Matemática I

The curricular unit combines lectures, which present theoretical foundations and practical examples, with practical-theoretical classes focused on problem-solving and student support. The Moodle platform is used to provide supporting materials, such as lecture slides, exercise books, and practical worksheets, as well as to launch challenges to motivate students. Tools like Wolfram Alpha and Matlab are integrated to complement the study of the topics covered. These methodologies promote active and autonomous learning, encouraging students to apply the knowledge acquired in new contexts.

The main objectives of this curricular unit are to understand and apply the concept of the integral of a real-valued function of a real variable and to acquire fundamental knowledge of Linear Algebra. It aims to develop skills in abstract reasoning, result interpretation, and practical problem-solving in the fields of Engineering and Industrial Management. The unit fosters autonomous learning, building on prior secondarylevel knowledge, and employs methodologies such as lectures, practical classes, and digital tools like Moodle and calculation software (Wolfram Alpha, Matlab).

1. Funções hiperbólicas e funções trigonométricas inversas.
2. Primitivação de funções reais de variável real: definição, propriedades, métodos (por partes, substituição, frações racionais e funções trigonométricas).
3. Cálculo Integral em ?: integral definido (de Riemann), Teorema Fundamental do Cálculo, integração por partes e substituição. Aplicações: áreas, comprimentos de curvas, volumes de sólidos de revolução. Integral indefinido e impróprio de primeira espécie.
4. Álgebra Linear: matrizes (definição, operações, matrizes especiais, método de Gauss, matriz inversa), determinantes (definição, propriedades, operações, matriz adjunta e inversa), resolução de sistemas lineares (regra de Cramer).

• - Atividades (2*15%) e teste (70%) ou Exame (100%) - 100.0%

NAO