Descriptive summary of curricular unit In this curricular unit students are expected to acquire the basic skills for logical-mathematical development. The importance of capacity development, organizational methods, problem-solving and outcome analysis are the key of this course that allows the applicability in real situations related to areas of economics and management. In addition to the methodological issues, it is sought to develop the students' autonomy, the critical spirit, the work of research and investigation of basic knowledge regarding mathematical models that allow the decision-making and results' optimization. In general, the covered topics allow students to obtain calculation and analysis tools essential for problem-solving applied in everyday situations and specifically related to the area of economics and management.
Objectives and expected learning outcomes The objectives of this curricular unit are to lead students to: - Apply mathematical concepts of algebra and calculus on the resolution of systems of linear equations with more than one real variable; - Identify real-life situations of concepts' application; - Identify and be able to solve problems with the application of mathematical concepts; - To study mathematical models that involve the study of real functions of real variable; - optimize mathematical applications' solutions in a real context and to interpret economically the solutions.
Skills to be developed Create and develop skills that enable: - the ability to make decisions and solve problems in a diversified and constantly changing reality; - the identification of problems, so that the student is induced to think first to perform in the best way all the necessary operations; - the ability to develop self-directed learning by being able to identify, organize, process and analyze the information; - the numerical aptitude and the use of calculation tools that allow data analysis, interpretation, and extrapolation, with the development of logical-mathematical reasoning; - developing the ability to program, analyze and formalize information in order to optimize problem-solving; - the development of mathematical, logical, critical, analytical reasoning and students' autonomy in the application to the resolution of everyday problems.
Programme
1. LINEAR ALGEBRA
a. Matrices: General Concepts
i. Matrix Operations: Properties
ii. Inverse Matrix: definition, properties, inverse matrix calculation
b. Determinants: definition, properties, calculation of determinants
c. Systems of linear equations
i. Gauss's Method and Cramer's Rule
ii. Resolution of linear systems by the inverse matri
iii. Discussion of systems of equations as a function of parameters
2. INTRODUCTION TO INTEGRAL CALCULUS
a. Notion of primitive and indefinite integral
b. Basic integration rules
c. Integration by decomposition, by parts and by replacement
d. Definition of definite integral. Calculation of areas
e. Economic applications
3.OPTIMIZATION OF FUNCTIONS OF VARIOUS REAL VARIABLES
a. Optimization without restrictions. Hessian matrix.
b. Optimization with constraints. The Lagrange Multipliers method.
c. Economic applications.
Demonstration of the syllabus coherence with the curricular unit's learning objectives
With chapter 1 the student will be able to apply mathematical concepts of algebra and calculus to the resolution of systems of linear equations with more than one real variable, being able to find solutions for real life situations.
With Chapter 2, it will be possible for the student to study mathematical models that involve the study of real functions of real variable and that allow the resolution of problems related to the economic area.
Main literature
Lima, E. L.;Análise no Espaço Rn, IMPA Rio de Janeiro, 11.ªed, 2014
Supplementary Bibliography
Gonçalves, Ricardo;Álgebra Linear - Teoria e Prática, Edições Sílabo, Lda., 2015. ISBN: 9789726188179
Barreira, Luís; Valls, Cláudia;Exercícios de Álgebra Linear, IST Press, 2011
Learning Methods
The essential issues, problem-solving and practical activities of application of the contents will be approached in theoretical-practical classes.
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 course unit and show its usefulness.
Monitoring and orientation of students in the study and search for solutions will be directed towards to solve the problems proposed.
Assessment Components
Avaliação distribuída com exame final
Assessment Components
Description
Type
Time (hours)
Conclusion Date
Attendance (estimated)
Lessons
45
Study
20
Teste/Exame
3
Trabalho laboratorial ou de campo
2
Study
90
Total:
160
Continuous Assessment
Two individual written tests (with a weight of 80%: each test has a 40% weighting) and the resolution of a practical worksheet (with a weight of 20%).
Under the terms of the Bachelor's Regulation:
1. The actual presence of the students in the classes will be registered and, if the number of absences per student exceeds 30% of the total number of contact sessions provided for each course unit, it will automatically be transferred to the final evaluation of the normal time.
2. In the written tests and in the evaluation elements referred to in points b) to e) of paragraph 2 of Article 39 it is necessary to obtain a minimum grade of 7.5 (seven point five) values.
3. If the student is absent or has a grade lower than 7.5 points in the tests or evaluation elements referred to in the preceding paragraph, he will be automatically transferred to the final evaluation of the normal season.
4. If the student fails to obtain a grade of less than 7.5 points in the second written test (held on the same date as the final written test of the normal time), he / she may apply for evaluation at the time of appeal.
Final Exam
Individual written test: 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.