Descriptive summary of the unit In this course unit students are expected to acquire the basic skills for logical-mathematical development. The importance of capacity development, organizational methods, problem solving and results analysis are the key to the discipline that allows the applicability in real situations related to areas of economics and management. In addition to the methodological issues, students will develop autonomy, critical thinking, research work and basic knowledge of mathematical models that allow decision-making and optimization of results. In general, the topics covered allow us to obtain calculation tools to solve problems applied in everyday situations and specifically related to the area of the economics and management.
Learning objectives and expected outcomes 1. Identify real-life situations of application of concepts; 2. Identify and be able to solve problems of with the application of mathematical concepts; 3. To study mathematical models that involve the study of real functions of real variable; 4. Optimize mathematical applications solutions in real context and economically interpret their solution.
Skills to be developed 1. The ability to make decisions and solve problems in a diversified and constantly changing reality; 2. The identification of problems, so that the student is induced to think first to perform in the best way all the necessary operations; 3. Numerical aptitude and use of calculation tools that allow data analysis, interpretation and extrapolation, with development of logical-mathematical reasoning; 4. To develop the mathematical, logical, critical, analytical reasoning and the students' autonomy in the application to the resolution of daily problems.
Programme
I - Matrices, Determinants and Systems of Linear Equations
I.1 Vectors and Matrices; I.2 Operations and Properties; I.3 Transposition and Properties; I.4 Determinants and Properties; I.5 Inverse Matrix; I.6 Systems of linear equations and their discussion; I.7 Solving systems of linear equations: Gauss elimination method; Cramer's rule and Inverse matrix.
II - Real functions of several real variables
II.1 Domain, counter domain; II.2 Partial derivation; II.3 Free optimization; II.4 Conditioned optimization: substitution method, Lagrange multiplier method; II.5 Problem solving: consumer problem and producer problem
III - Primitive
III.1 Immediate and quasi-immediate primitives; III.2 Application in the area of economics/management
Demonstration of the syllabus coherence with the curricular unit's learning objectives
Chapter I will deal with mathematical models that involve the study of real variable functions and the optimization of mathematical solutions of real context applications.
Chapter II and III will allow you to work with mathematical models that involve the study of real functions of real variables and work with an important level of abstraction in the deduction of model properties.
Therefore,
- Objectives 1 and 2 will be achieved in all chapters.
- Objective 3 will be achieved in Chapter I and II, which will provide the student with the acquisition of knowledge and calculation tools in R.
- Objective 4 will be achieved in Chapter II by introducing the concept of partial derivative.
Main literature
James Stewart;Cálculo, vol. I e II, tradução da 8a edição norte-americana,, Cengage Learning, 2017
Edwin Jed Herman & Gilbert Strang;Calculus, volumes 1, 2 e 3, OpenStax, 2018
Supplementary Bibliography
Jaime Carvalho e Silva ;Princípios de Análise Matemática Aplicada, Mc Graw-Hill, 1999
FERREIRA, J. Campos;Introdução à Análise Matemática, Fundação Calouste Gulbenkian, Fundação Calouste Gulbenkian, 2014
Gonçalves, Ricardo;Álgebra Linear - Teoria e Prática, Edições Sílabo , 2015. ISBN: 9789726188179
Pires, Cesaltina;Cálculo para Economia e Gestão, Escolar Editora, 2011
Cerqueira, António de Melo da Costa; Beleza de Vasconcelos, Paulo José A;Funções Reais Definidas em IRn: Exercícios e Aplicações, Litexa editora, 1996
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
45
Autonomous Study
Study
112
Evaluation
Teste/Exame
3
Total:
160
Continuous Assessment
1st Test: Weight 30%; *
2nd Test: Weight 50%; *
Work: Weight 20%
* The individual written tests will be without consultation and without recourse to any calculation aid.
According to the General Regulation:
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 foreseen in the assessment will have to be submitted in the Turnitin database, available on ISAG's E-Learning platform, with a similarity rate up to 30% acceptable.
Final Exam
Exam: Weight 100%
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.