
Course unit
MATHEMATICAL ANALYSIS 1 (Numerosita' canale 3)
IN10100190, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Basic courses 
MAT/05 
Mathematical Analysis 
12.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
12.0 
96 
204.0 
No turn 
Prerequisites:

Solid knowledge of the fundamental results of differential and integral calculus for real functions of one variable. 
Target skills and knowledge:

Learning essential elements of infinitesimal, differential and integral calculus. 
Assessment criteria:

Written test comprising a part of exercises and a part of theory. 
Course unit contents:

Real numbers. Functions. Induction. Inf, sup, max, min.
Sequences: definition, limit, limit operations. Main theorems about sequences.
Functions: definition, limit, limit operations. Main theorems about continuous functions.
Derivatives: definition, geometrical meaning, operations with derivatives.
Applications of derivatives. Relative max and min. Fermat, Rolle, Lagrange theorems. Monotone functions. Convex functions.
Taylor formula and its use in order calculate limits.
Definite and indefinite integrals. Integration's methods. Integral function and main theorem about the integral function.
Numerical series and their convergence.
Introduction to differential equation. 
Planned learning activities and teaching methods:

Frontal lessons on the blackboard. Proposed weekly exercises. 
Textbooks (and optional supplementary readings) 

Giusti, Enrico, Analisi matematica 1Enrico Giusti. Torino: BollatiBoringhieri, 2002.

Giusti, Enrico, Esercizi e complementi di analisi matematicaEnrico Giusti. Torino: Bollati Boringhieri, 1991.


