Mathematics Part 4

General Data
Academic program	ECAM LaSalle Mechanical and Electrical Engineering Programme			Module Manager(s) : AUDREN Loïc
EC Type : Lectures	Mathematics Part 4 (LIIEEng02EMathematics4)
Tutorials : 20h00 Lectures : 10h00 Individual work : 30h00 Total duration: 30	Status	Period Semester 2	Teaching language : English

General objectives
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.

General objectives

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.

Content
o Differential Equations o Polynomials o Integration 2

Corequis
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

Assessment(s)
N°	Nature	Coefficient	Observable objectives
1	Chapters seen during the dedicated period.	1	90-minute examination No calculator, nor electronic device, neither document
2		1	Written exam