2024
Complex Analysis
Name: Complex Analysis
Code: MAT00903L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese
Regime de Frequência: Presencial
Presentation
In this compulsory subject taught in the 5th semester, it is intended that students achieve sufficient mastery and autonomy in the study of the field of complex numbers and analytical functions on the complex plane.
Sustainable Development Goals
Learning Goals
The intended outcomes are the sufficient mastery and autonomy by the student in the study of the field of complex numbers and analytic functions defined on the complex plane. To become experienced in the use of complex numbers. To understand some fundamental aplications, in algebra, geometry and integral calculus.
Contents
Complex plane geometry and topology; holomorphic functions (Cauchy-Riemann equations, harmonic functions); elementary functions; complex integration (theorem of Cauchy, Cauchys integral formula, Liouvilles theorem, the fundamental theorem of algebra and the maximum modulus theorem); Taylor and Laurent series, analytic continuation; zeroes and poles, residue theorem (applications to integral calculus); Rouchés theorem; conformal transformations; further on harmonic maps.
Teaching Methods
Structured exposition, with worked exercises.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done
preferably during the classes, weighting 100% of the classification, the number of which is to be defined by
the professor who is responsible for the course unit in each academic year, or by a final exam. Students
who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade
is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process;
the elements of formative evaluation will have no weight on the final mark.
The evaluation may be either continuous, done through between two and six partial tests and quizzes, done
preferably during the classes, weighting 100% of the classification, the number of which is to be defined by
the professor who is responsible for the course unit in each academic year, or by a final exam. Students
who achieve a grade of 18 or above may have to do an extra oral exam. For these students the final grade
is the maximum between 17 and the simple average of the previous grade and the oral exam.
Formative evaluation is done in or by tasks to be done outside class, to improve the learning process;
the elements of formative evaluation will have no weight on the final mark.
Teaching Staff
- Jorge Maurício Salazar Serrano [responsible]
Certificações
