Complex Analysis

Cod: 21005

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

Complex Analysis is an essential component in the training of mathematicians, physicists and engineers as well as a key component in other branches of pure and applied sciences. In this course unit students are provided a first approach to the subject.

1.Complex Analysis

2.Cauchy Theorem

3. Residues

1. Complex numbers

2. Holomorphic functions

3. Integration of complex functions

4. Cauchy's theorem;

5. Power series representations of holomorphic functions

6. Residues

7. Harmonic functions

8. Complementary developments

2. Holomorphic functions

3. Integration of complex functions

4. Cauchy's theorem;

5. Power series representations of holomorphic functions

6. Residues

7. Harmonic functions

8. Complementary developments

Natália Bebiano da Providência, Análise Complexa, Trajectos / Ciência, Gradiva, 2009 (ISBN: 978-989-616-294-8)

Additional Bibliografy:

Pedro Martins Girão, Introdução à Análise Complexa, Séries de Fourier e Equações Diferenciais, Colecção Ensino da Ciência e da Tecnologia, IST PRESS, 2014 (ISBN: 978-989-8481-31-3)

Luís Barreira e Cláudia Valls, Exercícios de Análise Complexa e Equações Diferenciais, IST PRESS, 2010 (ISBN: 978-972-8469-95-5)

E-Learning.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).

This course unit requires knowledge on *Elements of Infinitesimal Analysis II*.