Mathematics II

Code:

1GE109

Acronym:

MAT II

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2021/2022 - 2S

Active?	Yes
Responsible unit:	Agrupamento Científico de Matemática e Sistemas de Informação
Course/CS Responsible:	Bachelor in Business Administration

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LGES	322	Bologna Syllabus since 2012	1	-	6	63	162

Teaching language

Portuguese

Objectives

The main goal of the Matemática II course is to give the students a basic knowledge of Integral Calculus and Linear Algebra. It is expected that the students understand the main concepts and results studied in the course and are able to apply them to theoretical and pratical problems, namely in the context of Economics.  It is also expected that the students develop other skills, in particular a logical and abstract reasoning.

Learning outcomes and competences

It is intended that students obtain basic skills in Integral Calculus and Linear Algebra and are able to apply the acquired knowledge to other situations of their academic and professional life.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Program

Part I -Integration 

1. Indefinite Integrals


2. Definite Integrals


3. Improper Integrals


4. Double Integrals


5. Applications

Parte II- Linear Algebra  

1. Matrices: Introduction


2. Determinants and rank of a matrix 


3. Systems of linear equations 


4. The vector space Rⁿ 


5. Eigenvectors and eigenvalues of a square matrix


6. Applications

Mandatory literature

Vítor Matos; Matemática para Ciências Económicas, 2020

Complementary Bibliography

Pires, C.; Cálculo para Economia e Gestão, Escolar Editora, 2011. ISBN: 978-972-592-298-9
Larson, Hostetler e Edwards; Cálculo, Volume I, Mc Graw Hill, 2006
Gilbert Strang; Linear Algebra and Its Applications, Thomson Learning, 1988

Teaching methods and learning activities

Practical and theoretical classes

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	99,00
Frequência das aulas	63,00
Total:	162,00

Eligibility for exams

Calculation formula of final grade

There are three assessment moments in the course:
(i) distributed assessment;
(ii) examination of the normal season;
(iii) examination of the appeal period.

The evaluation is divided into two groups of equal weight:
Group I - Integration and Applications.
Group II - Linear Algebra and Applications.

The distributed assessment consists of three tests (the last one being carried out simultaneously with the normal exam). The first test and half of the third form the assessment of the Group I. The second test and half of the third form the assessment of the Group II.

The final grade of the distributed assessment is calculated using a weighted average in which the first and second tests weigh both 25% and the third test weighs 50%.

Exam assessment comprises two parts, one referring to Group I and the other to Group II, each weighing 50%.

In addition to the average there is a benchmarks in each of the Groups corresponding to 35% of its weight, which is 50%. Therefore, a minimum grade is 17.5% in each group.
Transforming to "valores", each Group is worth 10 "valores" ​​and a minimum score in each Group is 3.5 "valores".

The final grade is rounded to the nearest unit (notes with a fractional component greater than or equal to 0.5 will be rounded to the next unit).

Function
int(x) : largest integer not greater than x

Algorithm:
t1 ← score from the first test (by RAC imposition, quoted to 20 values).
t2 ← score from the second test (by RAC imposition, quoted to 20 values).
p1 ← score of the first part of the third test (quoted to 10 values).
p2 ← score of the second part of the third test (quoted to 10 values).
If {Continuous Assessment = True}
then{
   g1 ← 0.25*t1 + 0.5*p1
   g2 ← 0.25*t2 + 0.5*p2
}
else{
   g1 ← Group I exam score (quoted for 10 values).
   g2 ← Group II score from the exam (quoted to 10 values).
}
If {g1 < 3.5 or g2 < 3.5}
then { Final Grading = "Failed for Missing Component"}
else { Final Grade = int(g1+g2+0.5) }

Classification improvement

Students cannot improve the rating by continuous evaluation.