ECTS
5 credits
Component
Faculty of Science
Description
This UE is an introduction to analysis (functions of one real variable) for the first year students of the PCSI portal.
Objectives
- Rudiments of logical reasoning (connectors, quantifiers, reasoning by the absurd...)
- Rudiments on sets and applications.
- Continuous functions: general theorems, intermediate value theorem, continuous image of an interval.
- Derivable functions: general theorems, chain-rule, finite increments theorem, and reciprocal bijection theorem. Notion of C∞ function. Basics of Taylor's formula.
- Bestiary of classical functions: power, polynomial, exponential, logarithm, trigonometric functions, and reciprocal trigonometric functions.
- Integral calculus: properties and techniques (integration by parts and change of variable)
- Differential equations of order 1 (non-linear, separation of variables...)
Necessary pre-requisites
Required prerequisites*:
High school mathematics program.
Recommended prerequisites*:
expert mathematics option.
Knowledge control
2 continuous tests (written) + 1 final exam (written).
Additional information
Content manager: laurent.guieu@umontpellier.fr