Continuum Mathematics
A.Y. 2023/2024
Learning objectives
The course is aimed at rigorously providing the basic tools of Mathematical Analysis, in order to provide the basic tools to tackle theoretical and applied problems, which are essential to successfully attend a university undergraduate program in a scientific area.
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. 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.
Lesson period: year
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
year
Course syllabus
The annual course of Continuum Mathematics rigorously presents 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
-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
Homeworks on each topic
Online forum for discussions
Self-assessment online tests
Homeworks on each topic
Online forum for discussions
Self-assessment online tests
Teaching Resources
Web site:
https://matematicacontinuo.ariel.ctu.unimi.it
Reference book:
1) G. Anichini, G. Conti, M. Spadini, Analisi Matematica 1, 3rd Edition, Pearson.
Other useful references:
2) P. Marcellini, C. Sbordone, Elementi di Analisi Matematica 1, Liguori Editore.
3) G. Catino, F. Punzo, Esercizi svolti di Analisi Matematica e Geometria 1 (Additional exercises).
https://matematicacontinuo.ariel.ctu.unimi.it
Reference book:
1) G. Anichini, G. Conti, M. Spadini, Analisi Matematica 1, 3rd Edition, Pearson.
Other useful references:
2) P. Marcellini, C. Sbordone, Elementi di Analisi Matematica 1, Liguori Editore.
3) G. Catino, F. Punzo, Esercizi svolti di Analisi Matematica e Geometria 1 (Additional exercises).
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 use of notes, books or calculator is not allowed during the exam.
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. Results will be communicated on the SIFA through the UNIMIA portal.
The use of notes, books or calculator is not allowed during the exam.
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. Results will be communicated on the SIFA through the UNIMIA portal.
MAT/01 - MATHEMATICAL LOGIC
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 48 hours
Lessons: 64 hours
Lessons: 64 hours
Educational website(s)
Professor(s)
Reception:
Wednesday 15:30-16:30 or by appointment
Math Department in via C. Saldini 50. Office: 1.007
Reception:
By appointment (to be agreed upon via email)
Room 2102, Dipartimento di Matematica "F. Enriques", Via Saldini 50