Mathematics For Engineers 7

Données Générales
Programme Académique	ECAM LaSalle Mechanical and Electrical Engineering Programme			Responsable(s) Module : BITAR Diala,DAVAL Gauthier
Type d'EC : Cours	Mathematics For Engineers 7 (LIIEEng03EMathEng7)
TD : 60h00 Cours : 30h00 Travail personnel : 48h00 Durée totale: 138h00	Status	Periode Semester 3	Langue d'enseignement : English

Objectifs Généraux
This course is in 2 parts: * Vector calculus: to revise and acquire calculation tools and methods, in order to confidently navigate through multivariable calculus and its applications. In particular, students will: - (outcome C1) be able to confidently use and apply differential operators for functions of several variables (multivariate chain differentiation, implicit differentiation, etc.) - (outcome C2) be able to perform multidimensional integration and line integration. * Linear Algebra: Acquire a good understanding of matrix algebra and methods. In particular, students will - (outcome LA1) understand the fundamental subspaces related to a matrix (as a linear map) - (outcome LA2) acquire fundamental techniques such as orthogonal projections in R^n or diagonalisation of matrices.

Objectifs Généraux

This course is in 2 parts:
* Vector calculus: to revise and acquire calculation tools and methods, in order to confidently navigate through multivariable calculus and its applications.
In particular, students will:
- (outcome C1) be able to confidently use and apply differential operators for functions of several variables (multivariate chain differentiation, implicit differentiation, etc.)
- (outcome C2) be able to perform multidimensional integration and line integration.

* Linear Algebra: Acquire a good understanding of matrix algebra and methods.
In particular, students will
- (outcome LA1) understand the fundamental subspaces related to a matrix (as a linear map)
- (outcome LA2) acquire fundamental techniques such as orthogonal projections in R^n or diagonalisation of matrices.

Contenu
- Multivariable calculus: ° multivariate calculus (coordinate systems, scalar functions, vector functions, conservative vector fields, differential operators, Taylor expansions for functions from R^n to R^p, Implicit function theorem, simple PDE, Local Inverse Theorem) ° multiple and line integral (substitutions, volume integrals, area integrals, curvilinear integrals, Green-Riemann Theorem) - Linear algebra ° Introduction to linear spaces/subspaces in R^n, bases. ° Fundamental subspaces of a matrix - Rank Nullity theorem. ° Orthogonality ° Eigenvalues and Eigenvectors

Contenu

- Multivariable calculus:
° multivariate calculus (coordinate systems, scalar functions, vector functions, conservative vector fields, differential operators, Taylor expansions for functions from R^n to R^p, Implicit function theorem, simple PDE, Local Inverse Theorem)
° multiple and line integral (substitutions, volume integrals, area integrals, curvilinear integrals, Green-Riemann Theorem)

- Linear algebra
° Introduction to linear spaces/subspaces in R^n, bases.
° Fundamental subspaces of a matrix - Rank Nullity theorem.
° Orthogonality
° Eigenvalues and Eigenvectors

Prérequis
Mathematics for engineers 1 and 2, (in particular continuity, differentiation, integration, for functions of 1 variable, and preferably also 2 variables, simple matrix algebra.)

Bibliographie
Course lecture Notes. G. Strang: Linear algebra and its applications (Wellesley-Cambridge Press) N. Piskunov: Differential and integral calculs. (Mir, Moscow, 1969) J. Stewart: Calculus, early transcendentals.

Évaluation(s)
N°	Nature	Coefficient	Objectifs
1	Midterm : C1, partially C2	0,25	Mid Term
2	Continuous Assessment	0,20	online quizzes.
3	Midterm : C2, LA1	0,30	Final exam:
4	Written exam	0,25	Midterm : C2, LA1