20810232 - ANALISI MATEMATICA I

Allow the acquisition of the method deductive logic and provide the basic mathematical tools of the calculation of differential and integral. Each topic will be introduced and strictly the treaty, carrying, sometimes, detailed demonstrations, and also doing large reference to physical meaning, geometric interpretation and application number. Proper methodology and a reasonable skill in the use of the concepts of calculation and its entirety and differential results will put in grade students in principle to face so easy application more topics that will take place in the following courses.

Curriculum

Canali

teacher profile | teaching materials

Programme

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

Core Documentation

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

Type of delivery of the course

Traditional

Type of evaluation

Written exam, oral exam, evaluation.

teacher profile | teaching materials

Programme

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

Core Documentation

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

Canali

teacher profile | teaching materials

Mutuazione: 20810232 ANALISI MATEMATICA I in Ingegneria informatica L-8 CANALE 1 TOLLI FILIPPO

Programme

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

Core Documentation

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

Type of delivery of the course

Traditional

Type of evaluation

Written exam, oral exam, evaluation.

teacher profile | teaching materials

Mutuazione: 20810232 ANALISI MATEMATICA I in Ingegneria informatica L-8 CANALE 2 NATALINI PIERPAOLO

Programme

N and induction principle, Newton binomial; Z, integers modulo n; Q, axiomatic construction of R, Archimedean property, density of Q in R, powers with real exponent; complex numbers, polar representation and n-th roots of the unit; rudiments of topology of R (isolated and accumulation points, open / closed sets); real functions of a real variable, domain, co-domain, and inverse functions; Limits of functions and their properties, limits of monotone functions ; limits of sequences, significant limits, Nepero number, bridge theorem infinite series and convergence, geometric series, convergence tests for series with positive terms (comparison, asymptotic comparison, root, ratio, condensation) and for generic series (absolute convergence, Leibniz); continuous functions and their properties, continuity of elementary functions, types of discontinuities and monotone functions, fundamental theorems on continuous functions (zeros, intermediate values, Weierstrass); derivatives of a functions, derivatives of elementary functions, fundamental theorems of differential calculus (Fermat, Rolle, Cauchy, Lagrange, de l' Hospital, Taylor's formula), monotony and sign of the derivative , local maxima /minima, convex / concave functions; graph of a function; Riemann integral and its properties, integrability of continuous functions, primitive of elementary functions, I and II fundamental theorem of (integral) calculus; integration by substitution and by parts, rational functions, some special substitutions; improper integrals; Taylor series expansions, expansions of some elementary functions.

Core Documentation

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