Learning outcomes of the course unit
Course aims: To give first year students the main basic notions of Mathematics; other basic notions will be given in Mathematics II course. Mathematics I and Mathematics II are courses with only one integrated examination.
Rational and irrational numbers. Powers and radicals. Logarithms, exponentials. Basic notions of geometry in plane and of trigonometry.
Course contents summary
Complex numbers. Binomial coefficients, binomial theorem. Matrices. Systems of linear equations. Basic notions in vector algebra. Basic notions of geometry in plane (lines, conics in canonic form) and in space ( planes, lines, quadrics in canonic form).
Sequences, series. Functions, composite functions, one to one functions and their inverse functions. Limits, continuous functions. Computations of limits. Differential calculus: definition of derivative, geometrical interpretation. Differentiation and Continuity. Main theorems about the derivative (Fermat's theorem, Lagrange's theorem and its inferences, De L'Hospital's theorem). Applications of derivatives to the graphical study of functions. Taylor's formula. Integral calculus: primitives. Integration rules. Defined integral. The fundamental theorem of integral calculus. Improper integrals. Functions of two or more variables: limits, continuity, first and second order partial derivatives. Directional derivatives. Differentiable functions. Taylor's formula. Local maxima and minima for functions of two variabiles.
Recommended textbooks: M. Bramanti, C.D. Pagani, S. Salsa, MATEMATICA (Calcolo Infinitesimale e Algebra Lineare), Zanichelli Editore, Bologna
Other usefull textbooks:
M. Bertsch, Istituzioni di Matematica, Bollati Boringhieri, Torino.
A. Avantaggiati, Istituzioni di Matematica, Casa Edit. Ambrosiana, Milano.
G. Prodi, Istituzioni di Matematiche, McGrow-Hill, Milano.
A.Zaccagnini, M.G.Rinaldi, Esercizi per i corsi di Istituzioni di Matematiche, Azzali, Parma.
Frontal lectures and exercises .
The exam consists of written and oral tests.