ECTS
3 credits
Component
Faculty of Science
Description
The aim of this UE is to rework certain analysis concepts from high school, deepening them and developing the practice and interpretation of calculations.
Objectives
The high school contents revisited are those of the Remediation UE: usual functions, limits, derivation, primitives and integration.
This content is worked on in depth through two themes: elementary studies of curves and surfaces, and differential equations.
The aim is not to develop theoretical tools or advanced techniques, but to study and understand objects through the study of examples.
It also means working towards the same goals:
- Translating into equations and solving equations
- Function studies
- Writing and organizing calculations, solving equations, studying functions
- Geometric interpretation of results, drawing curves
- Articulating reasoning and calculation
Contents :
- Let's review:
- Standard functions
- Limits
- Bypass
- Primitives and calculating integrals
- Elementary studies of curves and surfaces
- Representative curves of functions, geometric properties
- Functions of several variables, definition of partial derivative
- Parametric curves in plane and space
- Space surfaces
- Level lines
- Differential equations :
- Integration and primitives, Integration:by parts and change of variable
- Linear differential equations of order 1
- Example studies of differential equations of order 1 and order 2.
- Solution study
Necessary prerequisites
High school mathematics program, at least first and final year specialties.
Recommended prerequisites :
High school mathematics program, final year specialization and expert mathematics option.
Further information
Hourly volumes :
CM : 0 h
TD: 27 h
TP: 0
Land: 0