Curricular Unit:Code:
Principles of Mathematics987FMAT
Year:Level:Course:Credits:
1UndergraduateBusiness Sciences5 ects
Learning Period:Language of Instruction:Total Hours:
Winter SemesterPortuguese/English65
Learning Outcomes of the Curricular Unit:
This course endows students with basic mathematical tools which allow to understanding and applying algebraic algorithms. These should promote the full comprehension of other courses as well as enable the identification and application of tools to support economic and business decisions. Students should acquire (i) capacity for analysis and synthesis; (ii) capacity and autonomy to resolve problems; (iii) ability to apply knowledge; (iv) ability to collect, select and interpret relevant information to support judgments and proposed solutions; (v) ability to work independently and in group.
Syllabus:
CP1. Basic mathematical concepts for Business and Economics. CP2. Functions and Derivatives. CP3. Matrixes. CP4. Determinants. CP5. System of Linear Equations.
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
CP1. Objectives: (i) be able to (i) apply mathematical concepts exposed (ii) identify practical situations in which these concepts can be applied.
CP2. Objetivos: (i) Discuss the types of functions, (ii) be able to derive a (iii) function to recognize alternative uses of the derivation.
CP3. Objetivos: (i) identifying types of matrices (ii) be able to perform operations with matrices
(iii) determining the inverse matrix (iv) solving matrix equations.
CP4. Objetivos:(i) be able to calculate the determinant of a square matrix (ii) determine the inverse of CP5. Objetivos:(i) be able to represent a system of linear equations in a matrix form (ii) find the solution of the system, if any, using the triangulation method of Gauss, Gauss-Jordan, of the explicit method and Cramer's rule (iii) determine the inverse of a matrix using the Gauss-Jordan.
Teaching Methodologies (Including Evaluation):
CP1.Basic mathematical concepts essential to understanding the economic language. CP2.Concepts of relation, function, domain and image, the functional notation and different functional forms. Concept of derived, forms of calculation and application to economic problems, in particular the determination of marginal functions and calculation of multipliers and elasticities. CP3. Concept of matrices, perform operations and their properties. Concepts and formula for calculating the characteristic condensation and inverse matrix. CP4. Concept of determinant, calculation formulas and applying the matrix inversion. CP5.Concept and the classification of systems of linear equations and several alternatives for solving systems of linear equations in matrix form after reduction. All contents are display with the resolution of various exercises. 2 tests (40% - CP1.e 2.; 60% - CP3.,4. e 5.)
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
Given the essentially practical nature of that course all exposed concepts are applied to the resource to solve a number of exercises. This methodology allows to achieve the specific goals listed in each chapter enabling students to achieve general competence: (i) ability to analyze and synthesize; (ii) the ability and autonomy to solve problems; (iii) ability to apply knowledge; (iv) ability to collect, select and interpret relevant information that supports judgments and recommended solutions; (v) ability to work independently and in groups.
Reading:
[1] Anton, H., Rorres, C. (2010). Elementar Linear Algebra. John Wiley & Sons, Inc.
[2] Ferreira, M. A. M.; Amaral, I. (2008). Matemática. Álgebra Linear. Matrizes e Determinantes. Vol1. 7ªEdição. Edições Sílabo.
[3] Gonçalves, R. J.. C. (2018). Álgebra Linear. Teoria e Prática. 2ªEdição. Edições Sílabo.
[4] Hamers, H., Kaper, B. and Klepper, J. (2013). Mathematics for Business Economics. Academic Service.
[5] Harshbarger, R. J. e Reynolds, J. (2006). Matemática Aplicada. Administração, Economia e Ciências Sociais e Biológicas. 7ª Edição. McGraw-Hill.
[6] Informação Estatística - https://ine.pt/xportal/xmain?xpgid=ine_main&xpid=INE
[7] Mateus, R. (2015). Cálculo Financeiro. Teoria e Prática. Escolar Editora. (Anexo I)