Mathematics Part 4

General Data
Academic program	Formation ECAM LaSalle Ingénieur spécialité Mécanique et Génie Electrique (ENGINEERING PROGRAM)			:
Type d'EC	Classes (LIIEEng02EMathematics4)
Lectures : 12h00 Tutorials : 18h00 Total duration : 94h00	Status :	Period : Semester 2	Education language : English

Learning Outcomes
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.

Learning Outcomes

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 Polynomials o Limits & Functions o Taylor Series o 2D/3D Geometry o Asymptotic curves o Parametric representations o Functions with two variables

Pre-requisites / co-requisites
Mathematics for engineers - Level 1

Bibliography
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	90-minute examination No calculator, nor electronic device, neither document	35	Chapters seen from the beginning of the semester to the week before examination.
2	90-minute examination No calculator, nor electronic device, neither document	35	Chapters seen from the last examination to the week before examination.
3	90-minute examination No calculator, nor electronic device, neither document	30	Chapters seen from the last examination to the week before examination.