- Docente: Luca Migliorini
- Credits: 7
- SSD: MAT/03
- Language: Italian
- Moduli: Luca Migliorini (Modulo 1) Sergio Venturini (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
At the end of the course the student knows the main facts of complex analysis in one variable, with an emphasis on its geometric content. He is able to apply this knowledge to toher fields of Mathematics and to solve simple problems arising form applied science
Course contents
Examples of complex functions. Polynomials, rational linear transformations, exponential, logarithm, trigonometric functions. Holomorphic functions, Cauchy Riemann equations. Curvilinear integral of a holomorphic function. Cauchy Theorem, Cauchy formula. Liouville theorem. Development in power series of a holomorphic function.Singularities of holomorphic functions. Poles, essential singularities. Weiestrass theorem on the behaviour of a function near an essential singularity. Meormorphic functions. The residue theorem. Examples of use of the residue theorem to compute definite integrals. A few words on Riemann mapping theorem, Montel theorem, and elliptic functions.
Readings/Bibliography
Theodore Gamelin: Complex Analysis.
Springer UTM
Teaching methods
Lectures at the blackboard
Assessment methods
Oral exam
Office hours
See the website of Luca Migliorini
See the website of Sergio Venturini