ECTS
4 credits
Training Structure
College of Sciences
Time of year
Fall
Description
This course is an introduction to the differential calculus of functions of several variables. It is intended for first-year PCSI students and provides an introduction to the mathematical tools used—among other things—in thermodynamics.
Objectives
- Concept of functions onR² andR³: graphs, contour lines, partial functions.
- Partial derivatives and the differential. Properties and formulas. Schwarz's theorem.
- Curves in 2 and 3 dimensions (basic concepts: velocity vector, parameterization, composition with a function).
- Concept of a vector field; example: gradient.
- The concept of a 1-form on a region of the plane. Closed and exact forms. Integration along a path.
Class Hours
- Mathematical Tools 2 - CMLecture6:00 p.m.
- Mathematical Tools 2 - TutorialTutorials6:00 p.m.
Mandatory Prerequisites
High School Mathematics Curriculum + Mathematical Tools 1 Course Unit.
Knowledge Assessment
Requiredprerequisites*: 1 ongoing assessment (written) + 1 final exam (written).
Recommended prerequisites*: Advanced Mathematics elective.
Additional Information
Content Manager: laurent.guieu@umontpellier.fr