Mathematics for Engineers 1

General Data
Academic program	ECAM ENGINEERING PROGRAM			:
Type d'EC	Classes
Lectures : 48h00 Tutorials : 48h00 Total duration : 192h00	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 Introduction to matrices o Introduction to vector spaces o Functions o Differentiation o Integration o Polynomials o Ordinary Differential Equations o Limits and Sequences o Infinite series

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 basc 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 basc 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	Midterm examination (M11) - 45 minutes	0,25	Chapters seen from the beginning of the year to the week before examination.
2	Midterm examination (M12) - 45 minutes	0,25	Chapters seen from the last examination (M11) to the week before examination.
3	Final examination (F1) of Semester 1	0,50	Written exam