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Elements of Mathtematics II

Code:

TPSIA10

Sigla:

EM II

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2021/2022 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=2018
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
TPSIA	21	Plano de Estudos	1	-	6	60	162

Língua de trabalho

Portuguese
Obs.: Portuguesa

Objetivos

Provide students with the basic mathematical knowledge required in the professional training of a professional higher technician.

Resultados de aprendizagem e competências

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 indefinitive 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)

Previous mathematical knowledge acquired through the course unit Elementos de Matemática I, in particular differential calculus.

Programa

1. Antiderivatives

1.1 Definition and properties. Immediate antiderivatives.
1.2 Methods: Parts, Substitution and Decomposition


2. Integral Calculus

2.1 Riemann integral. Properties.
2.2 Indefinite integral. Properties. Fundamental Theorem of Calculus, Barrow’s formula.
2.3 Integration by parts and integration by substitution.
2.4 Areas and volumes of solids of revolution.
2.5 Improper integrals.

Bibliografia Obrigatória

Fernandes, Sérgio; Cálculo Integral em R, Departamento de Matemática, 2019

Bibliografia Complementar

Stewart, J.; Cálculo, 7ª edição, 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

The classes are theoretical-practical. The fundamental concepts of the different subjects of the program are presented. Exercises are also solved in way to  illustrate the topics covered. Under the guidance of the teacher, students will carry out a series of exercises that will allow them to gain a deeper understanding of the topics covered.

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

The use of the Curricular Unit (UC) can be obtained through two evaluation processes: Continuous Assessment and Examination Evaluation.

Continuous Evaluation

The continuous evaluation is based on the performance of two tests. Access to continuous assessment requires attendance of at least 75% of classes.

The approval conditions for continuous assessment are as follows:

1. If CF (rounded to the units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to CF (if booth tests are greater than or equal to 7.0).
2. If CF (rounded to the units) is greater than or equal to 18, the student will have to take an oral test, the final grade being the average of these two marks. If you do not attend the oral test the final classification will be 17 values.
3. If CF is less than 10, the student can perform the recovery of the test with the lowest grade, on the same day and time of the normal period exam, having to previously choose to perform the recovery test or the exam.

Remark:
If the student is not able to perform one of the tests and through justification presented to the responsible teacher of the UC (personally or via email), or if the student give up one of the tests, the student can only recover that test.

Examination Evaluation

The examination evaluation is based on the performance of an examination. The conditions of approval being as follows:


If E is the grade obtained in the exam (rounded to the units),

1. If E (rounded to the units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to E.
2. If E is greater than or equal to 18, the student will have to take an oral test, obtaining as a final mark the average of the classifications of said oral test and the exam. If you do not attend the oral test, the final grade will be 17 points.

Fórmula de cálculo da classificação final

Assigning by T1 and T2 the scores (from 0 to 20 values, rounded to the tenths) obtained in the 1st test and in the 2nd test, the final grade CF (rounded to the units) will be calculated as follows:

CF=(T1+T2)/2

or Exam evaluation

Avaliação especial (TE, DA, ...)

Students covered by article 217 of the Rules of Academic Activities and Guidelines for Assessment and School Performance of Students of the IPS must, by the second week of the beginning of the semester, contact the responsable for the course, in person or by email carla.rodrigues @ estsetubal.ips.pt, in order to present their specific characteristics, under the terms established in the respective diplomas, failing which they can not be executed due to lack of objective conditions.

Melhoria de classificação

According to Article 11 of the IPS Student Performance Assessment Guidelines, the improvement of classification may occur in the school year of enrollment, at the time of appeal, or in the school year following that of approval, at any time examination, with the exception of the special season.

Observações

• Each test has a duration of 2 hours and the exam lasts 2 hours and 30 minutes.
• The use of mobile phones or any other means of remote communication during the tests or exams is not allowed or shown as a reason for canceling the test, regardless of whether or not themselves.
• Students must perform the test/exam resolution on their own IPS sheets, by first purchasing the test booklet (1 cover and 4 continuation sheets) in the reprography.
• It is mandatory to enroll in the examinations up to one week before the date of its accomplishment. 
• On the day of the exam, the students must be the student card holder, which will serve as an identification element. In case they do not have a student card, they must present the Identity Card / Citizen Card, or document with photograph and similar identification value.
• The abandonment of the room in case of withdrawal can only be done one hour after the start of the examination and will imply the final delivery of the test. • No proof or written questions are accepted in pencil.
• Communication with students is done exclusively for the institutional address (@ students.ips.pt). It is up to the student to consult his area in the information system, as well as to manage and periodically consult his email account in the IPS domain, using it to communicate with the IPS services.