Complex Analysis
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2023/2024 - 2S
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
The student should know: the basic results about sequences and series of complex numbers, continuity and derivability of complex functions of a complex variable, as well as its application to the computation of integrals of complex functions of a real variable.Learning outcomes and competences
The student should know: the basic results about sequences and series of complex numbers, continuity and derivability of complex functions of a complex variable, as well as its application to the computation of integrals of complex functions of a real variable.Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Multivariable Calculus.
Program
1. Complex numbers
The complex number fiels. Topology of the complex plane.
2. Holomorphic functions and analytic functions
Differentiation. Power series. Analytic functions
3. Cauchy theory
Paths and loops. Cauchy's theorem and its applications. Analiticity of the holomorphic functions.
4. Singularities of analytic functions
Laurent series of analytic functions. Regular points and isolated singularities. The residue theorem and its applicatiosn.
Mandatory literature
Aníbal Coimbra A. de Matos;
Curso de análise complexa. ISBN: 9789725921159
Complementary Bibliography
Serge Lang;
Complex analysis. ISBN: 0-387-98592-1
Reinhold Remmert;
Theory of complex functions. ISBN: 0-387-97195-5
David C. Ullrich;
Complex made simple. ISBN: 9780821844793
Teaching methods and learning activities
Lectures and classes: The contents of the syllabus are presented in the lectures, where examples are given to illustrate the concepts. There are also practical lessons, where exercises and related problems are solved. All resources are available for students at the unit’s web page.keywords
Physical sciences > Mathematics > Mathematical analysis
Evaluation Type
Distributed evaluation with final exam
Assessment Components
designation |
Weight (%) |
Exame |
50,00 |
Teste |
50,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
designation |
Time (hours) |
Estudo autónomo |
114,00 |
Frequência das aulas |
48,00 |
Total: |
162,00 |
Eligibility for exams
Attending classes is not compulsory: students are not required to attend the classes.
Calculation formula of final grade
There will be two tests, each corresponding approximately to half the syllabus. The second test may take place on the day for which the normal exam is scheduled. Students who do not pass through both tests can, in the second exam (which will be divided into two parts), use the classification obtained in one of the tests and only take the part of the exam corresponding to the other test. This possibility does not apply to anyone who improves their grade.
Grades above 17 will only be awarded after making an extra test.