Mathematics Part 6

Données Générales
Programme Académique	ECAM LaSalle Mechanical and Electrical Engineering Programme			Responsable(s) Module : AUDREN Loïc,BARILLON Cristelle,DAVAL Gauthier
Type d'EC : Cours	Mathematics Part 6 (LIIEEng02EMathematics6)
TD : 20h00 Cours : 10h00 Travail personnel : 30h00 Durée totale: 60h00	Status	Periode Semester 2	Langue d'enseignement : English

Objectifs Généraux
MàJ 16/04/2025: This second semestre is dedicated to a deeper study of one-variable functions (asymptotic behaviour) and an enter into the field of multi-variable functions. Strong and useful links are constantly highlighted with Physics (parametric equations and Vectors/Geometry with Mechanics). A larger study of approximations is complete, initially introduced by the Taylor series. Lessons and assessments will priorize mental calculations instead of the use of the calculator. This TUC belongs to the TU Mathematics for Engineering 2. Amongst the skills/knowledges we would like students to acquire, there are : • To analyze a system or a problem • To exploit the model/design of a real/virtual system • To build an argumented and logical reasoning in a scientific way • To analyse a system by decomposing it into simpler sub-systems • To find an exact value or an approximation to a problem, by calculation or by graphical resolution or by a step-by-step process. • To react positively facing a new problem by finding at least an approach, then considering later other ways to solve it. • To understand the parallels between different fields in Mathematics (Algebra, Geometry, Calculus…) and the ways to pass from one to another.

Objectifs Généraux

MàJ 16/04/2025: This second semestre is dedicated to a deeper study of one-variable functions (asymptotic behaviour) and an enter into the field of multi-variable functions. Strong and useful links are constantly highlighted with Physics (parametric equations and Vectors/Geometry with Mechanics). A larger study of approximations is complete, initially introduced by the Taylor series.
Lessons and assessments will priorize mental calculations instead of the use of the calculator.

This TUC belongs to the TU Mathematics for Engineering 2.

Amongst the skills/knowledges we would like students to acquire, there are :
• To analyze a system or a problem
• To exploit the model/design of a real/virtual system
• To build an argumented and logical reasoning in a scientific way
• To analyse a system by decomposing it into simpler sub-systems
• To find an exact value or an approximation to a problem, by calculation or by graphical resolution or by a step-by-step process.
• To react positively facing a new problem by finding at least an approach, then considering later other ways to solve it.
• To understand the parallels between different fields in Mathematics (Algebra, Geometry, Calculus…) and the ways to pass from one to another.

Contenu
o Parametric representations o Functions with two variables o Double Integrals

Prérequis
Mathematics for engineers - parts 1 - 2 - 3

Bibliographie
Stewart, J. Calculus: Early Transcentals, 8th Ed. Strang, G. (1991). Calculus. Wellesley, Mass.: Wellesley-Cambridge Press. Kreyszig, Erwin. (1983). Advanced engineering mathematics. New York :Wiley

Évaluation(s)
N°	Nature	Coefficient	Objectifs
1	Chapters seen during the dedicated period.	1	90-minute examination No calculator, nor electronic device, neither document
2	Chapters seen from the last examination to the week before examination.	35	90-minute examination No calculator, nor electronic device, neither document
3	Chapters seen from the last examination to the week before examination.	30	90-minute examination No calculator, nor electronic device, neither document