Study-unit COMPLEX ANALYSIS
| Course name | Mathematics |
|---|---|
| Study-unit Code | A001552 |
| Curriculum | Didattico-generale |
| Lecturer | Carlo Bardaro |
| Lecturers |
|
| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2023/24 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | MAT/05 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Foundations of the theory of complex functions. Analytic functions, Taylor and Laurent'series, line integrals, CAuchy, Morera and Goursat theorems, residues. Conformal mappings and applications |
| Reference texts | 1. Carlo Presilla "Elementi di Analisi Complessa", Unitext, Volume 72, Springer, Second Edition, 2014. 2.2 Bak J, Newman DJ. "Complex Analysis", Springer-Verlag, New York, 1982 3.teaching material prepared by the teacher 4. Further didactical material available in UNISTUDIUM |
| Educational objectives | The student acquires the basic knowledge of complex function theory, for the purpose of a better understanding of the topics present in various courses, and hence the main target is a improvement of the scientific maturation, which is fundamental in order to prepare the student to the reading of advanced mathematical texts. In particular the study of the complex analysis is useful to clarify some aspects of the theory of functions of real variable, as the integral calculus and the convergence of power series.The target is to provide further tools and to develop the ability to solve problems also of an applicative nature |
| Prerequisites | The student must have knowledges of the basic topics from the first two courses of Mathematical analysis, in particular the theory of function of real variables in one and mnore dimension, the theory of line integrals and the differential forms |
| Teaching methods | The course will be held in 42 hours of lessons, with some session of practical exercises, which aim to prepare the students in solving concrete problems |
| Other information | The course is included among the subjects of master's degree in Mathematics, but is strongly suggested for students of the first three years. For students reception: see the website of the Department of Mathematics and Informatics. It ialso possible to carry out consultations with the docent remotely, using Teams. |
| Learning verification modality | the exam consists of an oral discussion lasting about 30-45 minutes, along with the resolution of some exercises. The exam aims to verify the level of understanding of the topics covered, the ability of the student to present the topics clearly and consciously and the skill acquired in solving simple exercises. It is strongly recommended to take the exam after having taken those of Mathematical Analysis II and III. Per informazioni sui servizi di supporto agli studenti con disabilità e/o DSA visita la pagina http://www.unipg.it/disabilita-e-dsa |
| Extended program | references on complex numbers; complex functions of a real variable; complex functions of one complex variable; limits and continuity; some references on the series with complex coefficients; complex derivation and analytic functions; elementary functions; line integrals in complex plane and Cauchy, Morera, Goursat theorems; Taylor and Laurent series; singularities and the residue theory; applications to integral calculus; some notes on conformal mappings; analytic continuation. Riemann surface of the cpmplex logarithm, integral calculus with multi-valued functions |