Mathematics For Engineers 8

General Data
Academic program	ECAM LaSalle Mechanical and Electrical Engineering Programme			Module Manager(s) : BARILLON Cristelle
EC Type : Lectures	Mathematics For Engineers 8 (LIIEEng04EMathEng8)
Tutorials : 60h00 Lectures : 30h00 Individual work : 72h00 Total duration: 90	Status	Period Semester 4	Teaching language : English

General objectives
This course will focus on extending calculus and algebra topics from previous semesters, in order to acquire or consolidate the theoretical mathematical tools of the engineer. Students will : - (outcome C1) learn how to study and interpret improper integrals - (outcome C2) learn how to study and interpret power series, use them to solve a broad range of calculus problems - (outcome C3) be able to solve differential systems of ODE and consolidate their knowledge of ODE techniques - (outcome LA1) extend Semester 3 linear (matrix) Algebra to general vector spaces and linear maps - (outcome LA2) be able to qualify linear isometries, in particular in R^2 and R^3 - (outcome LA3) Have a general understanding of some Linear Algebra application (eg image processing)

General objectives

This course will focus on extending calculus and algebra topics from previous semesters, in order to acquire or consolidate the theoretical mathematical tools of the engineer.

Students will :
- (outcome C1) learn how to study and interpret improper integrals
- (outcome C2) learn how to study and interpret power series, use them to solve a broad range of calculus problems
- (outcome C3) be able to solve differential systems of ODE and consolidate their knowledge of ODE techniques

- (outcome LA1) extend Semester 3 linear (matrix) Algebra to general vector spaces and linear maps
- (outcome LA2) be able to qualify linear isometries, in particular in R^2 and R^3
- (outcome LA3) Have a general understanding of some Linear Algebra application (eg image processing)

Content
1 - Improper integrals 2 - Power series 3 - Vector space and linear map 4 - Pre-Hilbert space 5 - Systems of differential equations 6 - Orthogonal transformation - Linear isometry 7- Spectral theorem and SVD

Corequis
EENG Mathematics for Engineers 1,2 and 3, in particular: - matrix algebra - infinite series - Riemann definite and indefinite integral

Bibliographie
Lecturese lecture notes Strang, Gilbert. Introduction to Linear Algebra. 5th ed. Wellesley-Cambridge Press, 2016. N. Piskunov: Differential and integral calculus Volume 1 and 2, Mir, Moscow 1969

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	C1, C2 and LA1	0,25	Midterm 1
2	Continuous Assessment	0,20	may contain quizzes and projects
3	Written or oral exam	0,30	final exam for evaluation of the whole semester, in particular: C3 - LA2 - LA3
4	Written exam	0,25	Midterm 2