Elements of Mathematics II
Áreas Científicas |
Classificação |
Área Científica |
CNAEF |
Mathematics |
Ocorrência: 2023/2024 - 1S
Ciclos de Estudo/Cursos
Sigla |
Nº de Estudantes |
Plano de Estudos |
Anos Curriculares |
Créditos UCN |
Créditos ECTS |
Horas de Contacto |
Horas Totais |
TINFT |
21 |
Plano Estudos_2018_19 |
2 |
- |
6 |
60 |
162 |
Docência - Responsabilidades
Língua de trabalho
Portuguese
Obs.: Portugês
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:
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.
Understand the indefinite integral and apply the Fundamental Theorem of Integral Calculus.
Calculate areas and volumes of revolution by integration.
Compute improper integrals.
Modo de trabalho
Presencial
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
Sérgio Fernandes; Cálculo Integral em ℝ, 2019 (Available in Moodle)
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 (%) |
Participação presencial |
85,00 |
Teste |
15,00 |
Total: |
100,00 |
Componentes de Ocupação
Designation |
Tempo (Horas) |
Estudo autónomo |
0,00 |
Frequência das aulas |
0,00 |
Total: |
0,00 |
Obtenção de frequência
The use of this curricular unit can be obtained through two assessment processes: Continuous Assessment or Assessment by Exams.
Continuous evaluation
It consists of two Tests (if possible, face-to-face) and a set of Lesson Questions. The Tests have classifications from 0 to 20 and the Class Questions have classifications from 0 to 2, these classifications being rounded to the nearest tenth (failure to answer a Class Question corresponds to a classification of zero values in that question).
Access to continuous assessment requires attendance of at least 75% of classes.
Designating by MT the average of the classifications of the Tests and MQA the average of the classifications of the Class Questions, the final classification CF (rounded to the nearest integer)
CF= 0.85*MT+0.15*MQA.
The Continuous Assessment has the following approval conditions:
1. If the Tests are carried out in person and if CF is greater than or equal to 10 and less than 18, the student is approved with that grade, provided that the classification in each Test is greater than or equal to 7.0 values and CF greater than or equal to 8.5 values. 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 referred oral test. If the student does not attend the oral test, the final classification will be 17 points.
2. If the Tests are not carried out in person and if CF is greater than or equal to 10 and less than 15, the student is approved with that grade, provided that the classification in each Test is greater than or equal to 7.0 values and CF greater than or equal to to 8.5 values. If CF is greater than or equal to 15, the student must take an oral test (possibly via videoconference), obtaining as a final grade the average of the classification obtained and the referred oral test. If the student does not attend the oral test, the final classification will be 14 points.
Recovery of one of the tests
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), a student who has a classification greater than or equal to 7.0 in one of the Tests has the option of performing the recovery of one and only one of the Tests, on the same day and time as the Regular Season Exam. Under these conditions, if the student has scored less than 7.0 in one of the Tests, has not been able to take it or has given up, he can only take the recovery of that Test. It will not be possible to recover a Test in order to improve the grade.
- Assessment by Exam
Students who choose not to take the Continuous Assessment, or who, having opted for it, have not been approved, may take the Exam.
1. If the Exam is carried out in person and if the same grade (rounded to the nearest units) is greater than or equal to 10 and less than 18, the student is approved with that grade. If the Exam grade is greater than or equal to 18, the student must take an oral exam, obtaining as a final grade the average of the classification obtained and the referred oral exam. If the student does not attend the oral test, the final classification will be 17 points.
2. If the Exam is not carried out in person and if the same grade (rounded to the nearest units) is greater than or equal to 10 and less than 15, the student is approved with that grade. If the Exam score is greater than or equal to 15, the student must take an oral test (possibly via videoconference), obtaining the average of the classification obtained and the said oral test as a final score. If the student does not attend the oral test, the final classification will be 14 points.
Note: In tests carried out at a distance, any student may be asked to take an oral test to confirm the knowledge revealed in the resolution of the test. If the student does not attend the oral test, without due justification, the test will be canceled.
Fórmula de cálculo da classificação final
Designating by MT the average of the classifications of the Tests and MQA the average of the classifications of the Class Questions, the final classification CF (rounded to the nearest integer)
CF= 0.85*MT+0.15*M