Complex Analysis

Recommended Prerequisites

Solid background in Real Infinitesimal Analysis.

Teaching Methods

The course is expository. Some sessions of tutorials are provided.

Learning Outcomes

The main objective is to provide knowledge in the area of complex analysis, essential in the background of a mathematician. The multiple applications of this area is a target always in mind and get special attention. 

Generic skills and competences to be developed:

Computation ability;

Competence in the use of computational tools;

Knowledge of mathematical results;

Ability for generalization and abstraction;

Ability to formulate and solve problems;

Logical argumentation;

Individual initiative;

Research capacity;

Autonomous learning ability;

Imagination and creativity.

Work Placement(s)

No

Syllabus

The Field of Complex Numbers, differentiability in C, integral calculus, Moebius Transformation, conformal mappings, Taylor and Laurent series, Singularities, residues, applications.

Head Lecturer(s)

Natália Isabel Quadros Bebiano Pinheiro da Providência e Costa

Assessment Methods

Assessment
Approval in this course unit requires to score at least 10 (out of 20). The students that perform, along the semester, the mid-term exams may be exempted from final examination. The sum of percentages corresponding to this component is 100%. The other students will be evaluated in a final exam which is worth 100%.: 100.0%

Bibliography

L Ahlfors, Complex Analysis. 3ªed. McGraw-Hill, 1979.

 

N. Bebiano,  Análise Complexa e Aplicações e laboratórios de MATHEMATICA, Gradiva, 2.ed. Lisboa, 2012.