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# Mathematics II

 Code 12083 Year 1 Semester S2 ECTS Credits 6 Workload TP(60H) Scientific area Mathematics Entry requirements No Mode of delivery Face to face. Work placements not applicable Learning outcomes >> Specific objectives:1. promote the learning of mathematical concepts in the field of differential and integral calculus in Rn;2. provide the basic fundamentals of Linear Algebra usually applied in the various areas of Economics;>> General objectives3. develop the ability to interpret a problem, model it and solve it with the appropriatemathematical knowledge and adequate techniques;4. develop the capacity for abstract and logical reasoning, and linguistic rigor. Syllabus 1. Functions of R^n in R^m (Part II)1.1 Free and conditional extrema1.2 Method of Lagrange multipliers 1.3 Integral calculus in R^n1.3.1 Fubini's Theorem. Areas and volumes. 2. Topics of Linear Algebra2.1 Matrices, Systems of linear equations and Determinants2.1.1 Generalities and operations with matrices2.1.2 Transpose and conjugate matrices. Symmetric and hermetic matrices 2.1.3 Ladder form and characteristic of a matrix2.1.4 Systems of linear equations2.1.5 Determinants: definition and properties2.1.6 Calculating the inverse of a square matrix2.1.7 Eigenvalues and eigenvectors of a square matrix2.2 Vector Spaces2.2.1 Definition, examples and properties 2.2.2 The n-dimensional Euclidean space 2.2.3 Linear dependence and independence 2.2.4 Generators and bases2.3 Linear applications of R^n on R^m2.3.1 Definition and examples2.3.2 Matrix of a linear application of R^n in R^m2.3.3 Eigenvectors of a linear application. Main Bibliography Azenha, A., Jerónimo, M. A. (1995), Elementos de Cálculo Diferencial e Integral em R e R^n, McGraw-Hill.Cabello, J. G. (2006), Álgebra Lineal. sus aplicaciones en Economía, Ingenierías y otras ciencias, Delta.Cabral, I., Perdigão, C., Saiago, C. (2009), Álgebra Linear, Escolar.DMAT-IST (2005), exercícios de análise matemática I e II, IST.Hoffmann, L., Bradley, G. (2010), Calculus for Business, Economics, and the Social and Life Sciences, McGraw-Hill.Lay, D. C. (1999), Álgebra linear e suas aplicações, LTC.Martins, A., Salomé, H., Silva, L., Pereira, J. (2018), Preparar o Exame 2019. Matemática A. 12.º, raiz.Pires, C. (2001), Cálculo para Economistas, McGraw-Hill.Santana, A. P., Queiró, J. (2018), Introdução à Álgebra Linear, gradiva.Santos, R. (2010), Álgebra Linear, http://www.mat.ufmg.br/~regi/livros.htmlStewart, J. (2013), Cálculo, Volume 2, Cengage Learning.Vários autores (vários anos), Testes e Exames, Moodle. Teaching Methodologies and Assessment Criteria The teaching-learning methodology is centered on the student, who, throughout the semester, acquires and applies the concepts under the guidance of the lecturer and, simultaneously, develops his autonomous work. The evaluation of the work developed by the student during the term is quantified by two written tests. The assessment during the exam period depends on the conditions for admission, more precisely on obtaining a) at least 6 marks in the final classification of teaching-learning; and b) 75% of class attendance (applicable only to students with first-time registration). Language Portuguese. Tutorial support is available in English.

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Economics
Last updated on: 2023-09-20

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