Mathematics I

Code:

1GE104

Acronym:

MAT I

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 1S

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	7	Bologna Syllabus since 2012	1	-	6	63	162

Teaching language

Portuguese

Objectives

The curricular unit of Mathematics I aims to study the real functions of several real variables. It is intended that students understand and assimilate the most important concepts related to the study of these functions and that they are able to apply them in real life situations, in particular in the area of Management. Given that one of the goals of management, as a decision support science, is the search for actions (i) that maximize the results due to constraints on the factors used or (ii) that minimize the factors used to achieve a given objective, among the subjects addressed, we highlight, in particular, the resolution of optimization problems, with and without restrictions. The curricular unit also aims to improve students' abilities in terms of abstract and logical reasoning and to express themselves with rigor of language.

Learning outcomes and competences

Upon completing the curricular unit, the student should be able to perform the study of real functions of several real variables, encompassing the aspects that are important in solving problems in the scope of the Management. Given a real function of several real variables, the student should be able to analyze it in particular, according to the following aspects: level curves, continuity, directions of greater/lower growth (studying the differentiability of the function), approximate value at a point, and the determination of maxima and minima, with or without restrictions.

Working method

Presencial

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

Mathematics knowledge from secondary education.

Program

Real functions of several real variables:

 1. Domain and graphic representation;
 2. Continuity;
 3. Partial derivatives and directional derivatives;
 4. Differentiability;
 5. Tangent plan;
 6. Taylor's polynomial. Functions approximation;
 7. Derivation of composite functions;
 8. Homogenous functions;
 9. Implicit functions;
10. Optimization: free extrema, extrema of implicit functions, extrema with constraints.

 

Mandatory literature

M. Aguiar, S. Furtado, J.M. Oliveira, H. Reis; Funções reais de várias variáveis reais - Texto teórico, FEP
M. Aguiar, S. Furtado, J.M. Oliveira, H. Reis; Funções reais de várias variáveis reais - Exercícios propostos, FEP
M. Aguiar, S. Furtado, J.M. Oliveira, H. Reis; Funções reais de várias variáveis reais - Exercícios resolvidos, FEP

Complementary Bibliography

Marsden Jerrold E.; Vector calculus. ISBN: 978-1-4292-2404-8
Chiang Alpha C.; Fundamental methods of mathematical economics. ISBN: 007-123823-9
Pires Cesaltina; Cálculo para economia e gestão. ISBN: 978-972-592-298-9
Cerqueira António de Melo da Costa; Funções reais definidas em IRn. ISBN: 972-578-130-9

Teaching methods and learning activities

Theoretical-practical classes.

The content will be developed on the basis of a theoretical-practical approach, either through exposition and illustration of concepts, or through practical problem solving. These approaches will be complemented, from an application perspective, with the illustration of simple practical problems in the field of Economics and Management.

The classroom course is accompanied by an on-line course located on the UP e-learning platform.

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

The evaluation in this course consists of two tests or a final exam.
Students with a final grade of 10 or higher (rounded to the units) are approved in the course unit.

Calculation formula of final grade

In the distributed evaluation regime the final classification is calculated by the rounding to the units of the result of the following expression:

0.5*t1+0.5*t2,

with t1 and t2, respectively, the grades obtained in the first and second tests, rounded to the nearest tenth.

The approval of a student through distributed assessment is conditioned by obtaining a value (rounded to the tenths) equal to or higher than 6.0 in each of the aforementioned grades ti, i=1,2.

In the final exam regime, the final grade is calculated by rounding the grade obtained in the exam to the nearest whole number.

Examinations or Special Assignments

None.

Internship work/project

None.

Special assessment (TE, DA, ...)

According to the RAC (Regulation of Evaluation of Knowledge).

Classification improvement

The improvement of classification to the discipline can not be done by the distributed evaluation method.

According to the RAC (Regulation of Evaluation of Knowledge).

Observations

1) A student is disconnected from the distributed assessment if he does not perform (more specifically, not deliver) the first or second test or if he obtains a t1 classification (described above) lower than 6.0 values.

2) A student in the conditions described in point 1) is automatically included in the evaluation system by final exam (normal and / or resource).

3) The first test will be carried out during the school year (on a date to be marked in due course). The second test will be held on the regular season exam day.

4) Any of the evaluation methods (distributed or exam) does not exclude the student from being able to carry out the examination of the appeal period (to obtain approval of the course or improvement of the classification obtained).