Prerequisites
Differential and Integral Calculus II
Objectives
Master of: - Resolution of elementary ordinary differential equations; resolution of linear differential equations and systems of linear differential equations. - Existence, uniqueness and continuous dependence of solutions of ordinary differential equations. - Gauss and Stokes theorems, general properties of the divergence and curl of vector fields, and applications. - Resolution of elementary linear partial differential equations of 1st and 2nd order. - General properties and convergence of Fourier series, Fourier transform and applications.
Program
Ordinary Differential Equations (ODEs): examples of solvable 1st order ODEs, integration factors; existence, uniqueness and continuous dependence of solutions of systems of 1st order ODEs; variation of constants formula; ODEs of order > 1; Laplace transform and applications to ODEs. Gauss and Stokes Theorems and introduction to Partial Differential Equations (PDEs): surfaces in R^3; surface integrals of scalar and vector fields; Gauss and Stokes Theorems; divergence and curl of vector fields; derivation of the continuity, wave, heat, Laplace and Poisson differential equations. PDEs and Fourier series: linear 1st order PDEs; wave, heat, Laplace and Poisson equations; trigonometric Fourier series; solutions of wave, heat, Laplace and Poisson equations, via separation of variables and Fourier series; Fourier transform and applications.
Evaluation Methodology
Exam/tests, possibly with minimum grade, complemented with continuous evaluation components and oral evaluation for grades above 17 (out of 20).
Cross-Competence Component
The UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.
Laboratorial Component
Not applicable.
Programming and Computing Component
Not applicable.
More information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938489999
