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Mathematics II

Mathematics II

Code	16471
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 objectives 3. develop the ability to interpret a problem, model it and solve it with the appropriate mathematical 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 extrema 1.2 Method of Lagrange multipliers 1.3 Integral calculus in R^n 1.3.1 Fubini's Theorem. Areas and volumes. 2. Topics of Linear Algebra 2.1 Matrices, Systems of linear equations and Determinants 2.1.1 Generalities and operations with matrices 2.1.2 Transpose and conjugate matrices. Symmetric and hermetic matrices 2.1.3 Ladder form and characteristic of a matrix 2.1.4 Systems of linear equations 2.1.5 Determinants: definition and properties 2.1.6 Calculating the inverse of a square matrix 2.1.7 Eigenvalues and eigenvectors of a square matrix 2.2 Vector Spaces 2.2.1 Definition, examples and properties 2.2.2 The n-dimensional Euclidean space 2.2.3 Linear dependence and independence 2.2.4 Generators and bases 2.3 Linear applications of R^n on R^m 2.3.1 Definition and examples 2.3.2 Matrix of a linear application of R^n in R^m 2.3.3 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.html Stewart, J. (2013), Cálculo, Volume 2, Cengage Learning. Vários autores (vários anos), Testes e Exames, Moodle.
Teaching Methodologies and Assessment Criteria	Students with more than one enrollment may choose between a comprehensive exam or two tests — this is the only option available for students with a single enrollment. (Choice must be made on Moodle by March 13; if no response is given: two tests will apply.) In the comprehensive exam option, the final grade is the exam grade (0–20). In the two-test option, the final grade consists of 19 points from the tests (95%) + 1 point for attendance (5%), provided the student does not exceed 5 absences. If this limit is exceeded, attendance will not be counted and the test grade will be converted to a 20-point scale. Attendance (only applicable in the two-test option) is counted from the 2nd class onward and requires punctuality, participation, and compliance with the rules.
Language	Portuguese. Tutorial support is available in English.