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Curso Preparatório em Matemática

Code:

5020

Sigla:

CPM1

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 2S (on the 04-03-2024 a 03-05-2024)

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
CPM1S	18	Plano Oficial do ano letivo 2023	1	-	3	54	81

Língua de trabalho

Portuguese

Objetivos

It is intended that trainees who attend the course acquire, recapitulate and consolidate knowledge/concepts of basic Mathematics, develop reasoning, work and independent study skills, which are fundamental prerequisites for attending courses taught at Higher Schools of Technology in IPS.

Resultados de aprendizagem e competências

At the end of the course, the trainee should be able to:

• Solve simple trigonometric equations;


• Interpret and analyze real functions of a real variable and their graphical representation;


• Interpret the definition of limit and continuity of a function at a point. Calculate limits and analyze the continuity of real functions of a real variable;


• Interpret the definition of derivative geometrically. Calculate derivatives using the derivation rules.


• Apply derivatives to the study of function graphs.

Modo de trabalho

Presencial

Programa

Trigonometry

• Problems involving triangles. Trigonometric circle. Sine, cosine and functions


• Tangent;


• Fundamental trigonometric relations;


• Elementary trigonometric equations

Real functions of real variable

• Functions: definition, domain, codomain, properties (injectivity, surjectivity, parity, sign, monotony, concavities) and graphic representation;


• Polynomial functions (first and second degree), rational and trigonometric;


• Exponential function and logarithmic function with base greater than one.

Limits and continuity

• Definition of limits and continuity;


• Property of finite and infinite limits. Indeterminacies. Notable Limits;


• Properties of continuous functions. Bolzano's theorem.

Differential calculation

• Definition and geometric interpretation of the derivative of a function;


• Derivation of polynomial, rational, trigonometric, exponential and logarithmic functions;


• Derivation rules;


• Application of derivatives to the study of graphs of functions in simple cases;


• Asymptotes.

Bibliografia Obrigatória

Departamento de matemática; Documentos do curso

Métodos de ensino e atividades de aprendizagem

It is considered a B-Learning approach, with 3 hours in person taught weekly to solve exercises (practical classes) and 3 hours remotely to present the material with application examples (theoretical-practical classes).

Autonomous work is promoted by offering students a set of exercises to solve.

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

Designation	Peso (%)
Participação presencial	70,00
Teste	30,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	30,00
Frequência das aulas	70,00
Total:	100,00

Obtenção de frequência

Students who successfully complete the course receive a certificate of completion (micro-credential).

Fórmula de cálculo da classificação final

100% class attendance