# CECO 1295A - Maths for economists

Type d'enseignement : Elective

Semester : Spring 2017-2018

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 with more than one variable to investigate maximum and minimum values of those functions with economics applications in mind. Students will also see how to solve linear systems and then how to turn them into problems involving matrices, then learn some of the important properties of matrices. This course will focus on topics in linear algebra and multivariable differential calculus suitable for economic applications. The course textbook is : Carl Simon and Laurence Blume, Mathematics for Economists. The course covers chapters 6 to 9 and 16 to 19 of the textbook and their two main sections : Part 1 : Linear Algebra. System of Linear equations: Gaussian and Gauss-Jordan Elimination, Elementary row operations, Systems with many or no solutions, Rank - The fundamental criterion, The linear Implicit function theorem. Matrices : matrix Algebra, Determinants, inverse of a matrix, Cramer's rule. Vector Spaces : Linear dependence, Basis, Rank of a Matrix Eigen value, Eigen Vector. Part 2 : Multivariable calculus : Quadratic Forms : Definiteness, linear constraints Unconstrained Optimization : First order conditions, Second order conditions, Global maxima and minima. Constrained Optimization : First Order Conditions, equality constraints, Inequality constraints, Mixed constraints, Constrained optimization problems, Kuhn-Tucker formulation, the meaning of the multiplier. Envelope theorems.

## 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%.