Università Roma Tre

Numerical sets (N, Z, Q and R), R assiomatic construction of R by upper extremity, Archimede properties, Q in R density, N construction and induction principle, Newton binomial and combinatorial calculus, Inequality of Bernoulli; Topology elements in R (isolated and accumulated points, open / closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; Complex numbers, polar representation and n-th roots of the unit; Real functions of real variable, domain, co-domain, and inverse functions; Function and property limits, monotone function limits; Succession limits, significant limits, Nepero number, bridge theorem, limsup / liminf, sequences and topology, compact sets, and characterization; Continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); Function and function derivative, elementary function derivatives, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de Hopital, Taylor's formula), monotony and derivative sign, local degradation maxima / minima, convex functions / concave; Function graph; Integration according to Riemann and property, integrability of continuous functions, primitive elementary functions, I and II fundamental theorem of integral calculation, integration for substitution and parts, rational functions, some special replacements; Numerical series and convergence, geometric series, convergence criteria for positive terms series (comparison, asymptotic comparison, root, ratio, condensation) and for series at any time (absolute convergence, Leibnitz); Taylor series developments, developments of some elementary functions; Improper integrals.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

Numerical sets (N, Z, Q and R), R assiomatic construction of R by upper extremity, Archimede properties, Q in R density, N construction and induction principle, Newton binomial and combinatorial calculus, Inequality of Bernoulli; Topology elements in R (isolated and accumulated points, open / closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; Complex numbers, polar representation and n-th roots of the unit; Real functions of real variable, domain, co-domain, and inverse functions; Function and property limits, monotone function limits; Succession limits, significant limits, Nepero number, bridge theorem, limsup / liminf, sequences and topology, compact sets, and characterization; Continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); Function and function derivative, elementary function derivatives, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de Hopital, Taylor's formula), monotony and derivative sign, local degradation maxima / minima, convex functions / concave; Function graph; Integration according to Riemann and property, integrability of continuous functions, primitive elementary functions, I and II fundamental theorem of integral calculation, integration for substitution and parts, rational functions, some special replacements; Numerical series and convergence, geometric series, convergence criteria for positive terms series (comparison, asymptotic comparison, root, ratio, condensation) and for series at any time (absolute convergence, Leibnitz); Taylor series developments, developments of some elementary functions; Improper integrals.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

Number sets (N, Z, Q and R), axiomatic construction of R via supremum, Archimedean property, density of Q in R, construction of N in R and the inductive method, binomial formula and combinatorial calculus, real powers, the Bernoulli inequality; topological concepts in R (accumulation and isolated points, open/closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; complex numbers, polar representation and n-roots of unity; real functions with a real variable, domain, image and inverse functions; limits for functions and properties, limits of monotone functions; limits for sequences, special limits, the Napier number, the bridge theorem,
limsup/liminf, sequences and topology, compact sets and characterization; continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeroes, intermediate values, Weierstrass); derivative of a function and properties, derivatives of elementary functions, the fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l'Hopital, Taylor's formula), monotonicity and sign of the derivative, degenerate local maxima/minima, convex/concave functions; graph of a function; Riemann integration and properties, integrability of continuous functions, primitives for elementary functions, I and II fundamental theorems of integral calculus, change of variables and integration by parts, rational functions, some special change of variables; numerical series and convergence, geometric series, convergence criteria for positive series (comparison, asymptotic comparison, n-th root, ratio, condensation) and for general series (absolute convergence, Leibniz); Taylor series, series of some elementary functions; improper integrals.

