Università Roma Tre

NUMERICAL SETS. REAL NUMBERS. DEFINITION OF FUNCTIONS AND THEIR REPRESENTATION IN THE CARTESIAN PLANE.
ELEMENTARY FUNCTIONS. MONOTONE FUNCTIONS. INVERTIBLE FUNCTIONS. COMPOSITION OF FUNCTIONS. LIMITS OF FUNCTIONS, OPERATIONS WITH LIMTS. CONTINUITY. PRPERTIES OF CONTINUOUS FUNCTIONS. WEIERSTRASS THEOREM. THEOREM ON THE EXISTENCE OF THE ZEROS. DERIVATIVE AND ITS GEOMETRICAL AND MECHANICAL MEANING.
RULES OF DERIVATION. THEOREMS OF ROLLE, LAGRANGE AND CAUCHY. RULE OF DE L'HOPITAL. MAXIMUM AND MINIMUM RELATIVE. GRAPHIC OF A FUNCTION. TAYLOR'S FORMULA. DEFINITION OF DEFINITE INTEGRALS. PRIMITIVE OF A FUNCTION. TORRICELLI-BARROW'S THEOREM. INTEGRALS OF ELEMENTARY FUNCTIONS. ELEMENTARY METHODS OF INTEGRATIONS: SOSTITUTION AND BY PARTS. VECTORS IN THE PLANE AND SPACE. OPERATIONS WITH THE VECTORS. SCALAR PRODUCT AND VECTOR PRODUCT. MATRICES. DETERMINANTS. INVERS MATRIX. LINEAR SYSTEMS. CRAMER THEOREM. EIGENVALUES AND EIGENVECTORS.

[1] G. GENTILE, Lezioni di MATEMATICA - Modulo I - A.A. 2017-2018 - Corso di Laurea in Scienze Geologiche,
disponibile in rete: http://www.mat.uniroma3.it/users/gentile/2017-2018/MAT/lezioni.pdf
[2] N.S. Piskunov, Calcolo differenziale e integrale, vol. I, Editori Riuniti, Roma, 2010