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Mathematical Applications A

Code:

TGA21

Sigla:

AMA

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2324/course/view.php?id=1501
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	36	Plano de Estudos_2015_16	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

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

Resultados de aprendizagem e competências

1. Perform algebraic operations with matrices.
2. Use matrices to represent objects and solve linear problems.
3. Apply the matrix condensation process and solve systems of linear equations using the Gaussian elimination method.
4. Perform algebraic and geometric operations with vectors and apply their properties to solve geometric problems.
5. Organize a set of data to facilitate its analysis, whether through tables, graphs, or by calculating relevant statistical measures, and interpret them.
6. Identify and model the linear correlation between a dependent variable and an independent variable, in order to estimate the value of one based on the value of the other.
7. Calculate the probability of events from the proposed models and the properties of the concepts of probability and conditional probability, interpreting the result.
8. Calculate probabilities based on the family of normal models using a table of the standard normal distribution function.

Modo de trabalho

Presencial

Programa

1. Matrix Calculus
1.1. Notion of matrix and operations with matrices
1.2. Discussion and resolution of systems of linear equations

2. Vector Calculus
2.1. Notion of vector and operations between vectors
2.2. Inner product of vectors; norm and unit vector of a vector and their properties
2.3. Angle and orthogonal projection between two vectors; decomposition of vectors into two orthogonal components
2.4. Systems of orthogonal and orthonormal vectors
2.5. Determinant of order 3; cross product and scalar triple product of vectors: definition, properties, and applications

3. Descriptive Statistics. Probabilities of Events
3.1. Descriptive Statistics
3.1.1. Organization and interpretation of qualitative and quantitative data through frequency tables and graphs
3.1.2. Measures of central tendency and dispersion
3.1.3. Simple Linear Regression
3.2. Probabilities of Events
3.2.1. Definition of probability and its properties
3.2.2. Calculation of probabilities of events
3.2.3. Independence of events. Conditional probability
3.2.4. Total Probability Theorem and Bayes' Theorem
3.3. Normal Distribution

Bibliografia Obrigatória

DMAT; Apontamentos e exercícios; elaborados por docentes do Departamento de Matemática (Disponíveis na página da UC no Moodle)

Bibliografia Complementar

Luz, C., Matos, A. e Nunes, S.; ; Álgebra Linear (Volume I), ESTSetúbal, 2002. ISBN: ISBN 972-8431-16-9
Magalhães, L. T; Álgebra Linear como introdução à Matemática Aplicada, Texto Editora , 1989. ISBN: _972-47-0007-0
Galvão de Melo, F.; Probabilidades e Estatística, Escolar Editora, 1993
Murteira, B.; Antunes, M.; Probabilidades e Estatística, Volume 2, Escolar Editora
Montgomery, D.; Runger, G.; Applied Statistics and Probability for Engineers, John Wiley & Sons.

Métodos de ensino e atividades de aprendizagem

The UC Aplicações Matemáticas A has a teaching load of 4 hours per week (presential class).
In the classes, the fundamental concepts of the different topics of the course program will be presented. 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.
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 UC bibliography, worsheets and the support of the professor during the respective office hours.
The UC will have all the information centralized on the Moodle platform.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Trabalho escrito	20,00
Teste	80,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Frequência das aulas	60,00
Estudo autónomo	102,00
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 individual tests, one mini-teste and one group-work.

If T1, T2, MT and TG are the 1st test, 2nd test, the mini-test and the group work, respectively, the final classification MF (rounded to units) is
MF = 0.3T1 + 0.3T2 + 0.2MT + 0.2TG

The conditions for passing the continuous assessment are as follows:
1. If the final classification MF 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/mini-test the grade was greater than or equal to 7.0 values.
2. If CF of 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 tests/mini-test greater than or equal to 7.0 values), a student who has a classification greater than or equal to 7.0 in two of the tests/mini-test has the option to perform the recovery of one and only one of the tests/mini-test (the one with the lowest score), 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/mini-test, 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 1 hour and 30 minutes and the exams 2 hours and 30 minutes, being rated on a scale from 0 to 20.

Fórmula de cálculo da classificação final

MF = 0.3T1 + 0.3T2 + 0.2MT + 0.2TG.

or

Final Exame Classification

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, via email patricia.ribeiro@estsetubal.ips.pt 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.


• In tests, it is permitted to consult an A4 sheet, handwritten by the student.


• 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, with the exception of the 3rd chapter.


• 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.