Mathematics For Engineers 5

Données Générales
Programme Académique	ECAM LaSalle Mechanical and Electrical Engineering Programme			Responsable(s) Module : BARILLON Cristelle
Type d'EC : Cours	Mathematics For Engineers 5 (LIIEEng05EMathEng5)
TD : 30h00 Cours : 30h00 Travail personnel : 60h00 Durée totale: 120h00	Status	Periode Semester 5	Langue d'enseignement : English

Objectifs Généraux
This module is dedicated to the study of mathematical tools that are commonly used in applications (Fourier Series and Transform, Laplace Transform, classic examples of Partial Differential Equations, Distribution and/or optimization.) General objectives (learning outcomes : LO) : * LO1 to develop abstract reasonning skills (e.g. being able to comprehend the extension of analysis and algebra studied during the first two years to Hilbert spaces / Lebesgue integration / Generalized functions ) * LO2 to understand the foundations of common tools like Fourier Series, Fourier Transform, Laplace Transform * LO3 to be able to analyze a problem (for instance a PDE problem, optimization problem) and find the appropriate method to solve it (Fourier, Laplace,...) * LO3 to develop rigorous problem solving approaches

Objectifs Généraux

This module is dedicated to the study of mathematical tools that are commonly used in applications (Fourier Series and Transform, Laplace Transform, classic examples of Partial Differential Equations, Distribution and/or optimization.)

General objectives (learning outcomes : LO) :
* LO1 to develop abstract reasonning skills (e.g. being able to comprehend the extension of analysis and algebra studied during the first two years to Hilbert spaces / Lebesgue integration / Generalized functions )
* LO2 to understand the foundations of common tools like Fourier Series, Fourier Transform, Laplace Transform
* LO3 to be able to analyze a problem (for instance a PDE problem, optimization problem) and find the appropriate method to solve it (Fourier, Laplace,...)
* LO3 to develop rigorous problem solving approaches

Contenu
* Lebesgue integration and Hilbert Spaces - Parameter dependant integrals. * Fourier Series * Fourier Transform * Laplace Transform * Some Classical examples in Partial Differential Equations * optimization: non linear optimization (unconstrained and constrained optimisation for functions of several variables) linear optimisation (simplex method)

Prérequis
Calculus and algebra Year 1 and Year 2, Improper Integrals, Infinite Series, Vector Spaces,

Bibliographie
Essential Textbooks: James, G. & Dyke, P. (2018) Advanced Modern Engineering Mathematics, 5th Edn., Pearson Recommended textbooks: Croft, A. et al. (2017) Engineering Mathematics, 5th Edn., Pearson Education Stroud, K.A. (2020) Advanced Engineering Mathematics, 6th Edn., Red Globe Press Kreyszig, E. (2011) Advanced Engineering Mathematics, 10th Edn., John Wiley & Sons

Évaluation(s)
N°	Nature	Coefficient	Objectifs
1	LO1 and LO2	0,30	mid-term
2	LO3	0,25	labs
3	Written exam	0,45	Final Exam for the course - 2h written exam - Students need to be able to write clear and complete solution for given problem with a clear reasoning.