Mathematics

Scholar Year: 2023/2024 - 1S

Courses

Head Teacher Responsability Sandra Inês da Cunha Monteiro Head

Weekly workload Hours/week T TP P PL L TC E OT OT/PL TPL O S Type of classes 2 2 Lectures Type Teacher Classes Hours Theoretical Totals 1 2,00 Sandra Monteiro   2,00 Practices Totals 3 6,00 Maria João Ferreira   6,00 Sandra Monteiro   2,00

Teaching language

Portuguese

Intended learning outcomes (Knowledges, skills and competencies to be developed by the students)

Management students, in particular Accounting and Finance, need several important mathematical tools; among them are the knowledge of calculus and linear algebra, both present in economic theory and econometrics, which are key disciplines in this area. Mastering the basics of these areas is essential to the pursuit of studies in the field of business administration. This curricular unit aims to enable students in acquiring basic mathematical skills necessary for the development of logical reasoning, articulate and apply the various concepts to solve problems, develop reasoning analysis, scientific thinking and critical attitude.

Syllabus

1. MATHEMATICAL LOGIC AND SET THEORY
1.1 Designations and propositions
1.2 Propositional Calculus
1.3 Designatory Expressions and Propositional Expressions
1.4 Quantifiers
1.5 Set Notion
1.6 Set operations

2. VECTORS and MATRICES
2.1 Introduction to linear equation systems
2.2 Definition and geometric interpretation of vectors
2.3 Scalar Product
2.4 Vector Norm
2.5 Definition of matrix
2.6 Typology of matrices
2.7 Transpose matrix
2.8 Algebraic operations with matrices

3. DETERMINANT and INVERSE MATRIX
3.1 Definition of determinant for matrices of order 2
3.2 Definition of determinant for matrices of order larger than 2
3.3 Determinant properties
3.4 Inverse Matrix
3.5 Applications

4. REAL FUNCTIONS OF REAL VARIABLE
4.1 Definition of function
4.2 Real functions of real variable
4.3 Graphic representation
4.4 Properties
4.5 Basic Functions
4.6 Operations with Functions
4.7 Limits and continuity

5. DIFFERENTIAL CALCULUS
5.1 Definition of the derivative of a real function of a real variable
5.2 Rules of derivation
5.3 Applications

Demonstration of the syllabus coherence with the UC intended learning outcomes

Mathematic is curricular unit of the basic sciences essential to the development of reasoning. The contents are built to allow the acquisition of theoretical background needed in several areas of business and management for the consequent practical application of them. The program begins with mathematical logic and set theory arming students with mathematical language which is essential to understand the following contents. Then are introduced the most important concepts in the field of calculus and linear algebra allowing students to solidify basic knowledge previously acquired simultaneously with the learning of new contents, fulfilling one of the main goals of this course. In parallel the students are encouraged to solve practical exercises, real cases and problems that arise in a number of more specific courses fulfilling another objective of the course.

Teaching methodologies

The teaching methods applied are defined according to the type of classes and on the type of objective.
Theoretical Classes: Expository Methodology, by making use of participatory methodology whenever possible.
Practical Classes: Participatory Methodology through exercises.

Demonstration of the teaching methodologies coherence with the curricular unit's intended learning outcomes

The selection of methods to be used is based on defined objectives.
In the curricular unit of Mathematic lectures are given to a large number of students simultaneously and the educational objectives aimed predominantly a cognitive knowledge.
This theoretical classes are mainly based on expository methods but also supported by pratical examples and, whenever possible, encouraging students participation. This method used in the theoretical classes with the invitation to participate, helps to clarify concepts, helps to reflect on the contents and help students in structuring, discrimination and integration of cognitive elements, developing the critical thinking and the mathematical reasoning.
The practical classes are focused on the idea of “know-how”. The practical classes are supported on practical activities of solving exercises and problems through the application of concepts provided in the theoretical classes. Mainly the students should perform these activities; the teacher should only facilitate.
Sequential practical classes with exercises follow theoretical classes in order to apply all the knowledge learned in previous theoretical classes. These sequential exercises help and reinforce the knowledge to understand that the theoretical knowledge is essential to a good practical application of it.

