ISLA Santarém 505

Mathematics II

• ApresentaçãoPresentation

  Mathematics II provides a structural foundation for the development of abstract thinking and logical-deductive reasoning, promoting the ability to analyze, model, and solve problems in academic and professional contexts.
• ProgramaProgramme

  1. Functions with more than one variable: 1st and 2nd order Partial Derivatives. Optimization of Functions with more than one variable. Conditional Optimization and Lagrange Multipliers. 2. Multiple Integrals: Double integrals. Applications of double integrals. Triple integrals. Applications of triple integrals. 3. Ordinary Differential Equations: 1st order Ordinary Differential Equations. Homogeneous and non-homogeneous linear equations of second order. 4. Set theory and logic: Representation of sets. Relationship of belonging and inclusion of sets. Operations on sets: meeting, intersection, difference and complementation. Definition and logical value of a proposition. Propositional calculus. Truth tables. Properties of propositional calculus. Simplification of logical expressions.
• ObjectivosObjectives

  O1. Provide students with the knowledge that allows them to develop abstraction and logical-deductive reasoning skills. O2. Provide the student with knowledge about Logic. O3. Provide basic Mathematical Analysis tools necessary for the progression of the study. Competences: C1. Solve function systems with more than one variable. C2. Understand and use the concept of integral in an intuitive and rigorous way. C3. Use integral calculus knowledge. C4. Use knowledge of differential equations. C5. Apply set theory and logic to problem solving. C6. Demonstrate abstraction and logical-deductive reasoning skills.
• BibliografiaBibliography

  Cenzer, D. et al., (2020). Set Theory and Foundations of Mathematics: An Introduction to Mathematical Logic. World Scientific. Macedo, M. (2022). Funções Reais de Várias Variáveis Reais. Universidade Católica Editora. Valls, C. & Barreira, L. (2021).Equações Diferenciais Via Análise Real e Complexa. IST - Instituto Superior Técnico Vieira, Luís (2020). Cálculo Integral. Engebook.
• MetodologiaMethodology

  Face-to-face: 1. Expository methodology: addressing the concepts of different topics, following the demonstrative method in the practical exemplification of content. 2. Practical application: carrying out a series of exercises inside and outside the classroom, encouraging active and independent participation by students. 3. Active methods, using motivation strategies and active teaching methodologies such as flipped classrooms and gamification. Autonomous: 4. Consolidation of the content taught in class through additional research on the different topics covered and the development of supplementary work proposed by the teacher through the Moodle platform. The teacher provides feedback on the results obtained by the student in solving the proposed problems, either in person or through the Moodle platform.
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  6
• NaturezaNature

  Mandatory
• EstágioInternship

  Não
• AvaliaçãoEvaluation

  Avaliação Curricular (contínua):

  A1. Portfólio de exercícios práticos resolvidos ao longo das aulas.

  A2. Teste intermédio (indivudual).

  A3. Teste final (individual).

  O estudante é aprovado se a classificação final for igual ou superior a 9,5 valores em 20.

  A classificação final é calculada através da fórmula Classificação Final = 0,2*A1+0,4*A2+0,4*A3.

  Avaliação Final (A): O estudante realiza o exame completo (A=100%) e é aprovado se obtiver uma classificação igual ou superior a 9,5 valores em 20.

  Avaliação em Época de Recurso e Época Especial (A):

  O estudante realiza o exame completo (A=100%) e fica aprovado se obtiver uma classificação igual ou superior a 9,5 valores em 20.