ECAM Engineering Program
Combined Bachelor's / Master's Degree
General Data
Academic program ECAM Engineering Program :
Type d'EC Classes
Lectures : 38h00
Tutorials : 40h00
Total duration : : 78
Status :
Period :
Semester 1
Education language :
English
General objectives
This course will focus on fundamentals of mathematical analysis: continuity, differentiation and integration of single (S1) and several variables (S2) functions. Although calculus is the main point of the year, this course covers also classical results from complex numbers, planar and spatial geometry, sequences and infinite series (S1) as well an introduction to linear algebra (S2).
We aim not only at providing the mathematical tools needed to analyze and solve complex problems, but also a deep understanding of their foundations. Special attention will be given at constructing clear mathematical arguments and writing rigorous proofs.
Content
0 - Logic and reasoning
1 - Generalities on functions
2 - Usual real-valued functions
3 - Complex numbers
4 - Indefinite integral
5 - Introduction to Ordinary Differential Equations
6 - Sequences
7 - Continuity
8 - Geometry
Pre-requisites
Refresher course
Bibliography
Class lecture notes.
H. Hairer, G. Wanner, Analysis by Its History, Springer 2008,
N. Piskunov, Differential and Integral Calculus, (Mir 1969),
G. Strang, Highlights of Calculus, http://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/
G. Strang, Calculus, (Wellesley-Cambridge press, 2017).
Assessment(s)
Nature Coefficient Observable objectives
1Written exam0.45
2Continuous Assessment0.552 Tests , 2 Quizzes, 1 home assignement.
3Continuous Assessment0.1Written assignements