"Analisi Matematica 1", M. Bramanti, C.D. Pagani, S. Salsa, editore Zanichelli
"Analisi Matematica 1", C.D. Pagani, S. Salsa, editore Zanichelli
"Analisi Matematica 1", E. Giusti, editore Bollati Boringhieri
"Funzioni Algebriche e Trascendenti", B. Palumbo, M.C. Signorino, editore Accademica
"Analisi Matematica", M. Bertsch, R. Dal Passo, L. Giacomelli, editore MCGraw-Hill
"Esercizi di Analisi Matematica", S. Salsa, A. Squellati, editore Zanichelli
"Esercitazioni di Matematica: vol. 1.1 e 1.2", P. Marcellini, C. Sbordone, editore Liguori
"Esercizi e complementi di Analisi Matematica: vol. 1", E. Giusti, editore Bollati Boringhieri

Numerical sets (N, Z, Q and R), R assiomatic construction of R by upper extremity, Archimede properties, Q in R density, N construction and induction principle, Newton binomial and combinatorial calculus, Inequality of Bernoulli; Topology elements in R (isolated and accumulated points, open / closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; Complex numbers, polar representation and n-th roots of the unit; Real functions of real variable, domain, co-domain, and inverse functions; Function and property limits, monotone function limits; Succession limits, significant limits, Nepero number, bridge theorem, limsup / liminf, sequences and topology, compact sets, and characterization; Continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); Function and function derivative, elementary function derivatives, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de Hopital, Taylor's formula), monotony and derivative sign, local degradation maxima / minima, convex functions / concave; Function graph; Integration according to Riemann and property, integrability of continuous functions, primitive elementary functions, I and II fundamental theorem of integral calculation, integration for substitution and parts, rational functions, some special replacements; Numerical series and convergence, geometric series, convergence criteria for positive terms series (comparison, asymptotic comparison, root, ratio, condensation) and for series at any time (absolute convergence, Leibnitz); Taylor series developments, developments of some elementary functions; Improper integrals.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

Numerical sets (N, Z, Q and R), R assiomatic construction of R by upper extremity, Archimede properties, Q in R density, N construction and induction principle, Newton binomial and combinatorial calculus, Inequality of Bernoulli; Topology elements in R (isolated and accumulated points, open / closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; Complex numbers, polar representation and n-th roots of the unit; Real functions of real variable, domain, co-domain, and inverse functions; Function and property limits, monotone function limits; Succession limits, significant limits, Nepero number, bridge theorem, limsup / liminf, sequences and topology, compact sets, and characterization; Continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); Function and function derivative, elementary function derivatives, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de Hopital, Taylor's formula), monotony and derivative sign, local degradation maxima / minima, convex functions / concave; Function graph; Integration according to Riemann and property, integrability of continuous functions, primitive elementary functions, I and II fundamental theorem of integral calculation, integration for substitution and parts, rational functions, some special replacements; Numerical series and convergence, geometric series, convergence criteria for positive terms series (comparison, asymptotic comparison, root, ratio, condensation) and for series at any time (absolute convergence, Leibnitz); Taylor series developments, developments of some elementary functions; Improper integrals.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;

Numerical sets (N, Z, Q and R), R assiomatic construction of R by upper extremity, Archimede properties, Q in R density, N construction and induction principle, Newton binomial and combinatorial calculus, Inequality of Bernoulli; Topology elements in R (isolated and accumulated points, open / closed sets and characterization, closure of a set) and Bolzano-Weierstrass theorem; Complex numbers, polar representation and n-th roots of the unit; Real functions of real variable, domain, co-domain, and inverse functions; Function and property limits, monotone function limits; Succession limits, significant limits, Nepero number, bridge theorem, limsup / liminf, sequences and topology, compact sets, and characterization; Continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); Function and function derivative, elementary function derivatives, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de Hopital, Taylor's formula), monotony and derivative sign, local degradation maxima / minima, convex functions / concave; Function graph; Integration according to Riemann and property, integrability of continuous functions, primitive elementary functions, I and II fundamental theorem of integral calculation, integration for substitution and parts, rational functions, some special replacements; Numerical series and convergence, geometric series, convergence criteria for positive terms series (comparison, asymptotic comparison, root, ratio, condensation) and for series at any time (absolute convergence, Leibnitz); Taylor series developments, developments of some elementary functions; Improper integrals.

A. Laforgia, Calcolo differenziale e integrale, Ed. Accademica;
P. Marcellini e C. Sbordone, Esercizi di Matematica, Vol. 1, tomi 1--4, Ed. Liguori;