Continuum mathematics

A.Y. 2019/2020
12
Max ECTS
120
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The aim of the course is to provide the basic tools of Mathematical Analysis, both from a theoretical and practical point of view, which are essential to successfully attend a university undregraduate program in a scientific area. The course will propose the required mathematics prerequisites for the other courses of the program.
Expected learning outcomes
At the end of the course students should prove to have a sufficient knowledge of basic mathematics (set theory, real and complex numbers, elementary functions). Moreover students will be required to deepen the basic results in the theory of differential and integral calculus for functions of one real variable. Finally students will be able to state the main results and replicate some of the proofs presented during the course. One of the main skills which will be tested is the application of the theoretical results to solve elementary problems and exercises concerning topics presented in the course.
Course syllabus and organization

Single session

Responsible
Lesson period
First year
Course syllabus
The aim of this course is to rigorously present some classical topics of Mathematical Analysis which are a necessary prerequisite to any scientific degree.
-Preliminary practical aspects of Mathematics: review of elementary functions and their use in solving equations and inequalities.
-Preliminary theoretical aspects of Mathematics: set theory, sup/inf of a set, cardinality
-Complex numbers
-Sequences of real numbers
-Series of real numbers
-Real functions
-Limits and continuity
-Derivatives and differentiability
-Riemann Integral
Prerequisites for admission
No prerequisite
Teaching methods
Taught lectures
Teaching Resources
Web site:
https://matematicacontinuo.ariel.ctu.unimi.it

Reference book:
P. Marcellini, C. Sbordone, Elementi di Analisi Matematica 1, Liguori Editore (Versione semplificata per i nuovi corsi di laurea)

Suggested workbook:
G. Catino, F. Punzo, Esercizi svolti di Analisi Matematica e Geometria 1.
Assessment methods and Criteria
Written exam composed by exercises and theoretical questions on the topics developed during the course. The evaluation ranges out of thirty and is aimed at verifying the understanding of the theoretical notions and their application in specific cases of study.
The duration of the written test is commensurate with the number and structure of the assigned exercises, but in any case will not exceed 3 hours. There are 4 intermediate tests that replace the written exam. Results will be communicated on the SIFA through the UNIMIA portal.
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 72 hours
Lessons: 48 hours
Professor(s)
Reception:
On appointment
Department of Mathematics, office number 1005