This course is intended for students to acquire the basic skills for logical-mathematical development. The importance of capacity building, methods of organization, problem solving and results analysis are key to the discipline that allows the applicability in real situations related to economics and management. In addition to the methodological issues, students will seek to develop autonomy, critical thinking, research and investigation of basic knowledge concerning mathematical models that allow decision making and optimization of results. In general, the topics covered allow the calculation and analysis tools essential for solving problems applied in everyday situations and specifically related to economics and management.
LEARNING GOALS AND OUTCOMES
The objectives of this course are to lead students to:
1. apply mathematical concepts of algebra and calculus to solve systems of linear equations with more than one real variable;
2. study mathematical models involving the study of real functions of real variables;
3. identify and be able to solve problems with the application of mathematical concepts;
Create and develop skills that enable the student to:
- make decisions and solve problems in a diverse and constantly changing reality;
- identify problems and resolution methods;
- obtain numerical aptitude that allows the analysis, interpretation and extrapolation of data, with the development of logical-mathematical reasoning.
Programme
Chapter I - LINEAR ALGEBRA
1. Matrices
1.1 General Concepts
1.1 Matrix Operations: Properties
1.2 Inverse Matrix: definition, properties and calculation
2. Determinants
2.1 Definition, properties and calculation
2.2 Solving Linear Equation Systems
2.2.1 Gauss Method
2.2.2 Cramer's Rule
Chapter II - INTRODUCTION TO INTEGRAL CALCULATION
1. Concept of primitive and indefinite integral
1.1 Immediate Primitives
1.2 Defined Integral
2. Application: Area Calculation
Demonstration of the syllabus coherence with the curricular unit's learning objectives
Chapter 1 will allow students to apply mathematical concepts of algebra and calculus to solve systems of linear equations with more than one real variable.
Chapter 2 will focus on the study and application of mathematical models that involve the study of real functions of the real variable, namely, the calculation of areas.
Therefore: - Objective 1 will be achieved in Chapter I; - Objective 2 will be achieved in Chapter II; - Objectives 3 and 4 are achieved in both chapters.
Main literature
Gonçalves, Ricardo;Álgebra Linear - Teoria e Prática, Edições Sílabo, Lda., 2015. ISBN: 9789726188179
Supplementary Bibliography
Barreira, Luís; Valls, Cláudia;Exercícios de Álgebra Linear, IST Press, 2011
Lima, E. L.;Análise no Espaço Rn, IMPA Rio de Janeiro, 11ª ed, 2014
Learning Methods
Problem-solving and practical activities of application of the contents will be approached in theoretical-practical classes (using, whenever necessary, to technologies and audio-visual methods).
Introduction of the theoretical concepts using examples of direct application in the economic area directed to show the relevance of syllabus.
Application exercises of the contents in the resolution of daily problems, so that the student can select the most appropriate method and be able to develop the interest in the contents of the curricular unit and show its usefulness.
Monitoring and orientation of students in the study and search for solutions to solve the problems proposed.
Assessment Components
Avaliação distribuída com exame final
Assessment Components
Description
Type
Time (hours)
Conclusion Date
Attendance (estimated)
Lessons
30
Teste/Exame
3
Participação Presencial
4
Participação Presencial
70
Total:
107
Continuous Assessment
1st test: Content to evaluate: Chapter I; Weight: 40% * 2nd test: Content to be evaluated: Chapter II; Weight: 40% * 1st job: Weight: 10% 2nd job: Weight: 10%
* The individual written tests will be without consultation and without recourse to any calculation aid and in the elaboration of two (individual) works:
According to the regulations of the Degree:
a) The effective attendance of students in class will be recorded and, if the number of absences per student exceeds 30% of the total number of contact sessions for each course unit, will be automatically transferred to the final evaluation of the normal season;
b) In the written tests and in the defined evaluation elements it is necessary to obtain a minimum grade of 7.5 points;
c) If the student misses or achieves a grade lower than 7.5 points in the tests or evaluation elements referred to in the previous number, he / she will be automatically transferred to the final evaluation of the normal season;
d) If the student misses or achieves a grade lower than 7.5 points in the second written test (held on the same date as the final written test of the normal season), he / she may require registration for evaluation at the time of appeal;
e) The written academic work provided for in the assessment must be submitted to the Turnitin database, available on the ISAG E-Learning platform, with a similarity rate of up to 30% acceptable.
Final Exam
Final Exam: Content to evaluate: chapters I and II; Weight: 100%
Proofs and special works
Demonstration of the coherence between the teaching methodologies and the learning outcomes
Cognitive skills are developed through exposure and discussion in problem solving, but also in individual problem solving. The skills of sharing and teamwork are developed in supervised group work. Communication skills are acquired throughout the UC.