Assessment methodologies and evidences

Continuous evaluation

The continuous evaluation of knowledge is constituted by two evaluation moments:
C1 - 1stTest
C2 - 2ndTest


C1 and C2 grades are rounded to tenths.

The final classification, rounded to the units, will be
FC = 50% x C1 +50% x C2

C1 and 2 will have a minimum score of 7,5 values. If these scores are not reached for C1 and C2, or the final classification in less than 10 values the student must perform the final evaluation.
To obtain approval, a final grade of 10 (ten) values is required.
If the student makes the 1st test and misses the 2nd one, the student is prevented from taking the normal season exam.






Final evaluation
There are three epochs of final evaluation:

Normal Season | 1st season (intended for students who choose not be evaluate in the continuous evaluation)
A Final Exam constitutes the evaluation of the normal season. If the exam grade is less than 10, there will be no approval.
Time of Resource | 2nd season (intended for students who did not obtained approval in the normal season or in the continuous evaluation)
The evaluation system is the same as in the final evaluation of the Normal Season.
Special Season:
The evaluation system is the same as in the Resource Season.

Attendance system

No minimum level of attendance required

Assement and Attendance registers

Bibliography

APOSTOL, T. M. (1988) Cálculo, vol. 1, Editora Reverte, Ltda.
AZENHA, A., e JERÓNIMO, M.(1995) Elementos de Cálculo Diferencial e Integral em , McGraw-Hill, Lisboa.
BANDEIRA, L., COELHO, F. e FRANCO, N. (2016) Introdução à Matemática-Álgebra, Análise e Otimização, Lidel-Edições Técnicas.
BARNETT, R. A., ZIEGLER, M. R. e BYLEEN, K. E. (1999) Calculus, Prentice Hall, Eight Edition.
CARREIRA, A. (1999) Cálculo Matricial - Volume II Exemplos e Aplicações, Instituto Piaget.
FERREIRA, J. C., (2001) Elementos de Lógica Matemática e Teoria de Conjuntos, Dep. Matemática do IST.
FERREIRA, M. A. (1992) Matemática - Exercícios / Álgebra Linear (vol. 1: Matrizes e Determinantes), Ed. Sílabo, Lisboa.
FIGUEIRA, R. M. (1996) Fundamentos de Análise Infinitesimal, Textos de Matemática, vol. 5, Universidade de Lisboa, Faculdade de Ciências, Departamento de Matemática, Lisboa.
GONÇALVES, R. (2015) Matemática - Álgebra Linear, Teoria e Prática, Ed. Sílabo, Lisboa.
LANG, S. (1986) Introduction to Linear Algebra, Springer-Verlag, New York, Berlin, Heidelberg.
LARSON, R., HOSTETLER R. P. e EDWARDS, B. H. (2006) Cálculo – Volume I (8ª edição), MacGraw-Hill.
LUZ, C., MATOS, A. e NUNES, S. (2002) Álgebra Linear, vol I, Escola Superior de Tecnologia de Setúbal.
MONTEIRO, A. e PINTO, G. (1997), Álgebra Linear e Geometria Analítica, Problemas e Exercícios, McGraw-Hill, Lisboa.
PISKOUNOV, N. (2000) Cálculo Diferencial e Integral, vol. 1, Lopes da Silva Editora.
SANTOS, F. B. - Sebenta de Matemáticas Gerais - Álgebra Linear, Plátano Editora.
SEQUEIRA, F. (1982), Análise Matemática, vol 2, Exercícios resolvidos e propostos, Litexa.
SYDSAETER, K., e HAMMOND, P. J.(1995) Mathematics For Economic Analysis, Prentice- Hall International, Inc.

Bibliographical Notes

Observations

Note 1: The option between Continuous Evaluation and Normal Season is mandatory. The student will have to make this option through the MOODLE. If the student chooses continuous evaluation and is absent to tests, the student is prevented from taking the normal period exam.


Note 2: In evaluations, is not permitted calculator or any other electronic device.