Learning outcomes of the course unit
Presents basic concepts regarding vector spaces, function spaces, Fourier series and an optimisation problem, concepts useful for the study of the other curricular subjects.
Mathematics I and Mathematics II
Course contents summary
Vector spaces. Normed spaces. L-p spaces. Vector spaces with scalar product. Sequences of functions. Series of functions and different notions of convergence. Theorems of integration and derivation by series. Power series. Trigonometric series and Fourier series. Parseval's inequality. Complex form of Fourier series. Maxima and minima of two variables functions subject to side conditions. The Lagrange multiplier rule.
M. Bramanti, C.D. Pagani, S. Salsa, MATEMATICA (Calcolo infinitesimale e Algebra Lineare), Zanichelli, Bologna, 2004.
G.C. Barozzi, Matematica per l'ingegneria dell'informazione, Zanichelli, Bologna.
C.D. Pagani, S. Salsa, Analisi matematica 2, Masson, Milano.
C. Minnaja, Matematica Due, Decibel-Zanichelli, Bologna.
Frontal lectures and exercises.
The exam for Mathematic IV is integrated with that of Mathematics III . It consists of an oral exam.