PRINCIPLES OF MATHEMATICS
Learning outcomes of the course unit
Provides students with concepts and basic mathematical tools, as well as a rigorous language, good ability in formulating and solving problems and the ability to read and comprehend simple mathematcal texts.
Course contents summary
Elements of set theory. Numerical sets; N, Z, Q, R . Powers and radicals. Exponentials and logarithms. Elements of trigonometry. Complex numbers. Permutations, combinations, binomial coefficients. Binomial theorem. Vectors in plane and space. Basic notions in vector algebra. Matrices and algebra of matrices. Determinants. Systems of linear equations. Eigenvalues and eigenvectors of a square matrix. Some elements of analytic geometry in 2-3 dimensional spaces. Sequences; theorems on limits of sequences. Series. Real functions of one real variable. Composed functions. Invertible functions. Limits of functions. Continous functions. The derivative. Some differential calculus theorems. Applications of derivatives to the study of functions. Some notions on power series. Differentials. Indefinite integrals. Definite integrals. The fundamental theorem of integral calculus. Improper integrals. Real functions of two or more variables. Ordinary differential equations. Linear first order differential equations. Initial-value problems. Linear differential equations with constant coefficients.
M. Bramanti, C.D. Pagani, S. Salsa, MATEMATICA (Calcolo infinitesimale e Algebra Lineare), Zanichelli, Bologna, 2004.
M. Bertsch, Istituzioni di Matematica, Bollati Boringhieri, Torino.
G. Zwirner, Istituzioni di Matematiche (parti 1^ e 2^), Cedam, Padova.
Frontal lectures and exercises.
The exam consists of written and oral tests.