# Mathematics in Economics and Management II

lecge1230  2020-2021  Louvain-la-Neuve

Mathematics in Economics and Management II
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
6 credits
45.0 h + 30.0 h
Q1
Teacher(s)
Klaessens Pieter;
Language
French
Prerequisites

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Education focuses on the approach to modeling, and on solving problems or applications in economics, political and social, using mathematical or formal logic. It aims to develop a systematic analysis and resolution. Part 1: Linear Algebra. Indépendance linear bases, vector spaces. Fundamental theorem of linear algebra. Values and eigenvectors. Diagonalisation. Dynamical Systems. Quadratic forms. Part 2: Analysis and Optimization of functions on several variables functions Théorème implied partial derivative of higher order, Hessienne matrix. Optimization free Optimization under constraints (equalities and inequalities). Applications. Part 3: Introduction to linear programming. Modeling and mathematical formulation of problems of decision support and optimization. Primal Simplex, Dual simplex, economic interpretation of dual sensitivity analysis. Each topic is dealt with examples and illustrations in economics and management.
Aims
 At the end of this learning unit, the student is able to : 1 The second mathematics course is a continuation of Mathematics 1 and is devoted primarily to algebra and matrix calculus, in linear programming and optimization of functions of several variables. We can summarize the objectives and purposes of the course to two key dimensions: - Learning about the mathematical tool (which is directly targeted a set of knowledge). The achievements should be a reasonable ability to handle the concepts discussed in the course, which are the basic concepts used in the models and quantitative methods in social sciences. - The learning of a formalized and rigorous reasoning (which is more difficult to achieve and is more of "knowledge"; of mathematical modeling)
Content
Linear Algebra. Multivariate differential calculus. Unconstrained optimisation. Optimisation with equality constraints (Lagrange), with inequalitity constraints (Kuhn-Tucker). The enveloppe theorem. Interpretation of the multipliers. Linear programs. Duality.
Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Lectures and exercises sessions
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The grade will be determined by a final written examination. Depending on time and availability of rooms, a midterm test could be organised too.
Other information
Prerequisite course Mathematics 1
Online resources
Lecture notes and homeworks for the exercises sessions available on Moodle
Faculty or entity
ESPO
Force majeure
Teaching methods
In case, distance lessons are given by TEAMS
Evaluation methods
In case, exams will take place on Moodle

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Bachelor in Philosophy, Politics and Economics

Minor in Statistics, Actuarial Sciences and Data Sciences

Bachelor in Economics and Management

Minor in Economics