Mathematics 1
[FSAB1101]
[30h + 30h] 6 credits
This course is taught in the 1st semester.
Teacher(s): Abdou Kouider Ben-Naoum(supplée Vincent Wertz), Michel Verleysen, Vincent Wertz(coord.)
Language: French
Level: First
Aims
Content-oriented objectives :
" manipulate real functions of a single variable;
" master the basic notions of linear algebra;
" model simple phenomena using first order differential equations, and solve these equations;
Method-oriented objectives:
" analyze a mathematical statement, with the required rigor;
" formulate and write short proofs with the required rigor;
" read critically a mathematical statement;
" illustrate statements with examples and counterexamples;
" understand the various ways of mathematical proving techniques.
Main themes
" proofs of some fundamental theorems in calculus and algebra;
" construction of proofs for simple properties;
" modelling using first order differential equations.
Content and teaching methods
" Sets - relations - functions
" limits - continuity - derivative - integral
" parametric curves - first order differential equations
" complex numbers - complex exponential - sequences and series
" linear algebra : systems of linear equations - matrix algebra - vector spaces - linear maps
The teaching methodology should promote the student's active involvment in his/her own acquisition of the course material. The specific implementation of this methodology is left to the lec turer's best judgement, in accordance with the pedagogical guidelines set out by the Faculty.
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
- Workfiles for each of the parts (available on the website and in
printed version); Reference book: University Physics (Freedman and Young)