Mathematics Part 3

Formation ECAM LaSalle Ingénieur spécialité Mécanique et Génie Electrique (ENGINEERING PROGRAM)

General Data
Academic program	Formation ECAM LaSalle Ingénieur spécialité Mécanique et Génie Electrique (ENGINEERING PROGRAM)			:
Type d'EC	Classes (LIIEEng01EMathematics3)
Lectures : 8h00 Tutorials : 16h00 Total duration : 96h00	Status :	Period : Semester 1	Education language : English

Learning Outcomes
This first semester is mostly dedicated to the study of real-valued functions with one variable. Students will explore the concepts of limits, continuity, differentiability and integrability. Although Calculus is the main point, this course covers classical results from complex numbers and polynomials. It also provides the resolution of linear systems using matrices, and of ordinary differential equations (first and second orders). Special attention will be given at constructing clear mathematical arguments and applying processes to Physics. Lessons and assessments will priorize mental calculations instead of the use of the calculator. This TUC belongs to the TU Mathematics for Engineering 1. 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 first semester is mostly dedicated to the study of real-valued functions with one variable. Students will explore the concepts of limits, continuity, differentiability and integrability. Although Calculus is the main point, this course covers classical results from complex numbers and polynomials. It also provides the resolution of linear systems using matrices, and of ordinary differential equations (first and second orders).
Special attention will be given at constructing clear mathematical arguments and applying processes to Physics. Lessons and assessments will priorize mental calculations instead of the use of the calculator.

This TUC belongs to the TU Mathematics for Engineering 1.

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 Basic Mathematics o Trigonometry o Complex Numbers o Vectors o Matrices and Linear systems o Functions o Differentiation o Integration o Ordinary Differential Equations o Limits and Sequences

Pre-requisites / co-requisites
Any baccalaureate having a strong scientific content: - algebraic manipulation (fractions, surd form, power numbers...) - resolution of equations (linear, quadratic, simultaneous, trigonometric...) - trigonometry - vector manipulation (addition, decomposition, scalar product..) - function analysis (sketching, behaviour...) on basic functions (linear, quadratic, exponential, logarithmic...) - differentiation and integration of basic functions (linear, quadratic, exponential, logarithmic...)

Pre-requisites / co-requisites

Any baccalaureate having a strong scientific content:
- algebraic manipulation (fractions, surd form, power numbers...)
- resolution of equations (linear, quadratic, simultaneous, trigonometric...)
- trigonometry
- vector manipulation (addition, decomposition, scalar product..)
- function analysis (sketching, behaviour...) on basic functions (linear, quadratic, exponential, logarithmic...)
- differentiation and integration of basic functions (linear, quadratic, exponential, logarithmic...)

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