Mathematical Methods II

Code:

TGI42

Sigla:

MMII

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 3T

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Industrial Management and Techinology

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
TGI	86	Plano de Estudos 2016	1	-	4	-	108

Docência - Responsabilidades

Docente	Responsabilidade
José António da Conceição Palma

Docência - Horas

Theorethical and Practical :	2,00
E-Learning:	2,00

Type	Docente	Turmas	Horas
Theorethical and Practical	Totais	2	4,00
Theorethical and Practical	Ana Teresa Agostinho Barros dos Santos		4,00
E-Learning	Totais	1	2,00
E-Learning	Ana Teresa Agostinho Barros dos Santos		2,00

Língua de trabalho

Portuguese
Obs.: Português

Objetivos

• Develop mathematical reasoning;
• Provide students with the ability to solve problems;
• Develop a critical and analytical spirit;
• Acquire knowledge about concepts and applications related to matrix calculus and
determinants;
• Acquire knowledge about concepts and applications related to vector calculus.

Resultados de aprendizagem e competências

The aim of this Curricular Unit is to acquire and apply knowledge of Mathematics, so that the student can use basic tools in this area, such as techniques and methodologies for solving systems of equations and vector calculus and that allow the student to develop the ability of analysis and reasoning for certain phenomena, namely in the field of Engineering

Modo de trabalho

B-learning

Programa

1. Matrices
Matrix definition; algebraic operations with matrices; inverse matrix. dependency and
linear independence of rows and columns of a matrix; characteristic of a matrix and
elementary operations. Systems of linear equations and Gauss elimination method;
Calculation of the inverse matrix by the Gauss elimination method.
2. Determinants
Definition of determinant, its properties and calculation methods. Applications of
determinants: calculation of the inverse matrix; Cramer's rule.
3. Vector Calculation
1. Definition of internal, external and mixed products; properties and applications.

Bibliografia Obrigatória

Kreyszig, Erwin, ; Advanced Engineering Mathematics , John Wiley & Sons, 1999
Campos Ferreira, J., ; Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 1987

Métodos de ensino e atividades de aprendizagem

In theoretical and practical classes, the expository method and problem solving are combined.

Remotely on the Moodle platform and on the Microsoft Teams platform, they access the UC contents through various materials and are proposed to carry out weekly activities.

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	86,00
Frequência das aulas	22,00
Total:	108,00

Obtenção de frequência

The use of this curricular unit can be obtained through two assessment processes: Continuous Assessment or Assessment by Exams.

Fórmula de cálculo da classificação final

Continuous Assessment

The continuous assessment is based on two tests (whose grades are considered rounded to the tenths). The conditions for continuous assessment are as follows:

If the average (rounded to the units) of the test grades is greater than or equal to 10 and less than 18, the student passes with a final grade equal to the said average, provided that in any of the tests the grade has been greater than or equal to 7.0;

If the average (rounded to the units) of the test grades is greater than or equal to 18, the student will have to present himself for an oral exam, with the final grade being the average of these two grades. If the student does not attend the oral exam, the final grade will be 17;

If the student obtains at least 7.0 in one of the tests, but the grade of the other test is less than 7.0 or the average (rounded to the units) is less than 10, the student will have the option to take a recovery test instead of the Normal Period exam. In these conditions, the test to be recovered will always be the test with the lowest grade or that has not been taken (in case the student has missed or given up).

A student who passes cannot take a recovery test with a view to improving the grade. To take a recovery test, the student will have to register, in the ways and deadlines that will be indicated in due course.

Exam Assessment

Students who choose not to take continuous assessment, or who, having opted for it, have not passed, may attend regular exam periods.

The assessment based on exams follows the usual rules, with the following conditions:

if the exam grade (rounded to the units) is greater than or equal to 10 and less than 18, the student passes with a final grade equal to the exam grade (rounded to the units);

if the exam grade (rounded to the units) is greater than or equal to 18, the student will have to present himself for an oral exam, obtaining as a final grade the average of the grades of the said oral exam and the exam. If he does not attend the oral exam, the final grade will be 17.

Unless otherwise indicated by the competent bodies, tests and exams will be in person. If this is not possible, these assessments will be carried out online and the assessment standards and their respective procedures will be updated and timely disclosed on the UC page on Moodle.

Grade Improvement

According to Article 11 of the Regulation of Academic Activities and Guidelines for the Evaluation of Students’ School Performance of IPS, the improvement of the grade may occur in the academic year of registration, in the appeal period, or in the academic year following approval, in any of the exam evaluation periods, except

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