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MATHEMATICAL ANALYSIS I

Degree course Information and Communication Technologies (ICT) Engineering
Curriculum Curriculum unico
Learnings Orientamento unico
Academic Year 2016/2017
ECTS 9
Scientific Disciplinary Sector MAT/05
Year First year
Time unit First semester
Class hours 72
Educational activity Basic training activities

Canale: A-L

Professor LUISA ANGELA MARIA FATTORUSSO
Objectives N.D.
Programme Traduttore
Disattiva traduzione istantanea
Elements of logic
real numbers and functions.
Numerical sets. Extremes of a numerical set. Topology of the line. General information on
functions. numeric functions and their properties elementari.Funzioni injecting, surjettive, bijective. Graph of a function. Operations on functions. elementary functions .Funzione composed and inverse function (I CFU).

Limit of a function.
Definition of the limit of its reale.Grafici variable real functions. Theorems of uniqueness of the limit, the comparison and dellapermanenza sign. Theorem on monotone functions limits. Operations on the limits and indeterminate forms.
significant limitations. Asymptotes. Infinite and infinitesimal and their comparison. substitution principle of infinitesimal and
infinite (II CFU).

continuous functions.
Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theorem
the existence of zeros. Intermediate value theorem. Roots of an equation: graphical methods for research.
Continuous functions on a closed bounded interval. Weierstrass. uniform continuity (III CFU).

Differential calculus for functions of one real variable.
Definition of derivative and its geometrical meaning and kinematic. Straight tangent to the graph. derivatives of
elementary functions and derivation rules. Differentiability and continuità.Teorema.Condiz. necessary and sufficient for the existence of the der. before. Maximum and relative minimum. Fermat's, Rolle, Cauchy and Lagrange and their geometrica.Corollari interpretation of T. Lagrange.Primitive of a function. Monotony and differentiability. functions
zero derivative. singular points, angular, with vertical tangent and cusps. Differential and linear approximation.
successive derivatives. Theorems of de l'Hôpital. Taylor's formula and McLaurin. Expressions of the rest.
Approximation of functions by polynomials. Limitations with the Taylor formula.
Convex and concave functions. inflection points. fundamental properties. Lipschitz continuity. Study the graph
of a function. (IV-V-VI CFU).

integral calculus for functions of one real variable.
The Riemann integral of functions of one variable. geometric interpretation. properties of
defined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theorem
of calculus. elementary methods to search for a primitive: immediate integration for
break it down into the sum and by substitution. Integration by parts. of primitive search for some classes of
functions: rational, trigonometric and irrational. or improper integrals. basic examples.
Comparison theorem. Asymptotic comparison. Criterion of the infinite and infinitesimal. (VII-VIII CFU).
Sequences and series.
Limit of a sequence. Theorems of uniqueness of the limit, the sign permanence and confrontation. Theorem
"Bridge" and nonexistence of limits. Calculating the limits. the existence of a limit theorem for a sequence
monotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonica
generalized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence of
serious. Series in terms of constant sign. Criterion of comparison, root and ratio. Series
absolutely convergent. Series in terms of alternating signs. Alternating series test.
complex numbers and their representation in the plane of Gauss.Forma Algebraic and trigonometrica.Radici n-ble (IX CFU).


Elements of logic
real numbers and functions.
Numerical sets. Extremes of a numerical set. Topology of the line. General information on
functions. numeric functions and their properties elementari.Funzioni injecting, surjettive, bijective. Graph of a function. Operations on functions. elementary functions .Funzione composed and inverse function (I CFU).

Limit of a function.
Definition of the limit of its reale.Grafici variable real functions. Theorems of uniqueness of the limit, the comparison and dellapermanenza sign. Theorem on monotone functions limits. Operations on the limits and indeterminate forms.
significant limitations. Asymptotes. Infinite and infinitesimal and their comparison. substitution principle of infinitesimal and
infinite (II CFU).

continuous functions.
Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theorem
the existence of zeros. Intermediate value theorem. Roots of an equation: graphical methods for research.
Continuous functions on a closed bounded interval. Weierstrass. uniform continuity (III CFU).

