Math Fundamentals

Teaching Methodologies

The methodology is based on theoreticalpractical classes, in which the exposition of concepts of analysis, ODEs, linear algebra, and statistics is immediately accompanied by examples and guided exercise solving, promoting active and gradual learning. Worksheets and applied problems are proposed, to be solved individually and in small groups, encouraging discussion and the autonomous construction of problemsolving strategies. The systematic use of spreadsheets connects conceptual mastery with practical and technological dimensions, reinforcing the studentcentered pedagogical model and fostering the development of skills in calculation, critical interpretation of results, and simple modeling with real data.

Learning Results

The curricular unit aims to provide fundamental knowledge of analysis, firstorder ordinary differential equations (ODEs), linear algebra, and elementary notions of statistics, including simple linear regression, suitable for students without prior training in Mathematics. The intention is to develop skills in calculation, graphical representation, solving linear systems, and formulating simple models (ODEs and linear regression). Competences in the critical interpretation of results and the use of spreadsheets as a support tool will also be fostered. Compatibility between objectives and teaching methods is ensured through theoreticalpractical classes, guided exercise solving, and practical work with spreadsheets.

Program

Topic 1

– Real functions of a real variable.

– Derivatives: geometric interpretation and differentiation rules.

– Immediate and almost immediate antiderivatives.

– Definite integral: basic properties and application to the calculation of areas of closed plane regions.

Topic 2

– Concept of firstorder ordinary differential equation (ODE).

– Firstorder separable differential equations.

Topic 3

– Matrices and matrix operations.

– Determinants. Systems of linear equations.

– Use of spreadsheets in solving linear systems and performing matrix operations.

Topic 4

– Statistical variables (nominal, ordinal, interval, ratio scales).

– Simple linear regression model.

– Pearson correlation coefficient and coefficient of determination.

– Use of spreadsheets in graphical representation and adjustment of simple linear regression models.

Curricular Unit Teachers

Sara dos Santos Escudeiro Cruz

Internship(s)

NAO

Bibliography

Alves de Sá, A., & Louro, B. (2022). Cálculo diferencial e integral em R. Escolar Editora.

Abell, M. L., & Braselton, J. P. (2024). Introductory differential equations (6th ed.). Academic Press.

Macedo, M. (2023). Álgebra linear: Matrizes, determinantes e sistemas. UCP Editora.

Murteira, B., Ribeiro, C. S., Silva, J. A., Pimenta, C., & Pimenta, F. (2023). Introdução à estatística (4.ª ed.). Escolar Editora.

Martins, A., & Alturas, B. (2025). Aprenda Excel com casos práticos (3.ª ed.). Edições Sílabo.