Università degli Studi di Roma "Tor Vergata"

Differential and integral calculus for real functions: real and complex numbers; elementary real functions and their inverse: polynomial, exponential, logarithm, trigonometric etc.; 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; antiderivatives, integrals; improper integrals; series; elementary differential equations of first and second order. Introduction to multivariable calculus: continuity; differentiation, directional derivatives, gradient; higher order differentiations, Hessian matrix.

Tom M. Apostol: Calculus Vol.1, second edition; John Wiley & Sons, (1974). Claudio Canuto, Anita Tabacco: Mathematical Analysis I-Springer International Publishing, UNITEXT 84, (2015).

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.

Textbooks 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 .