Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT
| MMC0006 | Special Topics in Complex Analysis |
| Teaching Staff in Charge |
Assoc.Prof. ANISIU Valeriu, Ph.D., anisiu math.ubbcluj.ro |
| Aims |
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Basic facts omitted during the main course in the theory of Complex functions and its applications are presented. The emphasis is on problem solving.
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| Content |
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Geometric properties of complex numbers. Geometric transforms.
Using complex numbers in synthetic geometry. The theorems of Ptolemeu, Pompeiu, Angheluţă, D. V. Ionescu Complex analytic Geometry. Insscribed polygons. Euler@s circle, generalizations. Moebius functions. Classifications of Moebius transforms. Models of non-Euclidean geometries (Lobacevski-Poincare). The Axioms. The circle, the elliptic, parabolic and hyperbolic transforms in Poincare@s model. The generalized Schwarz lemma. Sets of holomorphic functions, Montel@s theorem Univalent functions, Hurvitz@ theorem Conformal representation, the Riemann@s theorem. Elements of Geometric function theory. Fractal dimensions, examples. The dynamic of complex mappings. Atractors. |
| References |
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1. G. S. Sălăgean, Geometria planului complex, Promedia-Plus, Cluj-Napoca, 1997
2. P. T. Mocanu, T. Bulboacă, G. S. Sălăgean, Teoria geometrică a funcţiilor univalente, Casa Cărţii de Ştiinţă, Cluj-Napoca, Ed. I, 1999, Ed. II, 2006. 3. P. Hamburg, P. T. Mocanu, N. Negoescu, Analiză matematică (Funcţii complexe), Ed. Did. şi Ped., Bucureşti, 1982 4. G. Helmberg, Getting Acquainted with Fractals. DeGruyter, 2007 5. R. Deaux, Introduction to the Geometry of Complex Numbers. Dover, 2008 6. T. Andreescu, D. Andrica, Complex Numbers from A to … Z, Birkhauser, Boston, 2006 7. Krantz S.G. - Geometric Function Theory. Birkhauser, 2006 8. P. T. Mocanu, Funcţii complexe, Partea I, Lito. Universitaţii Cluj, 1972 9. R. Shakarchi, Problems and Solutions for Complex Analysis. Springer, 1999 10. M. Evgrafov, K. Bobejnov, Y. Sidorov, Recueil de problemes sur la theorie des functions analytiques, Edition Mir, Moscou, 1974 |
| Assessment |
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Midterm test and Final Exam.
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| Links: | Syllabus for all subjects Romanian version for this subject Rtf format for this subject |