ISLA Santarém 69

Applied Mathematics

• ApresentaçãoPresentation

  The Applied Mathematics course is a fundamental component of the Bachelor's Degree in Data and Technology Management in Health, providing students with a rigorous foundation in essential concepts of linear algebra, real-valued functions, and differential calculus. The course aims to develop analytical and quantitative skills that enable them to interpret, model, and solve problems in contexts related to health, technology, and data management. The program covers topics such as matrices and associated operations, solving linear systems, real-valued functions of one real variable, limits, continuity, derivatives, and theorems of differential calculus, enabling the application of mathematical methods to concrete situations. This course encourages the development of logical-mathematical reasoning, critical thinking, and analytical skills, providing a solid foundation for subsequent courses and professional practice in areas that require quantitative rigor and data interpretation.
• ProgramaProgramme

  1. ARRAYS 1.1 Definition and properties Operations with matrices 1.2 Elementary Operations, condensation and characteristic of an array 1.3 Application of arrays in classification and solving systems of linear equations: Gauss and Jordan 2. REAL FUNCTIONS of REAL VARIABLE 2.1 General information on real functions of real variable 2.2 Notion of limit; lateral limits; properties and operations 2.3 Continuous functions: definition, properties and extension by continuity 2.4 Theorems of Bolzano, Weierstrass and the continuity of inverse function 3. DIFFERENTIAL CALCULUS in R 3.1 Derivative of a function: definition and geometrical and physical interpretation 3.2 Lateral derivatives; differentiability; derivation rules; notion of differential 3.3 Theorems of Rolle, Lagrange, Cauchy 3.4 Cauchy and rule indeterminations 3.5 Higher-order Derivative 3.6 Monotony and extremes of functions. Scoops and inflection points 3.7 Asymptotes and Representation of the graph of a function
• ObjectivosObjectives

  O1. Correct use of vocabulary and mathematical symbol; O2. Correct calculation in R; O3. Solving linear equations and systems of linear equations using matrices; O4. Knowledge of the concepts of continuity, limits and derivatives; O5. Application of the study of functions and their graphs to interpretation and problem solving; O6. Application of differential calculus in the study of real functions of real variable; O7. Interpretation and critique of the results in the context of the problem; O8. Communication of concepts, reasoning and ideas with clarity and logical rigour.
• BibliografiaBibliography

  Anton H., Bivens I., Davis S. (2007). CÁLCULO, Vol.I, 8ª Edição. 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, M. (2022). Funções Reais de Várias Variáveis Reais. Universidade Católica Editora. Pires, G. (2022). Cálculo Diferencial e Integral em Rn. IST Press.
• MetodologiaMethodology

  Classes are of a mixed nature (theoretical-practical) with an expository component, presenting the fundamental concepts and demonstrating the main results, and an applied component with the resolution of practical exercises applied to Health Data. Students should acquire a global vision of the topics covered and their interconnections, and the ability to solve the problems formulated. In essence, the following methodologies will be used: MET 1. - Active methodologies such as cooperative learning; peer learning; gamification; problematisation, modelling and mathematical simulations. MET 2 - Project Based Learning for solving complex "real" problems involving the application of concepts inherent in the syllabus. MET 3 - Availability on the MOODLE platform of various educational resources (videos, links; APPs, summaries, exercises and applications, teacher's notes, etc.)
• LínguaLanguage

  Português
• TipoType

  Semestral
• ECTS

  5
• NaturezaNature

  Mandatory
• EstágioInternship

  Não
• AvaliaçãoEvaluation

  Época Normal - Avaliação curricular (contínua) (*): O estudante constrói um portfólio com base nas atividades de avaliação ativa desenvolvidas ao longo do semestre e realiza dois testes de avaliação individual. O estudante aprova se a classificação final for superior ou igual a 9.5 valores em 20 valores. A classificação final é calculada pela fórmula Classificação Final = 0.3*P+0.35*T1+0.35*T2, onde P, T1 e T2 denotam, respetivamente, as notas no portfólio e nos testes de avaliação individual.

  (*) A realizar no decorrer do semestre.

  Época Normal - Avaliação final: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores em 20 valores.

  Épocas de Recurso e Especial: O estudante realiza o exame completo e aprova se obtiver classificação superior ou igual a 9.5 valores em 20 valores.

   

  Descrição	Data	Ponderação
  Portfólio	Consultar Moodle, consoante a turma.	30%
  Teste 1	11-11-2025	35%
  Teste 2	13-01-2026	35%
  Exames	A agendar pelos serviços.	100%