The student will be able to formulate, solve and understand mathematically the problems arising in engineering. To do so it is necessary, in this second course of Calculus, to be familiar with the n-dimensional euclidean space, in particular in dimension 3, and with its more usual subsets. He/she must be able to manage (scalar and vectorial) several variables functions and its continuity, differentiability and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main integration theorems to compute areas and volumes, inertial moments and heat flow. He/she must know the concepts of ordinary differential equation and differential equations problem. The student will be able to solve the main first and second order differential equations.