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Elements of Mathtematics II

Code:

TGA10

Sigla:

EM II

Áreas Científicas
Classificação	Área Científica
CNAEF	Mathematics

Ocorrência: 2021/2022 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=622
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
TSPTGA	39	Plano de Estudos_2015_16	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

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

Resultados de aprendizagem e competências

By the end of term time, students should be able to:

1. Identify and calculate antiderivatives of elementary functions.


2. Calculate antiderivatives using integration by parts, integration by partial fraction decomposition and integration by substitution.


3. Interpret the Riemann integral and its properties.


4. Understand the indefinite integral and apply the Fundamental Theorem of Integral Calculus.


5. Calculate areas and volumes of revolution by integration.


6. Compute improper integrals.

Modo de trabalho

Presencial

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.

Programa

1. Antiderivatives

• Notion of antiderivative: motivation, definition and properties. Antiderivatives of elementary functions.


• Techniques of integration: by parts, by substitution and by partial fraction decomposition.

• Riemann integral and its geometric interpretation; properties.


• Indefinite integral and its properties. First and second fundamental theorems of calculus.


• Integration by parts and by substitution.


• Integral calculus' applications.


• Improper integrals.

Bibliografia Obrigatória

Vários; Apontamentos editados pelo Departamento de Matemática.

Bibliografia Complementar

Ricardo Almeida e Rita Simões; Primitivas, Escolar editora
James Stewart; Calculus: Early Transcendentals , Cengage learning, inc

Métodos de ensino e atividades de aprendizagem

During classes, the fundamental concepts on the different subjects of the course unit are presented, illustrated by some application examples. Afterwards, students will carry out exercises to consolidate knowledge on the covered topics under the guidance of the teacher.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

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

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Obtenção de frequência

The approval in this UC (curricular unit) can be obtained through two assessment processes: Continuous Assessment or Assessment by Exams.

Continuous asessment

The Continuous Assessment consists of carrying out two tests. Tests have ratings from 0 to 20, these ratings will be rounded to the nearest tenth. Access to continuous assessment requires attendance of at least 75% of classes. The final grade (CF) is the arithmetic mean of the grades of the two tests (rounded to the nearest unit).

The Continuous Assessment has the following approval conditions:

1. If CF is greater than or equal to 10 and less than 18, the student is approved with this grade, provided that the classification in each Test is greater than or equal to 7.0 values.


2. If CF is greater than or equal to 18, the student must take an oral test, obtaining as a final grade the average of the classification obtained and the aforementioned oral test. If the student does not attend the oral test, the final classification will be 17 values.


3. Test recovery: In order to complete the UC (final average greater than or equal to 10 and classification in both Tests greater than or equal to 7.0 values), a student can recover the grade of one of the tests with the following conditions:

• A student who has not scored 7.0 in the first test has the option of performing the recovery of that test on the same day and time as the second test. If he gets 7.0 or more in the recovery of the first test, you can perform the second test on the same day and time as the Normal Season Exam.


• A student who does not have a score greater than or equal to 7.0 in the second test has the option to perform the recovery of that test, on the same day and time as the Normal Season Exam.


• A student who has a classification greater than or equal to 7.0 in both tests but who does not have a CF of 10, has the option of performing the recovery of the second test, on the same day and time as the Normal Season Exam.

Assessment by Exam

Students who choose not to take the Continuous Assessment, or who, having opted for it, have not been approved, may take an Exam.

1. If the Exam grade (rounded up to units) is greater than or equal to 10 and less than 18, the student is approved with this grade.


2. If the Exam score is greater than or equal to 18, the student must take an oral test, obtaining as a final grade the average of the classification obtained and of the referred 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=(T1+T2)/2
or
Exam evaluation

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.

Observações

Rules for conducting tests and exams 

• The assessment tests and exams are preferably in person, and can be carried out remotely if there are restrictions that require it.


• Each test lasts 1h30m and the exams last 2 hours and 30 minutes.


• In all tests it is necessary to present an identification document with photo.


• The tests are individual, so any type of communication or consultation with third parties is expressly prohibited during the tests.


• The use of any electronic equipment, namely mobile phones is not allowed.


• Exams or questions written in pencil are not accepted.


• The student should only leave the room after authorization from the teacher.


• On the test day, before entering the room, the student has to give the teacher a test book (completely blank). The purchase of the test book (consisting of a cover and four sheets, which remains blank) is made in advance in the print shop.


• In tests and exams, it will be allowed to consult a form (sheet A4) handwritten by the student.