analysis and the first elements of differential calculus for functions of one variable
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.
Numerical sets, equations and inequalities, analytic geometry, trigonometrey.
Lecture classes and exercises classes.
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.
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.
Ricevimento: On appointment; take directly an appointment with the professor or write to perelli@dima.unige.it
ALBERTO PERELLI (President)
MARCO BARONTI
ROBERTUS VAN DER PUTTEN
Lessons start when first semester starts.
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.
The test aim at verify the ability of students in performing short computations and simple deductive reasonings.
On the AulaWeb page of the course you can find the text of previous written examnations and lists of exercises.
