ECTS
5 credits
Component
Faculty of Science
Description
This course is an introduction to analysis (functions of one real variable) for first-year PCSI students.
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 increase theorem and reciprocal bijection theorem. Notion of C∞ function. Rudiments of Taylor's formula.
- Bestiary of classical functions: power, polynomials, exponential, logarithm, trigonometric 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...)
Teaching hours
- Outils Mathématiques 1 - CMLecture22,5h
- Outils Mathématiques 1 - TDTutorial22,5h
Necessary prerequisites
Prerequisites*:
High school mathematics program.
Recommended prerequisites*:
expert mathematics option.
Knowledge control
2 continuous tests (written) + 1 final exam (written).
Further information
Content manager: laurent.guieu@umontpellier.fr