Ordinary differential equations of first and second order. Differential and integral calculus for functions of several variables and optimization. Plane curves.
Divergence theorem.
Bramanti, Pagani, Salsa: Matematica. Publishing house Zanichelli. Year of publication: 2000.
Learning Objectives
Solving ordinary differential equations of the first and the second order. Differential calculus and optimization problems for functions of several variables. Multiple integrals and curvilinear integrals.
Prerequisites
Courses required: none
Courses recommended: Mathematics I
Teaching Methods
Total number of hours for Lectures (hours): 36
Total number of hours for Laboratory-field practice : 20
Type of Assessment
The examination consists in a written and an oral test. Two or three in itinere tests will be performed during the course which can substitute the unique written test and, possibly, the oral test. There will be eight exam sessions per year.
Course program
Ordinary differential equations of first order; linear equations, separation of variables, Euler equations. Linear ordinary ordinary differential equations of second order: the homogeneous and non-homogeneous case.
Functions of several variables: continuity, partial and directional derivatives, gradient, differentiability. Optimization: critical points, Hessian matrix.
Lagrange multipliers.
Normal domains in the plane (and in the three dimensional case). Multiple integrals for functions of two (and three variables) in normal domains. Fubini's theorem; the use of polar (and spherical and cylindrical) coordinates .
Curves. Divergence Theorem.