Mathematics II

Code	15350
Year	1
Semester	S2
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	No
Learning outcomes	To develop student’s logical, critical and analytical reasoning, and to enhance students' autonomy in formulating and solving mathematical problems.
Syllabus	0.1 Motivation for Analysis 1. Functions from R^n to R^m 1.1 Free and constrained optimisation 1.2 Method of the Lagrange's multipliers 2. Integral calculus in R^n 2.1 Fubini's theorem 2.2 Areas and volumes 3. Real and complex numbers 3.1 The notion of field 3.2 General form and polar form of a complex number 3.3 Symmetric and conjugate of a complex number 3.4 Operations with complex numbers 3.5 Powers and roots 0.2 Motivation for Linear Algebra 4. Topics of Linear Algebra 4.1 Vector spaces 4.2 Linear dependence and independence 4.3 Generators and basis 4.4 Vector subspaces 5 Linear transformations and matrices 5.1 Kernel, image space and rank of a matrix 5.2 Eigenvalues and eigenvectors of a matrix 5.3 Determinants 5.4 Systems of linear equations
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. Correia, A. L., Martinho, C. (2022), Matrizes e aplicações, 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. Pires, C. (2001), Cálculo para Economistas, McGraw-Hill. Stewart, J. (2013), Cálculo, Volume 2, Cengage Learning. Vários autores (vários anos), Testes e Exames, Moodle.
Teaching Methodologies and Assessment Criteria	The methodology is student-centered, and the student is expected, during the semester, to acquire and apply the concepts through autonomous work. In this sense, the periodic assessment, which allows the student to show the acquired skills, is paramount. More concretely, three assessments will take place.
Language	Portuguese. Tutorial support is available in English.