Topics in Ordinary Differential Equations

Code: MAT11692D

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese, English

Regime de Frequência: B-learning

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

It is intended that students acquire competences at the level of the theoretical foundation of the different
methods to prove the existence of periodic solution for ordinary differential equations.

Deformation theorems, mountain pass theorems, saddle point theorems and wedding theorem.
Topological degree theory in finite and infinite dimensions.
Applications to ordinary and partial differential equations.
Fixed point theorems.
Lower and upper solutions method applied to boundary value problems: direct method, monotone iterative
method , existence of extreme solutions.

Teaching Methods

Classes are theoretical and practical, where it is used a structured exhibition methodology for the
presentation of the syllabus, supported by exemplification with emphasis on applications. In addition, the
students will carry out one written work.
The evaluation of the CU of Topics in Ordinary Differential Equations consists of one written test and one
written work elaborated by the student or else one final exam, with the possibility of performing an appeal
examination.