Mathematical Tools 2

This course unit is an introduction to differential calculus of functions of several variables. It is intended for first-year PCSI students and provides an introduction to the mathematical tools used in thermodynamics, among other fields.

- Concept of functions on^R2 and^R3: graphs, contour lines, partial functions.

- Partial derivatives and differentials. Properties and formulas. Schwarz's theorem.

- Curves in 2 and 3 dimensions (basic concepts: velocity vector, parameterization, composition with a function).

- Concept of vector fields; example: gradient.

- Concept of 1-form on a domain of the plane. Closed and exact forms. Integration along a path.

High school mathematics program + EU Mathematical Tools 1.

Requirements*: 1 continuous assessment (written) + 1 final exam (written).

Recommended prerequisites: Advanced Mathematics Option.

Content manager: laurent.guieu@umontpellier.fr