Class Quantitative Methods II

The main goal of the curricular unit is to introduce students to linear algebra and linear programming (operations research). The syllabus was chosen taking into account the studies’ cycle framework and the syllabus of other curricular units, so that students can continue their studies and develop their professional activity.

Not applicable

1) Linear Algebra - Introduction to systems of linear algebraic equations. - Matrices. Operations with matrices. - Solving linear systems using Gauss and Gauss-Jordan reduction methods. - Homogeneous systems. - Leontief's production model. - Inverse of a matrix: definition and properties. - Linear systems and inverses. - Determinants: definition and properties. - Matrix computations and solving linear systems in Matlab.   2) Linear Programming - Introduction. Steps in a decision-making process. Standard maximum and minimum type problems. Assumptions in linear programming. - Graphical solution of linear programming problems. - Simplex algorithm. - Solving problems with artificial variables. Two-phase method. - Applications, using Matlab.

Classes are of theoretical and practical nature, where the theoretical exposition of the syllabus is accompanied by the presentation of practical examples and exercises. The software Matlab/Octave is used. The evaluation is carried out taking into account the assessment regulation “Regulamento Geral de Avaliação da Universidade Lusófona”.   Pedagogical innovation practices: Pedagogical practices will be mediated by Information and Communication Technologies, using computers and/or mobile devices. Students will be exposed to interactive educational resources, such as quizzes. Problem-based learning will be promoted, where the students, guided by the teacher, should identify problems and plan and carry out resolution paths. The aim is to improve the teaching and learning process, to provide students with the necessary skills for the challenges that humanity currently faces and to increase their motivation regarding the studies’ cycle.

- Hill, M. M., e Marques dos Santos, M. (2018). Investigação Operacional - Vol. 1 - Programação Linear. Edições Sílabo.   - Hill, M. M., e Marques dos Santos, M. (2018). Investigação Operacional - Vol. 2 - Exercícios de Programação Linear. Edições Sílabo.   - Lay, D. C., Lay, S. R., e McDonald, J. J. (2020). Linear Algebra and Its Applications (6th edition). Pearson.