Mathematical Analysis 3

A.y. 2018/2019
9
Max ECTS
89
Overall hours
SSD
MAT/05
Language
Italian
Learning objectives
Understanding the main theoretical aspects related to the arguments of the programme; acquisition of practical
skills related to applied aspects.
Expected learning outcomes
Capability to relate different aspects of the subject, and self-confidence in the use of teh main techniques of
Calculus
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
Sequences and series of functions: pointwise and uniform convergence. Power series: the domain and the
radius of convergence. Abel's theorem. Taylor's series.
Functionals spaces connected with the uniform convergence. A fixed point theorem.
Implicit functions: Dini's theorem in the scalar and vector cases. The inverse function theorem. Constrained
optimization.
First order differential equations: the Cauchy problem, existence and uniqueness of solutions. Differential
equations of higher order. Linear equations.
Curves in R^n: length, integration along curves.
Differential forms, exactness and related results. Curves and differential forms. Conservative fields. Closed and
exact forms. Potentials.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 9
Practicals: 44 hours
Lessons: 45 hours
Professor(s)
Reception:
My office: Dipartimento di Matematica, via Saldini 50, first floor