Complex Analysis
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
In the end, students are expected to be able to know and understand the following concepts: complex numbers, holomorphic functions; integration of complex functions; Cauchy theorem; power series representation of holomorphic functions; residues; harmonic functions.
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
Main Bibliography:
Maria Adelaide Carreira e Maria Suzana Metello de Nápoles, Variável Complexa: Teoria Elementar e Exercícios Resolvidos,
“Textos de Matemática” do Departamento de Matemática da FCUL, 2016.
Additional Bibliografy:
Natália Bebiano da Providência, Análise Complexa, Trajectos / Ciência, Gradiva, 2009 (ISBN: 978-989-616-294-8)
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 digital written documents (e-folios) during the semester (40%) and a final digital test, Global e-folio (e-folio G) at the end of the semester (60%). In due time, students can alternatively choose to perform one final exam (100%).
This course unit requires knowledge on Elements of Infinitesimal Analysis II.