Differential calculus for functions of one real variable.
Definition of derivative and its geometrical meaning and kinematic. Straight tangent to the graph. derivatives of
elementary functions and derivation rules. Differentiability and continuità.Teorema.Condiz. necessary and sufficient for the existence of the der. before. Maximum and relative minimum. Fermat's, Rolle, Cauchy and Lagrange and their geometrica.Corollari interpretation of T. Lagrange.Primitive of a function. Monotony and differentiability. functions
zero derivative. singular points, angular, with vertical tangent and cusps. Differential and linear approximation.
successive derivatives. Theorems of de l'Hôpital. Taylor's formula and McLaurin. Expressions of the rest.
Approximation of functions by polynomials. Limitations with the Taylor formula.
Convex and concave functions. inflection points. fundamental properties. Lipschitz continuity. Study the graph
of a function. (IV-V-VI CFU).

integral calculus for functions of one real variable.
The Riemann integral of functions of one variable. geometric interpretation. properties of
defined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theorem
of calculus. elementary methods to search for a primitive: immediate integration for
break it down into the sum and by substitution. Integration by parts. of primitive search for some classes of
functions: rational, trigonometric and irrational. or improper integrals. basic examples.
Comparison theorem. Asymptotic comparison. Criterion of the infinite and infinitesimal. (VII-VIII CFU).
Sequences and series.
Limit of a sequence. Theorems of uniqueness of the limit, the sign permanence and confrontation. Theorem
"Bridge" and nonexistence of limits. Calculating the limits. the existence of a limit theorem for a sequence
monotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonica
generalized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence of
serious. Series in terms of constant sign. Criterion of comparison, root and ratio. Series
absolutely convergent. Series in terms of alternating signs. Alternating series test.
complex numbers and their representation in the plane of Gauss.Forma Algebraic and trigonometrica.Radici n-ble (IX CFU).


Reference documents:

• C. D. S. Pagani Salsa, Mathematical Analysis, Zanichelli, Bologna 2015
. Acerbi-Buttazzo, Mathematics ABC Analysis (op. 1 variable), Pythagoras publishing
• R. Adams Calculus 1 and 2. Edit. Ambrosiana
• James Stewart. Calculation "Func. a variable "and" more 'variables. "Edit. Apogee
• P. Marcellini, C. Sbordone, Esercuzi of Mathematics one (4 vol), Liguori Editore.
• Salsa-Squellati, Analysis Exercises Mathematics I, Zanichelli.
• A. Alvino, L. Carbone, G. Trombetti, The Practice of Mathematics, vol. I, Liguori Publishers, Naples.

The exam consists of a written test and an oral examination and any tests in progress (optional).


The exam consists of a written test and an oral examination and any tests in progress (optional).
Books Reference documents:

• C. D. S. Pagani Salsa, Mathematical Analysis, Zanichelli, Bologna 2015
. Acerbi-Buttazzo, Mathematics ABC Analysis (op. 1 variable), Pythagoras publishing
• R. Adams Calculus 1 and 2. Edit. Ambrosiana
• James Stewart. Calculation "Func. a variable "and" more 'variables. "Edit. Apogee
• P. Marcellini, C. Sbordone, Esercuzi of Mathematics one (4 vol), Liguori Editore.
• Salsa-Squellati, Analysis Exercises Mathematics I, Zanichelli.
• A. Alvino, L. Carbone, G. Trombetti, The Practice of Mathematics, vol. I, Liguori Publishers, Naples.
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation Yes
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation No
Internship evaluation No
Evaluation in itinere Yes
Practice Test No

Further information

Description Document
compito analisi 1 settembre 2016 (dispensa) Document
No news posted
No class timetable posted

Canale: M-Z

Supplying course 85T001 ANALISI MATEMATICA I in Ingegneria dell'Informazione L-8 A-L FATTORUSSO LUISA ANGELA MARIA
Professor Luisa Angela Maria FATTORUSSO
Objectives N.D.
Programme Traduttore
Disattiva traduzione istantanea
Elements of logic
real numbers and functions.
Numerical sets. Extremes of a numerical set. Topology of the line. General information on
functions. numeric functions and their properties elementari.Funzioni injecting, surjettive, bijective. Graph of a function. Operations on functions. elementary functions .Funzione composed and inverse function (I CFU).

Limit of a function.
Definition of the limit of its reale.Grafici variable real functions. Theorems of uniqueness of the limit, the comparison and dellapermanenza sign. Theorem on monotone functions limits. Operations on the limits and indeterminate forms.
significant limitations. Asymptotes. Infinite and infinitesimal and their comparison. substitution principle of infinitesimal and
infinite (II CFU).

continuous functions.
Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theorem
the existence of zeros. Intermediate value theorem. Roots of an equation: graphical methods for research.
Continuous functions on a closed bounded interval. Weierstrass. uniform continuity (III CFU).

