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 - The ability to develop self-directed learning by being able to identify, organize, process and analyze information; 4 - Numerical aptitude and use of calculation tools that allow data analysis, interpretation and extrapolation, with development of logical-mathematical reasoning; 5 - Develop the ability to program, analyze and formalize information in order to optimize problem solving; 6 - To develop the mathematical, logical, critical, analytical reasoning and the students' autonomy in the application to the resolution of daily problems.
Programme
I - Real functions of several real variables
1 Domain, counter domain; 2 Partial derivation; 3 Free optimization; 4 Conditioned optimization: substitution method, Lagrange multiplier method; 5 Problem solving: consumer problem and producer problem.
II - Primitive 1 Immediate and quasi-immediate primitives; 2 Application in the area of economics/management.
III - Matrices, Determinants and Systems of Linear Equations 1 Vectors and Matrices; 2 Operations and Properties; 3 Transposition and Properties; 4 Determinants and Properties; 5 Inverse Matrix; 6 Systems of linear equations and their discussion; 7 Solving systems of linear equations: Gauss elimination method; Cramer's rule and Inverse matrix.
Demonstration of the syllabus coherence with the curricular unit's learning objectives
Chapter I will allow the student to apply mathematical concepts of algebra and calculus to solve systems of linear equations with more than one real variable.
Chapter II will address mathematical models that involve the study of real variable functions and the optimization of mathematical solutions of applications in real context. 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 deducing model properties.
Consequently, - Objectives 1 and 2 will be achieved in all chapters. - objective 3 will be achieved in chapters I and II, which will provide the student with the acquisition of knowledge and calculus tools in R. - Objective 4 will be achieved in Chapter I, with the introduction of the partial derivative concept and its applications in the economic context.
Isabel Figueiredo, Helena Brás, Alzira Faria;Análise Matemática I ¿ Resumo Teórico, Exercícios Resolvidos e Propostos, Edições Silabo, 2021
Supplementary Bibliography
Barreira, Luís, & Valls, Cláudia; Exercícios de Álgebra Linear, IST Press, 2011
Ferreira, J. Campos;Introdução à Análise Matemática (11ª ed.), Fundação Calouste Gulben-kian, 2014
Gonçalves, Ricardo;Álgebra Linear - Teoria e Prática, Edições Sílabo, 2015. ISBN: 9789726188179
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
Learning Methods
Problem solving and practical activities of application of the contents will be approached in the theoretical-practical classes (using whenever necessary to the 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 the programmatic contents studied. Application exercises, of the contents covered, in the resolution of daily problems, so that the student select the most appropriate method and be able to develop interest in the contents of the curricular unit and show its usefulness. 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
First written test
Teste/Exame
1,5
Second written test / Exam
Teste/Exame
1,5
Problem solving in class
Participação Presencial
12
Study
Study
100
Total:
160
Continuous Assessment
2 Tests (individual) 70% (35% each) + First written work 15% + Second written work 15%. Works must be submitted through the ELearning platform in accordance with the final dates defined in the PIA, using the Turnitin database available on the ELearning platform.
Under the terms of the General Regulation:
a) The actual presence of students in classes will be recorded and, if the number of absences per student exceeds 30% of the total number of contact sessions planned for each curricular unit, it will be automatically transferred to the final assessment of the normal season; b) In written tests and defined assessment elements, it is necessary to obtain a minimum grade of 7.5; c) If the student is absent or obtains a grade lower than 7.5 in the tests or assessment elements referred to in the previous paragraph, they will be automatically transferred to the final assessment of the normal season; d) If the student is absent or obtains a grade lower than 7.5 in the second written test (carried out on the same date as the final written test of the normal period), he or she may request registration for assessment in the appeal period; e) All written academic work included in the assessment (reports, case studies, etc.) must be submitted to the Turnitin database, available on ISAG's E-Learning platform, with a similarity rate of up to 30% being acceptable.
Final Exam
Exam (individual) 100%.
Special Assessment (TE, DA, ...)
Exam (individual) 100%.
Improvement of final grade
Exam (individual) 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.