Università Roma Tre

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria.
Complex numbers.
Solution of linear differential equations and separable differential equations.

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill
Marcellini, Sbordone - Analisi matematica uno
Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.

Real numbers and functions, set theory, induction principle, infimum and supremum. Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order. Limits of function, continuity, link with the limits of sequences, theorems on continuous functions. Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Theory:
Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
S. Lang, A First Course in Calculus, Springer Ed.
L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Exercises:
Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
Marcellini, Sbordone - Analisi matematica uno Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.