Mathematics for Engineers 4

General Data
Academic program	Formation ECAM LaSalle Ingénieur spécialité Mécanique et Génie Electrique (ENGINEERING PROGRAM)			:
Type d'EC	Classes (LIIEEng04EMathEng4)
Lectures : 36h00 Tutorials : 36h00 Total duration : 144h00	Status :	Period : Semester 4	Education language : English

Learning Outcomes
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)

Learning Outcomes

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

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

Bibliography
Course 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	Midterm 1	0,25	C1, C2 and LA1
2	may contain quizzes and projects	0,20	Continuous Assessment
3	final exam for evaluation of the whole semester, in particular: C3 - LA2 - LA3	0,30	Written or oral exam
4	Midterm 2	0,25	Written exam