To apply to real life situations the concepts and mathematical tools described in the syllabus.
To apply concepts in approaches carried out in other curricular units.
To optimise Mathematics applications solutions in real context and appropriate software applications for their resolution and economically interpret their solution.
To use the concepts of derivative and integral in the resolution of problems and in routine academic and professional studies.
Competences to be developed:
The ability to develop self-learning, being capable of identifying, organising, treating and analysing information;
Numerical ability and the use of calculation tools that allow for the analysis, the interpretation and the extrapolation of data, with the development of logical mathematical reasoning;
The capability to programme, analyse and formalise information, in order to optimise the resolution of problems.
Programme
REAL FUNCTIONS AND REAL VARIABLES
1.1.- Definition and graphical representation of the two-variable functions field.
1.3.- Partial derivatives.
1.4.- Partial differentials and total differential.
1.5.- Homogenous functions.
1.6.- Euler¿s Theorem.
1.7.- Higher order derivatives and differentials.
1.8.- Derivations of compound functions and implicit functions.
1.9.- Application of the derivatives in economic problems.
INTRODUCTION TO INTEGRAL CALCULUS
2.1.- Notion of primitive and undefined integral.
2.2.- Basic integration rules.
2.3.- Integration by decomposition.
2.4.- Integration by parts.
2.5.- Integration by substitution.
2.6.- Definition of defined integral.
2.8.- Economic applications.
OPTIMISATION OF THE FUNCTIONS OF VARIOUS REAL VARIABLES
3.1.- Unrestricted optimisation.
3.2.- Hessian Matrix.
3.3.- Restricted optimisation.
3.4.- The Lagrange multiplier method.
3.5.- The Bordered Hessian Matrix.
3.6.- Economic applications.
Main literature
Lima, E. L.;Análise no Espaço Rn, IMPA Rio de Janeiro, 2004
The main subjects of the discipline, the resolution of problems and practical syllabus application activities will be approached in the theoretical-practical classes (by having recourse, whenever necessary, to tecnology and audiovisual methods).
Introduction of theoretical concepts using examples of direct application in the economic area, in order to show the significance of the studied syllabus.
Application exercises, of the approached subjects, in the resolution of daily problems, so that the student will be able to gain interest on the contents of the curricular unit and show its utility.
Student follow-up and study orientation and search of solutions for the resolution of the proposed problems.