Calculus I

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.

The Euclidean space. Several variables Functions. Continuity and differentiability. Polar, spherical and cylindrical coordinates. Free and conditional optimization. Iterated integration. Changes of variables. Integration along trajectories. Integration on surfaces. Computation of areas and volumes. Other applications of the integral. Green, Stokes and Gauss theorems. Laplace transform. Introduction to differential equations.

The docent methodology will include: - Master classes, where the knowledge that the students must acquire will be presented. To make easier the development of the class, the students will have written notes and also will have the basic texts of reference that will facilitate their subsequent work. - Resolution of exercises by the student that will serve as self-evaluation and to acquire the necessary skills. - Problem classes, in which problems proposed to the students are discussed and developed. - Partial controls. - Final control. - Tutorials.