Aims
Following this course, the students will be able to :
Contentoriented 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;
Methodoriented 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
" real valued functions of a single variable; first order differential equations; linear algebra;
" 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
Contents and 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, ...)
The evaluation has 2 components: an intermediary evaluation during the quadrimester and a final exam at the end of the quadrimester (written exam). The final mark is a combination of the scores in these two evaluations
 Workfiles for each of the parts (available on the website and in
printed version); Reference book: University Physics (Freedman and Young)
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