Subject: Mathematics I

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

# Overall objectives:

1 - O1. Ability to analytically manipulate algebraic and transcendental functions; knowing the concepts of limits and continuity; manipulate in a reasonable manner the differential calculus, both in R and in Rn; ability to generalise, to some extent, some of the concepts previously learned and to use them in other contexts of higher level courses.
2 - O2. Ability to operate matrices; knowing how to apply elementary operations in a matrix; ability to solve systems of linear equations using matrices; knowing how to compute eigenvalues and eigenvectors of a matrix and some of its applications.

# Syllabus:

1 - CT1. Real valued functions of real variables (domain, limits, continuity, differentiability, differentiation rules, graphical representation of functions).
2 - CT2. Differential calculus in Rn (basic notions and examples; partial derivatives; total differential; the chain rule; implicit differentiation); Extrema of functions of two or more variables.
3 - CT3. Linear Algebra (matrix algebra, the method of Gauss elimination, rank of a matrix, determinants, eigenvalues and eigenvectors); System of linear equations (the Cramer's rule).

# Literature/Sources:

Apostol Tom M. , 1983 , Cálculo , Reverté Ltda
J. Campos Ferreira , 2005 , Introdução à Análise Matemática , Fundação Calouste Gulbenkian, 8ª edição
Magalhães, L.T. , 1998 , Álgebra Linear como Introdução à Matemática Aplicada , Texto Editora, Portugal
Monteiro, A., G. Pinto, e C. Mendes , 1998 , Álgebra Linear e Geometria Analítica: Problemas e Exercícios , McGraw- Hill
Cabral, I., C. Perdigão e C. Saiago , 2012 , Álgebra Linear, 3.ª ed , Escolar Editora

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
M1. Lectures: Whiteboard; documentation provided by the teacher M2. Solving exercises: Whiteboard; documentation provided by the teacher