Mathematics for Engineers 5

General Data
Academic program	ECAM ENGINEERING PROGRAM			:
Type d'EC	Classes
Lectures : 30h00 Tutorials : 30h00 Total duration : 120h00	Status :	Period : Semester 5	Education language : English

Learning Outcomes
This semester is dedicated to a 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

Learning Outcomes

This semester is dedicated to a 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

Content
* 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)

Pre-requisites / co-requisites
Calculus and algebra Year 1 and Year 2, Improper Integrals, Infinite Series, Vector Spaces,

Bibliography
W. Rudin: Real and Complex Analysis N. Piskunov: Differential and Integral Calculus E. Kreyszig: Advanced Engineering Mathematics

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	mid-term	0,33	LO1 and LO2
2	labs	0,27	LO3
3	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.	0,40	Written exam