- Aims: To reinforce and extend the ideas and methodology of the analysis 1 of the elementary theory ofreal numbers, properties of Reals (superma and Infima, Maxima and Minima. The Completeness Axiom.) Complexes Numbers. Sequences. Limits of sequences in epsilon-N notation. Bounded sequences and monotone sequences. Cauchy sequences. Algebra-of-limits theorems. Subsequences. Limit Superior and Limit Inferior. Bolzano-Weierstrass Theorem. Functions, Limits and Continuity. Continuity.
-
Objectives: By the end of the module, students should be able to read and understand statements expressing, with the use of quantifiers, convergence properties of sequences. They should also be capable of investigating particular examples to which the theorems can be applied and of understanding, and constructing for themselves, rigorous proofs within this context.
- Prerequisites: Part of the ministerial program for secondary schools, namely:
- Basic algebra: monomials, polynomials, rational functions, powers, roots, exponentials and logarithms
- Solving basic equations and inequalities
- Basic theory of functions, elementary functions and their graphs, graphic interpretation of inequalities
- Basic analytic geometry on the plane: lines, circles and parabolas
- Basic trigonometry: sine, cosine and tangent, addition formulas.
- Solving basic equations and inequalities
- Basic theory of functions, elementary functions and their graphs, graphic interpretation of inequalities
- Basic analytic geometry on the plane: lines, circles and parabolas
- Basic trigonometry: sine, cosine and tangent, addition formulas.
- Enseignant: Soumia IDRISSI