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Mathematical Applications B

Code:

REID21

Sigla:

AMB

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2023/2024 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2324/course/view.php?id=1537
Curso/CE Responsável:	Professional Technical Higher Education Courses in Smart Grids and Home Automation

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
REID	31	Plano de Estudos 2018/19	1	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

The general objective of this course unit is to provide students with the complementary basic mathematical knowledge to the one acquired under the previous course unit Fundamentals of Calculus.

Resultados de aprendizagem e competências

By the end of term time, students should be able to:

1. Identify the algebraic, trigonometric and exponential representations of a complex number and perform operations with complex numbers.


2. Carry out algebraic operations between matrices.


3. Apply the matrix condensation process and solve systems of linear equations by Gauss elimination method.


4. Calculate the determinant of a matrix and apply its properties to compute invertible matrices and solve systems of linear equations.


5. Carry out operations with vectors and apply their properties.


6. Calculate the dot, cross and triple products between vectors.


7. Recognize straight lines and conic sections and identify their associated geometric elements.

Modo de trabalho

Presencial

Programa

1. Complex numbers
1.1 Complex numbers introduction: algebraic representations, conjugate and modulus.
1.2 Operations with complex numbers.
1.3 Trigonometric and exponential representations of a complex number.
1.4 nth root of a complex number.

2. Matrix calculus
2.1 Matrix notions and operations.
2.2 Discussion and resolution of systems of linear equations.

3. Determinants
3.1 Definition of determinant, its properties and calculation methods.
3.2 Applications of determinants: calculation of the inverse matrix using the adjoint matrix; Cramer's rule.

4. Vector calculus
4.1 Vector notion and operations between vectors.
4.2 Inner product of vectors; norm of a vector, unit vector and its properties.
4.3 Angle and orthogonal projection between two vectors; orthogonal and orthonormed vectors.
4.4 Cross and triple products between vectorss: definition, properties and applications.

5. Analytic geometry in a plane
5.1 Slope and equations of a straight line in a plane; parallelism and perpendicularity between straight lines.
5.2 Distance between straight lines; distance between a point and a straight line.
5.3 Conic sections: circle, ellipse, hyperbola and parabola.

Bibliografia Obrigatória

Luz, C., Matos, A. e Nunes, S.; Álgebra Linear (Volume I), ESTSetúbal/IPS, 2002. ISBN: 972-8431-16-9 (Available at the school library)

Bibliografia Complementar

Monteiro, A. e Pinto, G.; Álgebra Linear e Geometria Analítica - problemas e exercícios, McGraw-Hill, 1997. ISBN: 972-8298-66-8 (Available at the school library)
Sullivan, M.; Precalculus - 11th edition, Pearson, 2020. ISBN: 978-0135189405

Métodos de ensino e atividades de aprendizagem

Student-centered approach is the pedagogical methodology applied.
During classes, the fundamental concepts on the different subjects of the course unit are firstly presented, illustrated by some application examples. Afterwards, students will carry out exercises to consolidate knowledge on the covered topics through collaborative working group, under the guidance of the teacher.

Tipo de avaliação

Distributed evaluation without 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 approval in this UC (curricular unit) can be obtained through two assessment processes: Continuous Evaluation or Exam Evaluation.

CONTINUOUS EVALUATION
The Continuous Evaluation presupposes the accomplishment of four summative tests and, for freshmen students, a compulsory attendance of at least 75% of the classes.
Let T be the grade (from zero to 8 values, rounded to tenths) obtained in the summative test and MT1, MT2, MT3 the grades (from zero to 4 values, rounded to tenths) obtained in the short summative tests. The final classification CF (rounded to units) will be the plain sum of the four grades.

The approval conditions are as follows:

1. If CF is greater than or equal to 10 and less than 18, the student passes on with a final grade equal to CF.
   
   


2. If a student fails the approval conditions referred in point 1, he can recover the grade obtained in T on the date of the normal period exam. 

EVALUATION BY EXAM
Students who have not obtained approval for Continuous Assessment may take an exam, being approved as long as they obtain a grade of 10 or higher.

NOTE: In any of the evaluation processes, whenever the final classification is greater than or equal to 18 values, the student must carried out an oral test, obtaining as a final grade the average of the classifications of the written test and of the said oral test . If the student does not attend the oral test, the final classification will be 17 values.

Fórmula de cálculo da classificação final

CF = MT1 + T + MT2 + MT3
or
Exam evaluation

Avaliação especial (TE, DA, ...)

Working students, high-level athletes, association leaders and students under the Religious Freedom Law must address, until the second academic week of the semester, to the head of the Curricular Unit to present their pertinent specificities, in accordance with the terms of the respective diplomas under penalty of failure to enforce them for lack of objective conditions.

Melhoria de classificação

In this course unit passed students of this academic year may only apply to their improvement classification in the supplementary period exam.

Observações

• The summative test shall be of 90 minutes, the short summative tests shall be of 45 minutes, the recovery test of 90 minutes and each exam of 150 minutes.


• To perform the recovery test and/or exams, an identification document with photo has to be presented.


• During assessment tests and examinatiom, only the enquiry form given by the teacher is allowed; handling or displaying any electronic equipment is prohibited.