Mathematics Elements I

Knowledge of mathematics of basic and secondary levels.

The following teaching methodologies are used in this curricular unit:
1) Verbal methods (say), making use of the following educational resources: Exposition, Explanation, Dialogue and questioning;
2) Intuitive Methodologies (show), making use of the following educational resources: Demo, Audiovisual, written texts;
3) Active Methodologies (doing), making use of pedagogical resources: problem solving; technology.

Provide students with the basic mathematical knowledge needed in the professional training of a professional superior technician

1. Real Functions of Real Variable

– Introduction to mathematical language and logical operations.

– Generalities about real functions of real variable. – Study of inverse trigonometric functions.

– Notion of limit; lateral limits; properties and operations.

– Continuous functions, properties and continuity extension.

– Fundamental theorems of continuous functions.

2. Differential Calculus in R

– Notion of derivative of a function: definition and interpretations in geometric and physical terms; equations of lines tangent and normal to the graph of a function at a point.

– Side derivatives; differentiability and its properties; derivation rules; derivative of the composite function and the inverse function; derivatives of inverse trigonometric functions; notion of differential.

– Fundamental theorems of differentiable functions.

– Higher order derivatives; Taylor and Maclaurin formulas (Lagrange rest). Application to the study of monotony, extremes and concavities.

NAO

Anton, H., Bivens, I., & Stephen, D. (2014). Cálculo, Vol. I (10ª ed.). Bookman.

Campos Ferreira, J. (2014). Introdução à Análise Matemática (11ª ed.), F. Calouste Gulbenkian.

Stewart, J., Clegg, D.C., & Watson (2021). Calculus: early transcendentals, Metric edition (9th ed.). Cengage.

 Bibliography for reviews:

Secondary School textbooks (Mathematics A).