Theory of Partial Differential Equations

Code: MAT14362M

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese, English

Regime de Frequência: Presencial

Presentation

The UC Theory of Partial Differential Equations intends to provide foundations for the study and analysis of this type of equations, either in a theoretical aspect or in an interdisciplinary perspective and of initiation to research, through the study of mathematical models.

Sustainable Development Goals

4. 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

- Training in the theory of Partial Differential Equations and their applications (interdisciplinarities and initiation to the scientific work).
- Analysis of models (relevance on the nonlinearity, irreversibility, determinism and quantum models; development of the skills of abstraction, creative intuition and critical thinking).
- Literature search and selection of software/hardware (autonomy and communication skills, oral and written exposition of results).

- Phenomenology and modelling of the Heat Equation.
- Classification of PDEs and canonical forms.
- Series and Fourier transform. Applications.
- Solutions of the Heat Equation.
- The Burgers Equation.
- Variational methods.
- Energy and entropy methods.
- Main work options: a) Financial Mathematics (Black-Scholes Eq.); b) Applications to Biology (Transport Eqs.); c) Numerical Analysis (Hilbert-Huang Transform).

Teaching Methods

Mentoring of teamwork (with individual assessment); emphasis on applications and problem solving.
Evaluation: Continuous (the final grade will be the average of the works grades) or Final (oral) examination.