cod. 1008737

Academic year 2022/23
1° year of course - Second semester
- Sebastiano DI MAIOLO
Academic discipline
Analisi matematica (MAT/05)
Matematica, informatica e statistica
Type of training activity
72 hours
of face-to-face activities
9 credits
course unit

Learning objectives

Knowledge and understanding:
At the end of this course the student should know the essential definitions
and results in analysis in one variable, and he should be able to grasp how
these enter in the solution of problems.

Applying knowledge and understanding:
The student should be able to apply the forementioned notionsto solve medium
level problems, and to understand how they will be used in a more applied

Making judgements:
The student should be able to evaluate coherence and correctness of the
results obtained by him or presented him.

Communication skills:
The student should be able to communicate in a clear and precise way, also
in a context broader than mere calculus.


Elementary algebra, elementary equation and inequality, elementary logic

Course unit content

Integral and differential calculus

Full programme

PREREQUISITES: elementary algebra, trigonometry, analytic geometry, rational powers, exponentials and logarithms; elementary functions.

LOGIC: propositions and predicates, sets, functions, order relations and equivalence.

NUMERICAL SETS: natural numbers and the principle of induction, integers, rational, real numbers.
REAL FUNCTIONS: extrema of real functions, monotone functions, even and odd functions, powers, absolute value, trigonometric functions, hyperbolic functions, graphs of real functions.
SEQUENCES: overview of topology, sequences and their limits; comparison theorems and algebraic theorems, continuity, monotone sequences, key examples, the number of Napier; recursively defined sequences (overview).
CONTINUOUS FUNCTIONS: limits of functions, continuity, first properties of continuous functions, continuous functions on an interval (zeros, intermediate values​​); Weierstrass theorem, infinitesimals.
DERIVATIVES: definition of the derivative, the first properties; algebraic operations on derivatives, derivatives and local properties of functions; theorems of Rolle, Lagrange, Cauchy; indeterminate forms, de l'Hôpital theorem, Taylor's formula and various remains, asymptotic developments; functions convex qualitative study of functions.
INTEGRATION: construction and first properties of the integral, primitive, fundamental theorem of integral calculus, methods of integration.


• Enrico GIUSTI “Analisi matematica vol.1” Boringhieri
• Emilio ACERBI, Giuseppe BUTTAZZO “Analisi matematica ABC.
1-Funzioni di una variabile” Pitagora

Testi di esercizi
• V. DEMIDOVICH “Esercizi e problemi di Analisi Matematica”
Editori Riuniti.
• Enrico GIUSTI “Esercizi e complementi di analisi matematica vol.1”

• Domenico MUCCI “Analisi matematica - Esercizi 1. Funzioni di
una variabile” Pitagora

Teaching methods

Frontal lesson, exercise to little groups, use of tablet PC

Assessment methods and criteria

The examination is both written and oral.
In the written part, the student will show his basis knowledge and his ability in solving some particular paroblem. In the oral part, the student will show his knowledge of the foundamental theorems of Mathematical Analisys 1. The oral exposition must be done using a proper mathematical formalism.

Other information

The lessons, in pdf format, can be downloaded from my webpage.