- Docente: Enrico Obrecht
- Credits: 3
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)
Learning outcomes
Holomorphic functions and Hilbert space theory, in particular orthonormal systems.
Course contents
HILBERT SPACES. Definitions and examples of normed and Hilbert spaces. Complete orthonormal systems. Linear operators between normed spaces and between Hilbert spaces. Elements of spectral analysis for linear bounded operators in a Hilbert space.
HOLOMORPHIC FUNCTIONS OF A COMPLEX VARIABLE. Differentiability, Cauchy-Riemann equations, complex integration, Cauchy and deformation theorems, analyticity of holomorphic functions, isolated singular points of a holomorphic function and residues, computation of integrals by residue theorem. Laurent series and application to zeta transform.
Readings/Bibliography
Barozzi: Matematica per l'Ingegneria dell'informazione, Zanichelli.
Further bibliographic material will be given during the
lessons.
Teaching methods
The course consists of lessons describing the fundamental concepts of complex functions of one complex variable and of Hilbert spaces. Lessons are completed with examples and counterexamples illuminating the theoretical content. Futhermore several exercises are solved in the classroom.
Assessment methods
The course is integrated with Numerical Methods. The assessment of knowledge is verified by an oral examination, requiring the comprehension of the fundamental concepts and solving some exercises.
Teaching tools
None
Office hours
See the website of Enrico Obrecht