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Glossary
Semester (Sem)
1First Semester
2Second Semester
AAnnual course
Educational activities
BIdentifying activities
Language
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
  • Soft Skills
Course Details
Context
Academic Year 2015/2016
School School of Industrial and Information Engineering
Name (Master of Science degree)(ord. 270) - MI (487) Mathematical Engineering
Track MCS - Computational Science and Engineering
Programme Year 1

Course Details
ID Code 095958
Course Title REAL AND FUNCTIONAL ANALYSIS
Course Type Mono-Disciplinary Course
Credits (CFU / ECTS) 8.0
Semester First Semester
Course Description Set theory: basic notions, equivalence and order relations, cardinal and ordinal numbers. Axiom of choice. Topological spaces. Metric spaces. Continuous and semicontinuous functions. Measure space and measurable functions. Positive measures and measurable spaces. Lebesgue measure. Abstract integration. Comparison between Lebesgue and Riemann integrals. Convergences. Derivative of a measure and Radon-Nikodym theorem. Fundamental theorems of Calculus. Product measures and Fubini-Tonelli theorem. Normed and Banach spaces: spaces of integrable functions, linear operators, dual spaces and Hahn-Banach theorem, weak convergences, compact operators. Hilbert spaces: scalar product and its consequences, Riesz representation theorem, orthonormal basis, L^2 space and Fourier series, spectral theorem for compact symmetric operators, Fredholm alternative, unbounded linear operators with dense domain.
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU
B
MAT/05
MATHEMATICAL ANALYSIS
8.0

Schedule, add and removeAlphabetical groupProfessorLanguageCourse details
From (included)To (excluded)
--AZZZZGrasselli Maurizio
manifesti v. 3.3.3 / 3.3.3
Area Servizi ICT
06/04/2020