ECTS
4 credits
Component
Faculty of Science
Description
This UE is an introduction to the differential calculus of functions in several variables. It is intended for first year PCSI students and is an introduction to the mathematical tools used - among others - in thermodynamics.
Objectives
- Notion of function onR2 andR3 : graphs, contour lines, partial functions.
- Partial derivatives and differential. Properties and formulas. Schwarz's theorem.
- Curves in dimension 2 and 3 (basic notions: velocity vector, parameterization, composition with a function).
- Notion of vector field; example: gradient.
- Notion of 1-shape on a plane domain. Closed and exact forms. Integration along a path.
Necessary pre-requisites
High school mathematics program + EU Mathematical Tools 1.
Knowledge control
Necessary prerequisites*: 1 continuous assessment (written) + 1 final exam (written).
Recommended prerequisites*: Expert mathematics option.
Additional information
Content manager: laurent.guieu@umontpellier.fr