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Mathematical Applications A

Code:

ARCI21

Sigla:

AMA

Áreas Científicas
Classificação	Área Científica
CNAEF	Mathematics

Ocorrência: 2023/2024 - 2S

Ativa?	Yes
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:	Automation, Robotics and Industrial Control

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
ARCIL	30	Plano de Estudos_2015_16	1	-	6	60	162
TSPARC	27	Plano de Estudos_2015_16	1	-	6	60	162

Língua de trabalho

Portuguese
Obs.: Português

Objetivos

To provide students with the basic mathematical knowledge of Linear Algebra and Statistics necessary for performing tasks and as the foundation for the ongoing education of a professional higher 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

Azenha, A. e Jerónimo, M. A.; Cálculo Diferencial e Integral em R e Rn, McGraw-Hill, Portugal, 1995. ISBN: ISBN 972-8298-03-X
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
Murteira, B.; Antunes, M.; Probabilidades e Estatística, Volume 2, Escolar Editora
Montgomery, D.; Runger, G.; Applied Statistics and Probability for Engineers, John Wiley & Sons.
Sheldon M. Ross; Introduction to Probability and Statistics for Engineers and Scientist, , Elsevier/Academic Press
Siegel, A.F.; Statistics and data analysis : an introduction, New York : John Wiley & Sons.
Watson, Billingsley, Croft, Huntsberger; Statistics : for management and economics, Boston : Allyn & Bacon.

Métodos de ensino e atividades de aprendizagem

The course unit will be taught over 15 weeks. For each week, study materials will be provided, along with a set of activities that students should complete to succeed in the course unit.

In the classes, the theory will be presented and explained, along with examples of application and solution of exercises. Regularly, classes will be dedicated to solving exercises of direct application and studying problems.

Tipo de avaliação

Distributed evaluation with final exam

Componentes de Avaliação

Designation	Peso (%)
Participação presencial	75,00
Trabalho escrito	25,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Frequência das aulas	100,00
Total:	100,00

Obtenção de frequência

The completion of this course unit can be achieved through two assessment processes: Continuous Assessment or Assessment through Exams.

Fórmula de cálculo da classificação final

**Continuous Assessment**

Continuous Assessment involves the completion of 3 mini-tests and 1 group project. Letting MMT represent the average of the mini-tests grades (ranging from 0 to 20, rounded to the nearest hundredth) obtained in the tests, and NTG represent the grade of the group project, the final grade CF (rounded to the nearest integer) will be calculated as follows:
CF = MMT * 0.75 + NTG * 0.25

The passing conditions are as follows:
1. If CF is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to CF, provided that the grade in each of the mini-tests was greater than or equal to 7.00.
2. If CF is less than 10 and the student has obtained a positive grade in the group project, the student may take a recovery test for one of the mini-tests to improve the grade of that mini-test.

**Assessment by Exam**

Students who have not passed through Continuous Assessment may take an exam, and they will be considered approved if they obtain a grade of 10 or higher.

Note: In any of the evaluation processes, if the final grade is 18 or higher, the student must attend an oral exam, with the final grade being the average of the written exam and the oral exam. If the student does not attend the oral exam, the final grade will be 17.