Class Mathematical Analysis III

This curricular unit (UC) is part of the curriculum of this degree. The mathematics basis are taught on differential equations and calculation methods, necessary for the successful learning of subsequent curricular units. At the end of this course, students should have acquired skills to: - master the technical knowledge in fundamental mathematics, including ordinary differential equations of 1st order or higher order, systems of differential equations, integrals transforms of Laplace; - modeling engineering problems in transient state by applying the knowledge acquired; - be able to analyze complex situations, develop solutions and make judgments in situations of limited or incomplete information; - be able to apply the knowledge and ability to understand and solve problems in new and unfamiliar situations, in broad contexts and multidisciplinary.

Not applicable

1.Introduction to Differential Equations. Formulation and solutions. Order and degree. Initial Value Problems. General and particular solution. Existence and uniqueness of solutions. Applications in Engineering. 2. Ordinary differential equations of 1st order. Differential equations of variables separable, homogeneous, exact, linear and reducible to these types. Integrating factor. 3. Linear differential equations of order higher than the first. General solution of an equation with constant coefficients. Method of undetermined coefficients. 4. Systems of linear differential equations of 1st order. Systems of homogeneous equations with constant coefficients and its resolution. 5. Laplace transform. Definition, interpretation and properties. Reverse Transformation. Heaviside Step Function and Dirac Impulse. Application to differential equations. 6. Fourier transform. Definition, interpretation and properties. Applications. Partial differential equations

This UC will use some active methodologies that promote greater student involvement in pedagogical activities, such as Problem Based Learning in a collaborative environment. In terms of digital technologies, Moodle and Matlab will be used

- Azenha, A., Jerónimo, M. E. (1995), Elementos de Cálculo Diferencial e Integral em IR e IRn, Editora MacGraw Hill. - Kreyszig, E. (1998), Advanced Engineering Mathematics (6th Edition), Wiley. - Textos de apoio e coleções de exercícios fornecidos ao longo das aulas pelos docentes.