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.
Objetives and learning 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
I - Integral Calculation
I.1 Revision: Immediate and almost immediate primitivation; I.2 Primitivation by parts, substitution and rational; I.3 Definition of Definite Integral; I.4 Fundamental theorem of integral calculus and its properties; I.4 Applications of integral calculus to economics.
II - Complements of Differential Equations
II.1 1st order differential equations: homogeneous equation, exact equation and integrating factors; II.2 2nd order linear differential equations with constant coefficients.
Demonstration of the syllabus coherence with the curricular unit's learning objectives
Chapter I and II will focus on the study and application of mathematical models that involve the study of real functions of the real variable.
Chapter III will allow students to apply mathematical concepts of algebra and calculus to solve systems of linear equations with more than one real variable.
Therefore: - Objective 1 will be achieved in Chapter I and II; - Objective 2 will be achieved in Chapter III; - Objectives 3 and 4 are achieved in all chapters.
Margarida Macedo;Equações Funcionais - Equações diferenciais e equações com diferenças, UCP Editora, 2023. ISBN: 9789725408957
Supplementary Bibliography
Jaime Carvalho e Silva ; Princípios de Análise Matemática Aplicada, Mc Graw-Hill, 1999. ISBN: 9789729241550
Lima, E. L.;Análise no Espaço Rn, IMPA Rio de Janeiro, 11ª ed, 2014
Edwin Jed Herman & Gilbert Strang;Cálculo, vol. I e II, tradução da 8a edição norte-americana,, Cengage Learning, 2017
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
First written test
Teste/Exame
1
Second written test / Exam
Teste/Exame
1
Other
Participação Presencial
12
Study
Study
63
Total:
107
Continuous Assessment
Tests
(individual) 70% + 1st written assignment 15% + 2nd written assignment 15%.
The assignments must be submitted through the ELearning plataform according to the dates defined in the PIA, using the Turnitin database platform available in the ELearning pltaform.
In the written tests and all the other evaluation components a minimum 7,5 grade must be achieved.
The evaluation follows the ISAG-EBS general assessment systems.
Final Exam
Exam (individual) 100%. In the final exam, a minimum 9,5 grade must be achieved. The evaluation follows the ISAG-EBS general assessment systems.
Proofs and special works
Special Assessment (TE, DA, ...)
Exam (individual) 100%. In the final exam, a minimum 9,5 grade must be achieved. The evaluation follows the ISAG-EBS general assessment systems.
Improvement of final grade
Exam (individual) 100%. In the final exam, a minimum 9,5 grade must be achieved. The evaluation follows the ISAG-EBS general assessment systems.
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.