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 ¿¿economics and management.
OBJECTIVES AND RESULTS OF LEARNING
a) Identify real-life situations of application of concepts; b) Identify and be able to solve problems of with the application of mathematical concepts; c) Solve financial problems using geometric progressions. Analyze and interpret the solution obtained. d) To study mathematical models that involve the study of real functions of real variable; e) Optimize mathematical applications solutions in real context and economically interpret their solution.
COMPETENCES TO DEVELOP
a) The ability to make decisions and solve problems in a diversified and constantly changing reality; b) The identification of problems, so that the student is induced to think first to perform in the best way all the necessary operations; c) The ability to develop self-directed learning by being able to identify, organize, process and analyze information; d) Numerical aptitude and use of calculation tools that allow data analysis, interpretation and extrapolation, with development of logical-mathematical reasoning; e) Develop the ability to program, analyze and formalize information in order to optimize problem solving f) To develop the mathematical, logical, critical, analytical reasoning and the students' autonomy in the application to the resolution of daily problems.
Programme
1. Successions, progressions and series a. Real number sequences b. Arithmetic and geometric progressions. c. Geometric series. Financial investments
2. Real functions of real variable in IR a. Similar functions and quadratic functions. b. Logarithmic and exponential functions. c. Derivative and differential concept. d. 1st derivative test: relative critical and maximum and minimum points e. 2nd derivative test: inflection points, concavity and convexity f. Application of derivatives in solving economic problems
3. Real Functions of Real Variables in IR2 a. Definition and graphical representation of the domain of functions of two variables. b. Limits and continuity. Intuitive Approach c. Partial derivatives. Total differential. d. Homogeneous functions. e. Euler's Theorem. f. Derivatives and differentials of higher order. g. Application of derivatives to economic problems.
Demonstration of the syllabus coherence with the curricular unit's learning objectives
Chapter 1 will solve financial problems using progressions and identify and solve problems with the application of mathematical concepts.
Chapter 2 will address mathematical models that involve the study of real real variable functions and the optimization of mathematical application solutions in real context.
Chapter 3 will allow working with mathematical models that involve the study of real functions of real variables and working with an important level of abstraction in the deduction of model properties.
Main literature
CERQUEIRA, António de Melo da Costa/ BELEZA DE VASCONCELOS, Paulo José A.;Funções Reais Definidas em IR": Exercícios e Aplicações, Litexa Editora, 1996
Supplementary Bibliography
Pires, Cesaltina;Cálculo para Economia e Gestão, Escolar Editora, 2011
FERREIRA, J. Campos;Introdução à Análise Matemática, Fundação Calouste Gulbenkian, 11ª ed. 2014
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.
Accompaniment 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
Evaluation
Teste/Exame
3
Another contact hours
Study
17
Individual study
Study
93
Individual project
Trabalho laboratorial ou de campo
2
Total:
160
Continuous Assessment
Two individual written tests (weighting 40% each, total 80%), plus a resolution of a class practical task (20%)
Under the terms of the Bachelor's Regulation:
1. The students' attendance in classes will be recorded and, if the number of absences per student exceeds 30% of the total number of lessons scheduled for each course unit, the student will be automatically transferred to the final evaluation (regular season).
2. In the written tests and other assessment elements mentioned in paragraph 2 of Art. 39 it is necessary to obtain a minimum grade of 7.5 (seven point five) points.
3. If the student misses a test or receives a grade lower than 7.5 points in the tests or in another assessment element mentioned in the previous number, the student will be automatically transferred to the final evaluation (regular season).
4. If the student misses or obtains less than 7.5 in the second written test, held in the same date of the final exam in the regular season, they may apply for further evaluation in the Appeal season.
Final Exam
Individual written test: 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.