# Mathematics I

**Auditing and Taxation**

6 ECTS; 1º Ano, 1º Semestre, 30,0 T + 45,0 PL

**Lecturer**

- José Manuel Borges Henriques Faria Paixão

- Cristina Maria Mendes Andrade

**Prerequisites**

Not applicable.

**Objectives**

At the end of this module the students will be able to analyse, interpret and formulate problems in Linear Algebra, Mathematical Analysis, and Project Analysis, and have obtained the mathematical foundations that will allow the extrapolation of mathematical problems to economic problems.

**Program**

PROJECT ANALYSIS WITH NETWORKS: 1. Introduction to Microsoft Project 2. CPM and PERT 3. Financial analysis

LINEAR ALGEBRA: 1.Matrices(definition, types of matrices, matrix arithmetics, rank of a matrix, Gaussian elimination and systems of linear equations); 2. Determinants (definition, properties, Laplace expansion, the adjoint and inverse matrices, Cramer's rule and systems of linear equations).

1. FUNCTIONS AND DIFFERENTIAL CALCULUS IN IR

1.1. An overview of real value functions of real variable.

1.2. Brief mention to the limits calculation of a function in one variable. The derivative function. Differentiable functions. Geometric interpretation. Derivation rules. Higher derivatives.

1.3. Application of derivatives to the study of functions and to the study of some Economic's problems.

**Evaluation Methodology**

Continuous Assessment: written test (70%)(mínimum grade 6) and project with Microsoft Project (30%).

Exams assessment: Closed-book written test graded from 0 to 20.

**Bibliography**

- Anton, H. (2010). *Elementary Linear Algebra*. USA: John Wiley & Sons

- Strang, G. (2009). *Linear Algebra and its Applications*. USA: Wellesley Cambridge Press

- Ferreira, M. e Amaral, I. (2008). *Algebra Linear: Matrizes e Determinantes*. (Vol. 1). Portugal: Edições Sílabo

**Method of interaction**

Lectures designed to introduce concepts and discuss their applications. Practical lessons are designed develop autonomy in problem solving some of them with Microsoft Project.

**Software used in class**

Microsoft Project