At the end of this learning unit, the student is able to :

• Express metric notions in Rn using the language of general topology.
•  Study limits, continuity, directional derivatives and differentiability for functions of several variables.
• Apply Taylor polynomial in order to approximate a function.
• Locate and identify free extrema of a function; locate extrema under constraints of a function using the technique of Lagrange multipliers.
• Calculating multiple integrals possibly using a change of variables.
• Calculate line integrals, surface integrals, the flow of a vector field along a curve and the flow of a vector field through a surface possibly using Stokes type theorems.
• Apply the resolving method for linear differential equations with constant coefficients of order n.
• Analyse and write rigorously statements and demonstrations on the mathematical content specified below, and illustrate them with examples and counter-examples.