| Area of Mathematics: | Analysis | ||
| Semester: | 5ο | ||
| Course ID: | 51102 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 4 | Practice: 2 | Laboratory: 0 |
| ECTS : | 7 | ||
| Eclass: | For the course’s material, click here. | ||
| Instuctors: | Stamatis Pouliasis | ||
Description
- Complex numbers. Plane topology.
- Sequences – Series of complex numbers.
- Limits , continuity of complex functions.
- Curves in the plane. Simple, closed, smooth, piecewise smooth curves, Change of parameter, parametrized curves, sum of curves, reverse curve, length of curves.
- Curvilinear integrals.
- Holomorphic functions, Cauchy-Riemann equations.
- Power series, exponential and logarithmic function.
- Cauchy’s Theorem, Cauchy integral formula, Cauchy estimates, Liouville’s Theorem, Fundamental theorem of Algebra.
- Isolated singularities. Poles-roots. Laurent expansion, Residue theorem and applications.
Bibliography
- J.Marsden-M.Hoffman , Basic Complex analysis , 3rd edition , Freeman and Company , 1999
- R.Churchill-J.Brown , Complex Variables and Applications , 6th edition , McGraw-Hill , 1996
