# Mathematics I

**Accounting**, Publication in the Diário da República - Despacho nº 13772/2014 - 12/11/2014

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

**Lecturer**

- Ana Cristina Becerra Nata dos Santos

**Prerequisites**

Not applicable.

**Objectives**

At the end of this module the students will be able to analyse, interpret and formulate problems in Mathematical Analysis, Linear Algebra and Linear Programming, and have obtained the mathematical foundations that will allow them to extrapolate 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 6/20) and project with Microsoft Project (30%).

Final assessment: Closed-book summative test graded 0 to 20.

**Bibliography**

- Strang, G. (2016). *Introduction to Linear Algebra*. USA: Wellesley-Cambridge Press

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

- Davis, D. e Armstrong, B. (2003). *College mathematics: Solving problems in finite mathematics and calculus.*. USA: Pearson Education

- Marques dos Santos, M. e Magalhães Hill, M. (2009). *Investigação Operacional - Programação Linear*. (Vol. 1). Portugal: Edições Sílabo

**Method of interaction**

Lectures designed to introduce concepts and discuss their applications. Practical classes focusing on problem solving using Microsoft Project.

**Software used in class**

GeoGebra