ECTS
3 credits
Component
Faculty of Science
Description
The aim of this course is to rework certain concepts of analysis from high school, by deepening them, and by developing the practice of calculation and the interpretation of calculations.
Objectives
The contents of the high school that are revisited are those of the Remediation UE: usual functions, limits, derivation, primitives and integration.
These contents are worked and deepened from two topics: Elementary study 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 is also about working on the same objectives:
- Translation into equations and solving equations
- Studies of functions
- Writing and organizing calculations, solving equations, studying functions
- Geometric interpretation of results, drawing of curves
- Articulation of reasoning and calculation
Contents:
- Let's review:
- Usual functions
- Limits
- Bypass
- Primitives and calculation of integrals
- Elementary studies of curves and surfaces
- Representative curves of functions, geometric properties
- Functions of several variables, definition of partial derivative
- Parametric curves in the plane and in space
- Surfaces of the space
- Level lines
- Differential equations :
- Integration and primitives, Integration:by parts and change of variable
- Linear differential equations of order 1
- Example of studies of differential equations of order 1 and order 2.
- Study of solutions
Necessary pre-requisites
High school mathematics program, at least for the first and last year of high school.
Recommended prerequisites:
High school mathematics curriculum, senior specialization and expert math option.
Additional information
Hourly volumes:
CM : 0 h
TD : 27 h
TP : 0
Land : 0