# BMAT 12A03 - Quantitative and mathematical methods for social Sciences - Advanced level

Type d'enseignement : Seminar

Semester : Autumn 2018-2019

Number of hours : 24

Language of tuition : English

## Pre-requisite

aucun

## Course Description

In this course, students will learn basic linear algebra necessary to understand the operations regarding derivatives of functions to investigate maximum and minimum values of those functions or and antiderivatives of functions with economics applications in mind. Students will also introduce to vector space and linear transformation theory, with an introduction to matrices. This course will focus on topics in calculus (one variable and multivariable differential calculus and integration ) suitable for economic applications. The course textbooks are : Edward T. Dowling, Introduction to mathematical economics. James Steward, Calculus early transcendental, 7th edition. Part 1 : Algebra : 1st, 2nd and 3rd degree equations. Sequences : increasing or decreasing sequences, limits, series. Part 2 : Calculus : Basic functions (polynomials, powers, exponentials, logarithms etc). Limits, derivatives, antiderivatives, second derivatives (concavity and convexity). Unconstrained optimization: First order conditions, second order conditions, global maxima and minima. Constrained Optimization: First order conditions, equality constraint, Lagrange functions, the meaning of the multiplier. Part 3 : Linear algebra : Vector Spaces: linear dependence, basis, rank and kernel of a linear transformation, representation by matrices.

## Teachers

LE FLOCH, Christine (Professeur agrégé)

## Course validation

To validate the course, the student is expected to pass: 4 quizzes + 1 midterm exam + 1 final exam. Grading policy ; Quizzes : 30 % Midterm : 30 % Final : 40 %

## Required reading

Edward T. Dowling, Introduction to mathematical economics.