|
Docente
|
CIOLLI FABIO
(programma)
Basic elements. Real and complex numbers. Topologi of the rial line and the n-dimensional real space.
Differential calculus for real functions.
Elementary real functions and their inverse: polynomial, exponential, logarithm, trigonometric function. Concept of limit, limits of indefinite forms; continuity, properties of continuous functions, uniform continuity; derivatives, maxima and minima, the graph of a function; De L’Hopital’s Rule; Taylor expansions.
Introduction to multivariable calculus: continuity, differentiation, directional derivatives, gradient; higher order differentiations, Hessian matrix.
Integral calculus for real functions: antiderivatives, Riemann integrals; improper integrals.
Numerical series.
Introduction to ordinary differential equations of first and second order.
 Apostol, T. M., Calculus Vol.1, second edition; John Wiley & Sons, (1974).
Canuto C., Tabacco A., Mathematical Analysis I & II; Springer International Publishing, UNITEXT 84, (2015).
Trench, William F., Introduction to Real Analysis (2013). Faculty Authored Books. Book 7. http://digitalcommons.trinity.edu/mono/7 .
|
