Mathematics

High school mathematics knowledge.

Expository method in theoretical classes and collaborative in practical classes, with resolution of exercises by students with the coordination and guidance of the teacher. Classes presented in Portuguese.

With this training unit it is intended that the trainee develops reasoning, methodologies, and good practices of scientific thinking. The skills to be acquired include: understanding of elementary mathematical concepts, operations with real numbers, solving equations, etc.; interpret phenomena and solve problems using functions and their graphs; solve trigonometry problems, including the use of angles and trigonometric relations; apply mathematical knowledge in the scope of information and communication technologies.

Theme 1. Elements of trigonometry (trigonometric relations in the right triangle, trigonometric circle, trigonometric formulas).

Theme 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, representation of conditions in the complex plane, circumference, circle, mediatrix of a line segment).

Theme 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, equations of the line and plane, scalar product and vector product, geometric interpretation, parallelism and perpendicularity, intersection of planes and geometric interpretation, resolution of linear systems, classification, and geometric interpretation).

Theme 4. Real functions of real variable (notion of function, domain, range and image, injective, surjective, and bijective function, real function of real variable and graph, odd and even function, monotony, composite function, inverse function, relation between the graphs of a function and its inverse, polynomial functions (highlights n = 0, n = 1, n = 2), absolute value function, trigonometric functions, exponential function of base a, logarithm function of base a, particular case a = e, applications, limit and continuity).

Theme 5. Differential calculus (definition of the derivative and geometric interpretation, algebra of derivatives, derivative of the composite function, derivative of the inverse function, monotony and concavity, calculation of limits by the Cauchy rule, optimization problems without restrictions, applications).

Theme 6. Introduction to linear programming (formulation of the problem, linear programming model, admissible region and graphic resolution, particular cases: impossible problem and unlimited problem).

• - Exame - 100.0%

• - (Teste 1 + Teste 2 + Teste 3) / 3 - 80.0%
• - Trabalhos de Casa - 20.0%

NAO

Notes and Practice Sheets provided by teachers on 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.