Mathematical Analysis III

Code: MAT13046L

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Presentation

This curricular unit intends to contribute to personal and scientific training, in general, and contact with mathematical contents in the scope of Differential Geometry, Complex Analysis, Fourier Analysis, and Differential Equations, both in the theoretical and in the applications.

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

This unit is important in the personal and scientific training in general and mathematics education in particular. Therefore, students should:
- Develop skills in abstraction, logical deduction, and analysis.
- Acquire structuring methods and techniques of mathematical and scientific reasoning that provides a critical spirit.
- Know math concepts related to complex analysis, Ordinary Differential Equations, Fourier Series, and Differential Geometry in space and applications.
- Use mathematical skills in problem-solving and real phenomena interpretation.
- Acquire mathematical skills that could be developed and implemented in a professional context, business, research, or teaching.

1 Introduction to Differential Geometry.
2 Introduction to Complex Analysis.
3 Ordinary Differential Equations.
4 Systems of ordinary differential equations.
5 Fourier series. Fourier integrals.

Teaching Methods

Classes work in two phases for each syllabus:
Initially, slides will be presented with the syllabus followed by an explanation of their meaning, importance and applications.
Secondly, the resolution of a problem or concrete application is discussed, which illustrates the applicability of the theoretical result.
At both times, students will be encouraged to participate in the formulation of conjectures, resolution hypotheses or doubts that arise during the development of classes.

Assessment

The evaluation can be carried out through two processes, each of which is carried out with the possibility of consulting material produced by the person:
1. Assessment by Exam
The student will be approved if, in one of the exams to be taken in the appropriate period, after the academic period, he obtains a classification equal to or greater than 10 points.
2. Continuous Assessment
At the end of Chapters 3 and 5, frequencies will be carried out, focusing on the subject matter of the chapters taught.
The classification of this component will be the average of the classifications obtained.
The student will opt for Continuous Assessment if they present themselves for assessment in both frequencies and have, in each of them, a classification equal to or greater than eight points.
If the student chooses to undergo both evaluation processes, the final classification will be the best of the two classifications obtained.