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Elements of Mathtematics II

Code:

VE07

Sigla:

EM II

Áreas Científicas
Classificação	Área Científica
CNAEF	Mathematics

Ocorrência: 2022/2023 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2223/course/view.php?id=1311
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Professional Technical Higher Education Courses in Electric Vehicles

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
TSPVE	28	Plano de Estudos_2015_16	1	-	6	60	162

Língua de trabalho

Portuguese
Obs.: Português

Objetivos

Provide students with the basic mathematical knowledge required in the professional training of a professional 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. Interpret the indefinite integral and apply the fundamental theorems of 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)

Knowledge of Mathematics acquired in secondary education and in the curricular unit (CU) Elementos de Matemática I.

Programa

1. Antiderivatives 
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. Indefinite 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.

Bibliografia Obrigatória

Fernandes, Sérgio; Cálculo Integral em ℝ, 2019 (Available in Moodle)

Bibliografia Complementar

Stewart, J.; Calculus, Cengage Learning, 2014
Larson, R. E., Hostetler, R. P., Edwards, B. H.; Cálculo, Vol. I - 8ª edição, McGraw Hill, 2006
Apostol, T.; Cálculo, Vol. I - 2ª edição, Reverté, 1994

Métodos de ensino e atividades de aprendizagem

CU Elementos de Matemática II has a teaching load of 4 hours per week.
In the classes, the fundamental concepts of the different topics of the course program will be presented and the main results will be demonstrated. Students will carry out, under the guidance of the teacher, a set of exercises, with a view to a deeper understanding of the topics covered and a greater consolidation of knowledge. In class, students should acquire a global view of the themes and their interconnections, accompanied by a correct and objective formulation of mathematical definitions, the precise statement of propositions and the practice of deductive reasoning.
It will be up to the student, a posteriori, to carry out an autonomous study on the topics covered and deepen their knowledge, using the study material recommended in the CU bibliography and the support of the professor during the respective office hours.
The CU will have all the information centralized on the Moodle platform.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Obtenção de frequência

If there is no indication to the contrary by the competent bodies, the tests and exams will be in person. If this is not possible, these evaluations will be carried out online and the evaluation rules and the respective procedures will be updated and published in a timely manner on the UC page in Moodle.
The achievement of this curricular unit can be obtained through two assessment processes: Continuous Assessment or Assessment by Exam.

Continuous evaluation:
Continuous assessment is based on the completion of two tests (with grades rounded to the nearest tenth). Access to continuous assessment requires attendance of at least 75% of classes. The conditions for passing the continuous assessment are as follows:
1. If the average (rounded to units) of the test scores is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to the referred average, provided that in any of the tests the grade was greater than or equal to 7.0 values.
2. If the average (rounded to units) of the test scores 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.
Recovery of one of the tests:
The realization of the recovery of one of the tests is conditioned to the confirmation of its viability, given the limitations that may be defined for the performance of tests and the spacing between the date of the 2nd test and the date of the exam of the 1st season.
If its viability is confirmed, the conditions for its realization will be as follows:
1. in order to meet the approval conditions (final average greater than or equal to 10 and classification in both Tests greater than or equal to 7.0 values), a student who has a classification greater than or equal to 7.0 in one of the Tests has the option to perform the recovery of one and only one of the Tests, on the same day and time of the 1st season Exam;
2. a student who has scored less than 7.0 in one of the Tests, has not been able to take it or has given up, will only be able to make the recovery of that Test;
3. Passed students cannot recover a Test in order to improve their grade.

Exam Assessment:
Students who choose not to take the Continuous Assessment, or who, having opted for it, have not been approved, may take an Exam.
The approval conditions are as follows:
1. If the exam grade (rounded to units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to the exam grade (rounded to units);
2. If the exam grade (rounded to units) is greater than or equal to 18, the student will have to take an oral exam, obtaining as a final grade the average of the classifications of the oral exam and the exam. If you do not attend the oral test, the final classification will be 17 points.

The tests have a time limit of 2 hours and the exams 2 hours and 30 minutes, being rated on a scale from 0 to 20.

Fórmula de cálculo da classificação final

Continuous Assessment:
Let T1 and T2 be the test scores rounded to the nearest tenth and CF=0.5T1x0.5T2 (rounded to the nearest integer).

1. If the average (rounded down to units) of the test scores is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to that average, provided that in any of the tests the grade was greater than or equal to 7.0 ;


2. If the average (rounded to units) of the test scores is greater than or equal to 18, the student will have to take an oral exam, the final grade being the average of these two grades. If you do not attend the oral test, the final classification will be 17 values.

Exam Assessment:

1. If the exam grade (rounded to units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to the exam grade (rounded to units);


2. If the exam grade (rounded to units) is greater than or equal to 18, the student will have to take an oral exam, obtaining as a final grade the average of the classifications of the oral exam and the exam. If you do not attend the oral test, the final classification will be 17 points.

Avaliação especial (TE, DA, ...)

Students covered by special rights referred to in the Regulation of Academic Activities and Guidelines for Assessment and School Performance of IPS Students must, until the second week of the beginning of the semester, contact the person responsible for the curricular unit to present their relevant specifics, under the terms provided for in the respective diplomas, otherwise they cannot be executed due to lack of objective conditions.

Melhoria de classificação

In accordance with Article 11 of the Academic Activities Regulation and Guidelines for the Assessment of Academic Performance by IPS Students, the classification improvement may occur in the academic year of enrollment, at the time of appeal, or in the academic year following the of approval, in any of the evaluation periods by exam, with the exception of the special season.

Observações

1- Rules for conducting assessment tests:

• If requested by the UC professor, the student must register in Moodle up to one week before each evaluation (students will receive information via email about the opening and deadline of these registrations).


• 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 reprographics.


• A form is provided for consultation during the test, which will be made available in Moodle in advance.


• During the assessment tests, it will be mandatory to present an identification document with a photograph.


• Leaving the room can only take place one hour after the start of the test and will imply the final delivery of the test. In the case of exams, leaving the room is only allowed one and a half hours after the start of the exam and will imply the final delivery of the test.


• Tests or questions written in pencil are not accepted and the use of a corrector in tests/exams is not allowed.


• It is not allowed the handling or display of cell phones, or any other means of remote communication, during the test, being sufficient reason for the cancellation of the assessment test, regardless of whether or not they have been used.


• The use of calculating machines is not allowed.


• In case of suspected fraud or any other circumstance that leads to the need to confirm the knowledge evidenced in the resolution of a test, the student may be called to a face-to-face session, which will focus only on this knowledge. If the student does not attend this session, without due justification, the test will be considered invalid.


• According to the IPS rules, whenever there is a situation of proven fraud in assessment tests carried out in person or at a distance in this UC, it will be canceled and the student will be subject to the application of the IPS Student Disciplinary Regulation.

2- The office hours for students to clarify doubts can be consulted on the UC page in Moodle.

3- Communication with students is made exclusively to the institutional address (@estudantes.ips.pt). It is up to the student to consult their area in the information system, on the discipline page in Moodle, as well as to manage and periodically consult their email account in the IPS domain, using it to communicate with the IPS services.