Elements of Mathtematics II
Ocorrência: 2021/2022 - 2S
Ciclos de Estudo/Cursos
|Nº de Estudantes
|Plano de Estudos
|Horas de Contacto
|Plano de Estudos_2015_16
Docência - Responsabilidades
Docência - Horas
|Theorethical and Practical :
Língua de trabalho
The general objective of this course unit is to provide students with the basic mathematical knowledge required in the professional training of a top professional technician concerning integral calculus.
Resultados de aprendizagem e competências
By the end of term time, students should be able to:
- Identify and calculate antiderivatives of elementary functions.
- Calculate antiderivatives using integration by parts, integration by partial fraction decomposition and integration by substitution.
- Interpret the Riemann integral and its properties.
- Interpret the indefinitive integral and apply the fundamental theorems of calculus.
- Calculate areas and volumes of revolution by integration.
- Compute improper integrals.
Modo de trabalho
Pré-requisitos (conhecimentos prévios) e co-requisitos (conhecimentos simultâneos)
Previous mathematical knowledge acquired through the course unit Elementos de Matemática I, in particular differential calculus.
1.1. Antiderivative: motivation, definition and properties. Antiderivatives of elementary functions.
1.2. Techniques of integration: by parts, by substitution and by partial fraction decomposition.2. Integral Calculus
2.1. Riemann integral and its geometric interpretation; properties.
2.2. Indefinitive integral and its properties. First and second fundamental theorems of calculus.
2.3. Integration by parts and by substitution.
2.4. Integral calculus' applications.
2.5. Improper integrals.
Sérgio Fernandes; Cálculo Integral em ℝ, 2019
Acilina Azenha e Maria Amélia Jerónimo; Elementos de Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, 2000. ISBN: 9789728298036
Fernanda Sequeira; Análise Matemática 3º Volume - Exercícios Resolvidos e Propostos, Litexa Editora, 1982. ISBN: 9789725780497
Métodos de ensino e atividades de aprendizagem
Student-centered approach is the pedagogical methology applied. During classes, the fundamental concepts on the different subjects of the course unit are firstly presented, illustrated by some application examples. Afterwards, students will carry out exercises to consolidate knowledge on the covered topics through collaborative working group, under the guidance of the teacher.
Tipo de avaliação
Distributed evaluation with final exam
Componentes de Avaliação
Componentes de Ocupação
|Frequência das aulas
Obtenção de frequência
The approval in this UC (curricular unit) can be obtained through two assessment processes: Continuous Evaluation or Exam Evaluation. CONTINUOUS EVALUATION
The Continuous Evaluation presupposes the accomplishment of 4 summative tests and a compulsory attendance of at least 75% of the classes.
Assigning by MT1, MT2, MT3 and MT4 the grades (from zero to 5 values, rounded to tenths) obtained in each of the 4 summative tests, the final classification CF (rounded to units) will be the plain sum of the four grades.
The approval conditions are as follows:
EVALUATION BY EXAM
- If CF is greater than or equal to 10 and less than 18, the student passes on with a final grade equal to CF, provided that the classification in any of the sums P1=MT1+MT2 and P2=MT3+MT4 is greater than or equal to 3.5 values.
- If a student fails the approval conditions referred in point 1, the student can recover the lowest grade obtained in P1 and P2 by performing a recovery test on the date of the normal period exam, provided that P1 or P2 is greater than or equal to 3.5 values.
Students who have not obtained approval for Continuous Assessment may take an exam, being approved as long as they obtain a grade of 10 or higher.
NOTE: In any of the evaluation processes, whenever the final classification is greater than or equal to 18 values, the student must carried out an oral test, obtaining as a final grade the average of the classifications of the written test and of the said oral test . If the student does not attend the oral test, the final classification will be 17 values.
Fórmula de cálculo da classificação final
CF = MT1 + MT2 + MT3 + MT4
Avaliação especial (TE, DA, ...)
Working students, high-level athletes, association leaders and students under the Religious Freedom Law must address, until the second academic week of the semester, to the head of the Curricular Unit to present their pertinent specificities, in accordance with the terms of the respective diplomas under penalty of failure to enforce them for lack of objective conditions.
Melhoria de classificação
In this course unit passed students of this academic year may only apply to their improvement classification in the supplementary period exam.
- Each summative test shall be of 60 minutes, the recovery test of 90 minutes and each exam of 150 minutes.
- To perform the recovery test and/or exams, an identification document with photo has to be presented.
- During assessment tests and examinatiom, only the enquiry form given by the teacher is allowed; handling or displaying any electronic equipment is prohibited.