- Docente: Otto Edwin Liess
- Credits: 14
- SSD: MAT/05
- Language: Italian
- Moduli: Giovanni Dore (Modulo 1) Otto Edwin Liess (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Learning outcomes
The course is a continuation of the course onmathematical analysis
of the first semester.
At the end of the course the student should have acquired the basic
notions regarding the differential and integral calculus
Course contents
First semester (taucht by Giovanni Dore)
Preliminary notions on sets, equivalence relations,
functions.
The real numbers, sup and inf of sets of real numbers, NAtural and
rational numbers. Induction,
Infinite sets. The basic elementary functions.
Complex numbers. The topology of R and C. Limits and continuity of
real valued functions.
Second semester (taught by Otto Liess) The differential calculus of
real valued functions on the real line. Monotonicity.
The main emphasis will be on integration theory in one variable:
the Riemann integral. The fundamental theorem of the calculus.
Generalized integrals. Numerical series. Metric spaces. The
n-dimensional euclidean space. The topology in R^n:
compact sets in R^n, connectivity in the euclidean setting.
Readings/Bibliography
E.Giusti, E.Lanconelli, Pagani-Salsa, Analisi I, W.Rudin: Real and complex analysis
Teaching methods
books and written notes
Assessment methods
written and oral exam
Teaching tools
oral lectures, exercize classes
Office hours
See the website of Otto Edwin Liess
See the website of Giovanni Dore