2024
Partial Differential Equations
Name: Partial Differential Equations
Code: MAT00914L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Presentation
In this optional discipline, it is intended that the student acquires the basic knowledge of PDEs, emphasizing linear theory with a view to non-linear theory. It is also intended to be able to apply and solve concrete problems.
Sustainable Development Goals
Learning Goals
An introduction to the PDEs. Development of some linear theory in view of the nonlinear one. Understanding and fluid use of some essential techniques as well as the comprehension and the extension of the mathematical analysis knowledge. Ability to apply and to solve real world problems.
Contents
Linear and nonlinear equations.
Hyperbolic, parabolic and elliptic equations: classification and canonical forms.
Ill- and well-posed problems.
The problems for the wave, the diffusion and the Laplace equations.
Separation of variables, Fourier series (a motivation to the Hilbert spaces).
Introduction to the Fourier transform (a motivation to the Sobolev spaces).
Distributions, weak solutions and Green functions.
Characteristics and evolution (a motivation to the energy and variational methods;
implications for the nonlinear equations).
Hyperbolic, parabolic and elliptic equations: classification and canonical forms.
Ill- and well-posed problems.
The problems for the wave, the diffusion and the Laplace equations.
Separation of variables, Fourier series (a motivation to the Hilbert spaces).
Introduction to the Fourier transform (a motivation to the Sobolev spaces).
Distributions, weak solutions and Green functions.
Characteristics and evolution (a motivation to the energy and variational methods;
implications for the nonlinear equations).
Teaching Methods
The teaching methodology is twofold based: on, complementary, theory and exercise classrooms around the discussion and solution of given, specific, problems.
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.
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.
Teaching Staff
- Joaquim Manuel Cunha Correia [responsible]
Certificações
