Base Knowledge
High school mathematics knowledge.
Teaching Methodologies
Essentially expository method in theoretical classes and collaborative in practical classes, with students solving exercises with the coordination and guidance of the teacher.
Learning Results
This training unit is intended for the trainee to develop reasoning, attitudes, behaviors, methodologies and good practices of scientific thinking. The skills to be acquired include: understanding and using elementary mathematics concepts, operating with real numbers, solving equations, etc.; interpret phenomena and solve problems using functions and their graphs; solve trigonometry problems, including the use of generalizations of the notions of angles and trigonometric ratios; apply mathematical knowledge within the scope of information and communication technologies.
Program
Topic 1. Elements of trigonometry (trigonometric ratios in the right triangle, trigonometric circle, trigonometric formulas).
Topic 2. Complex numbers (algebraic form, geometric representation in the Argand plane, conjugate, module and argument, operations with complex numbers in algebraic form, trigonometric form, operations with complex numbers in trigonometric form).
Topic 3. Elements of analytical geometry (points and vectors in R^2 and R^3, operations with points and vectors, distance between points, norm of a vector, straight line and plane equations, scalar product, geometric interpretation, parallelism and perpendicularity, intersection of planes and geometric interpretation, resolution of linear systems, classification and geometric interpretation).
Topic 4. Real functions of a real variable (notion of function, domain, arrival set and codomain, injective, surjective and bijective functions, real function of a real variable and graph, even and odd function, monotony, compound function, inverse function, relation between the graphs of a function and its inverse, polynomial functions (highlights n=0, n=1, n=2), module function, trigonometric functions, exponential function with base a, logarithm function with base a, particular case a= and, representation of flat regions, limit and continuity).
Topic 5. Differential calculus (definition of derivative and geometric interpretation, derivation rules, derivative of the composite function, derivative of the inverse function, monotony and concavity, calculation of limits using Cauchy’s rule, unrestricted optimization problems, applications).
Topic 6. Introduction to linear programming (problem formulation, linear programming model, admissible region and graphical resolution, particular cases: impossible problem and unlimited problem).
Curricular Unit Teachers
Internship(s)
NAO
Bibliography
Notes and Practical Sheets provided by teachers on the InforEstudante and Moodle platforms.
Ferreira, M.A.M., & Amaral, I. (1995). Programação Matemática. Edições Sílabo.
Manuais escolares de Matemática A do 12º ano de escolaridade.
Software livre de matemática (Geogebra, Symbolab, Desmos).
Stewart, J. (2005). Cálculo. Thomson Pioneira.