ISLA Santarém 1

Mathematics I

• ApresentaçãoPresentation

  Mathematics I introduces the fundamental concepts of calculus and real analysis necessary for modeling and solving problems in scientific and technological contexts, providing essential foundations for further study.
• ProgramaProgramme

  1. Real functions of a real variable. 2. Limits and Continuity: Notion of limit. Limit definition. Lateral limits. Limit calculation theorems. Indeterminacy in the calculation of limits. Definition of continuity. 3. Differential Calculus: Definition of derivative. Geometric interpretation of derivative definition. Differentiability and Continuity. Derivation rules. Derived from the implicit function. Successive derivatives. Cauchy's rule and L'Hôpital's rule. Indeterminacy in the calculation of limits. Applications of derivatives. 4. Integral Calculus: Primitives. Integration rules. Integration by parts. Integration by substitution. Integration of rational functions. Definite integral. Fundamental theorem of calculus. Applications of integral calculus: areas and volumes. Improper integrals. 5. Numerical Series: Definitions and Generalities. Successions.Series and convergence. Integral criterion. Comparison of series. Alternate series. Quotient and root criteria. Power series.
• ObjectivosObjectives

  Objectives: O1. Provide students with the knowledge to use algebraic expressions. O2. Solve equations and inequalities and apply this knowledge to real practical problems. O3. Use real variable functions and their properties to model real situations and solve problems. Competences: C1. Master and apply the techniques of derivation and integration in IR. C2. Model and solve optimisation problems for differentiable functions. C3. Calculate the sum of geometric and reducible series and develop some functions in power series. C4. Apply integral calculus in IR to solve problems.
• BibliografiaBibliography

  Brokate, M., Manchanda, P., & Siddiqi, A. H. (2019). Calculus for Scientists and Engineers. Springer Singapore. Carneiro, C. E., Prado, C. P., & Salinas, S. R. (2020). Introdução elementar às técnicas do cálculo diferencial e integral. Instituto de Física. 3a edição. São Paulo (Brasil). Macedo, Margarida (2022). Cálculo Integral. UCP Editora Pires, G. (2022). Cálculo Diferencial e Integral em Rn. IST Press. Sá, Ana & Louro, Bento (2024). Sucessões e Séries - Teoria e Prática - 2ª Edição. Escolar Editora.
• MetodologiaMethodology

  Face-to-face: 1. Expository methodology: addressing the concepts of different topics, following the demonstrative method in practical examples of the 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 in the classroom 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 (individual).

  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.