Course Details
Name:
Analisi Matematica / Mathematical Analysis
Basic information
Credits:
Bachelor Degree in Computer Science: 9 Ects (a)
Degree(s):
Compulsory 1^{st} year Bachelor Degree in Computer Science curriculum General
Language:
Italian
Course Objectives
To give students a rigorous understanding of the theory of real and vectorvalued functions. Students will acquire an understanding of basic properties of the field of real numbers, concepts of infinity, limits of functions and methods for calculating them, continuity, differentiation, integration and Taylor series.
Course Content
 Set theory (basic notations and concepts), real numbers (basic properties, order, completeness), mathematical induction
 Sequences and series (convergence, divergence and irregularity, convergence criteria)
 Functions (injectivity, surjectivity, invertibility, composition)
 Limits (basic definitions, the Sandwich Rule, boundedness)
 Continuity (basic definitions, the Intermediate Value Theorem, numerical methods for solving equations)
 Differentiation (basic definitions, rules and properties, Rolle’s Theorem, the Mean Value Theorem), L’Hopital’s Rule (techniques and applications), Taylor’s Theorem (polynomial approximations to functions, convergence criteria for Taylor series)
 Integration (basic properties, the Riemann definition, the Fundamental Theorem of Calculus, integration by parts and substitution, improper integrals)
 Limits and continuity of functions of several real variables (basic techniques, polar coordinates)
 Differentiation of real and vectorvalued functions of several real variables (partial derivatives, gradient, differential, Jacobi matrix)
 Integration of real functions of several real variables (simple domains, FubiniTonelli's Theorem, integration by substitution)
Learning Outcomes (Dublin Descriptors)
On successful completion of this course, the student should

have a good knowledge and understanding of basic properties of real numbers, functions; demonstrate an understanding of basic topics in the analysis of functions, including limits, continuity, differentiation, TaylorMacLaurin series, and integration;
 be able to apply his knowledge and understanding to tackle basic problems from applied mathematics and engineering; understand formal mathematical definitions and theorems, and apply them to prove statements about functions;
 demonstrate skills in mathematical reasoning and ability to conceive a proof;
 be able to explain the main notions and results of mathematical analysis;
 demonstrate capacity to read and understand advanced texts.
Prerequisites and Learning Activities
Basic mathematical notions and methods as learnt at high school
Teaching Methods
Language: Italian
Lectures and exercise classes
Assessment Methods and Criteria
Written and oral exam
Textbooks
 Klaus Engel, Appunti del Corso di Analisi Matematica. http://people.disim.univaq.it/~klaus.engel/ana1.pdf
 A.Marson, P.Baiti, F.Ancona, B.Rubino, Corso di Analisi Matematica 1. Carocci.
 P.Marcellini, C.Sbordone, Esercitazioni di Matematica. Liguori.
 S.Salsa, A.Squellati, Esercizi di Matematica. Zanichelli. (vol. 1)
 M.Bramanti, C.D.Pagani, S.Salsa, Matematica. Zanichelli.
Online Teaching Resources
Course page updates
This course page is available (with possible updates) also for the following academic years:
Course information last updated on: 05 settembre 2016, 13:54