Mathematics II

Code:

1GE109

Acronym:

MAT II

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 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	332	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

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

Mandatory literature

Aguiar M., Furtado S., Oliveira J. and Reis H.; Apontamentos de Cálculo Integral e Álgebra Linear, 2015

Complementary Bibliography

Agudo, F. R. Dias; Introdução à Álgebra linear e Geometria Analítica, Escolar Editora, 1992
Ferreira, M. e Amaral, I.; Matemática. Primitivas e Integrais, edições Sílabo, 2006
Giraldes, E., Fernandes, V. H. e Smith, M. P. M.; Curso de Álgebra Linear e Geometria Analítica, McGraw-Hill, 1995
Stewart, J.; Cálculo, S. Paulo: Pioneira, 2001
Cabral, I, Perdigão, C., Saiago, C.; Álgebra Linear, Escolar Editora, 2010. ISBN: 978-972-592-309-2
Pires, C.; Cálculo para Economia e Gestão, Escolar Editora, 2011. ISBN: 978-972-592-298-9

Teaching methods and learning activities

Practical and theoretical classes

Evaluation Type

Distributed evaluation without final exam

Assessment Components

Designation	Weight (%)
Exame	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

In the continuous evaluation system, the final grade is obtained by rounding to units the next number:
0.5*n1+0.5*n2
where n1 and n2 are the marks of the first and second tests, respectively, rounded to one decimal place. However, if one of the test scores (t1 or t2) is less than 6 points, the student is not approved in the continuous evaluation system. 
In the final examination system, the final grade is the one obtained in the exam (rounded to unit).

Classification improvement

Students cannot improve the rating by continuous evaluation.

Observations

1) The continuous assessment consists of two tests, the first of which to be held during the scholar season.
2) The students evaluated in the first test of continuous evaluation system and with a mark not less than 6  can always choose to perform the second test or take the examination in the regular season.
3) The students evaluated in the two tests cannot be evaluated by exam in the normal season.
4) All students can be evaluated in the appeal season.