Università Roma Tre

DEFINITE INTEGRAL IN ONE VARIABLE. INDEFINITE INTEGRAL. FUNDAMENTAL THEOREMS OF THE INTEGRAL CALCULUS.
NUMERICAL SERIES: DEFINITION AND THEIR PROPERTIES. GEOMETRIC SERIES. CONVERGENCE CRITERIA FOR POSITIVE SERIES, HARMONIC SERIES.
EXTENSION OF THE CONVERGENCE CRITERIA. POWER SERIES AND TAYLOR SERIES.
FOURIER SERIES AND A MENTION OF FOURIER TRANSFORMS.
ORDINARY DIFFERENTIAL EQUATIONS; SOLUTION BY QUADRATURE AND BY SEPARATION OF VARIABLES. ORDINARY LINEAR DIFFERENTIAL EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFICIENTS; GENERAL SOLUTION. ORDINARY LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS OF THE SECOND ORDER AND THEIR GENERAL SOLUTION.
MENTION OF PARTIAL DIFFERENTIAL EQUATIONS: HOMOGENEOUS EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFICIENTS AND THEIR SOLUTION ON THE CHARACTERISTICS.
MENTION OF THE SECOND ORDER WAVE EQUATIONS.

1. MARCELLINI P.,SBORDONE C., ELEMENTI DI CALCOLO [ED. LIGUORI ]
2. NOTES FOR THE COURSE