Topics of Analysis

Cod: 22214

Department: DCET

Department: DCET

ECTS: 5

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 130

Total contact time: 20

Total contact time: 20

Banach spaces

Hilbert spaces

Linear operators

- Differential calculus and the Riemann integral (Review)
- The Lebesgue integral
- Normed and Banach spaces
- Inner product spaces and Hilbert spaces
- Linear operators in Banach spaces and some fundamental theorems
- Duality. Hahn-Banach theorem
- Linear operators in Hilbert spaces

**Compulsory Reading **

B.P. Rynne, M.A. Youngson: Análise Funcional Linear, Coleção Ensino da Ciência e da Tecnologia, vol. 39, IST Press, Lisboa, 2011 https://istpress.tecnico.ulisboa.pt/produto/analise-funcional-linear/

**Optional Reading **

Erwin Kreyszig; Introductory Functional Analysis with Applications, Wiley Classics Library, Wiley, New York, 1989

E-learning

**Pre-requisites: **Students are recommended to have previously knowledge in the Linear Algebra curricular units, in the Elements of Infinitesimal Analysis curricular units and in the Topology curricular unit of the 1^{st} cycle degree course on Mathematics and Applications (Universidade Aberta).