Differential calculus for functions of one real variable.
Definition of derivative and its geometrical meaning and kinematic. Straight tangent to the graph. derivatives of
elementary functions and derivation rules. Differentiability and continuità.Teorema.Condiz. necessary and sufficient for the existence of the der. before. Maximum and relative minimum. Fermat's, Rolle, Cauchy and Lagrange and their geometrica.Corollari interpretation of T. Lagrange.Primitive of a function. Monotony and differentiability. functions
zero derivative. singular points, angular, with vertical tangent and cusps. Differential and linear approximation.
successive derivatives. Theorems of de l'Hôpital. Taylor's formula and McLaurin. Expressions of the rest.
Approximation of functions by polynomials. Limitations with the Taylor formula.
Convex and concave functions. inflection points. fundamental properties. Lipschitz continuity. Study the graph
of a function. (IV-V-VI CFU).

integral calculus for functions of one real variable.
The Riemann integral of functions of one variable. geometric interpretation. properties of
defined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theorem
of calculus. elementary methods to search for a primitive: immediate integration for
break it down into the sum and by substitution. Integration by parts. of primitive search for some classes of
functions: rational, trigonometric and irrational. or improper integrals. basic examples.
Comparison theorem. Asymptotic comparison. Criterion of the infinite and infinitesimal. (VII-VIII CFU).
Sequences and series.
Limit of a sequence. Theorems of uniqueness of the limit, the sign permanence and confrontation. Theorem
"Bridge" and nonexistence of limits. Calculating the limits. the existence of a limit theorem for a sequence
monotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonica
generalized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence of
serious. Series in terms of constant sign. Criterion of comparison, root and ratio. Series
absolutely convergent. Series in terms of alternating signs. Alternating series test.
complex numbers and their representation in the plane of Gauss.Forma Algebraic and trigonometrica.Radici n-ble (IX CFU).


Elements of logic
real numbers and functions.
Numerical sets. Extremes of a numerical set. Topology of the line. General information on
functions. numeric functions and their properties elementari.Funzioni injecting, surjettive, bijective. Graph of a function. Operations on functions. elementary functions .Funzione composed and inverse function (I CFU).

Limit of a function.
Definition of the limit of its reale.Grafici variable real functions. Theorems of uniqueness of the limit, the comparison and dellapermanenza sign. Theorem on monotone functions limits. Operations on the limits and indeterminate forms.
significant limitations. Asymptotes. Infinite and infinitesimal and their comparison. substitution principle of infinitesimal and
infinite (II CFU).

continuous functions.
Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theorem
the existence of zeros. Intermediate value theorem. Roots of an equation: graphical methods for research.
Continuous functions on a closed bounded interval. Weierstrass. uniform continuity (III CFU).

Differential calculus for functions of one real variable.
Definition of derivative and its geometrical meaning and kinematic. Straight tangent to the graph. derivatives of
elementary functions and derivation rules. Differentiability and continuità.Teorema.Condiz. necessary and sufficient for the existence of the der. before. Maximum and relative minimum. Fermat's, Rolle, Cauchy and Lagrange and their geometrica.Corollari interpretation of T. Lagrange.Primitive of a function. Monotony and differentiability. functions
zero derivative. singular points, angular, with vertical tangent and cusps. Differential and linear approximation.
successive derivatives. Theorems of de l'Hôpital. Taylor's formula and McLaurin. Expressions of the rest.
Approximation of functions by polynomials. Limitations with the Taylor formula.
Convex and concave functions. inflection points. fundamental properties. Lipschitz continuity. Study the graph
of a function. (IV-V-VI CFU).

integral calculus for functions of one real variable.
The Riemann integral of functions of one variable. geometric interpretation. properties of
defined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theorem
of calculus. elementary methods to search for a primitive: immediate integration for
break it down into the sum and by substitution. Integration by parts. of primitive search for some classes of
functions: rational, trigonometric and irrational. or improper integrals. basic examples.
Comparison theorem. Asymptotic comparison. Criterion of the infinite and infinitesimal. (VII-VIII CFU).
Sequences and series.
Limit of a sequence. Theorems of uniqueness of the limit, the sign permanence and confrontation. Theorem
"Bridge" and nonexistence of limits. Calculating the limits. the existence of a limit theorem for a sequence
monotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonica
generalized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence of
serious. Series in terms of constant sign. Criterion of comparison, root and ratio. Series
absolutely convergent. Series in terms of alternating signs. Alternating series test.
complex numbers and their representation in the plane of Gauss.Forma Algebraic and trigonometrica.Radici n-ble (IX CFU).


Reference documents:

• C. D. S. Pagani Salsa, Mathematical Analysis, Zanichelli, Bologna 2015
. Acerbi-Buttazzo, Mathematics ABC Analysis (op. 1 variable), Pythagoras publishing
• R. Adams Calculus 1 and 2. Edit. Ambrosiana
• James Stewart. Calculation "Func. a variable "and" more 'variables. "Edit. Apogee
• P. Marcellini, C. Sbordone, Esercuzi of Mathematics one (4 vol), Liguori Editore.
• Salsa-Squellati, Analysis Exercises Mathematics I, Zanichelli.
• A. Alvino, L. Carbone, G. Trombetti, The Practice of Mathematics, vol. I, Liguori Publishers, Naples.

The exam consists of a written test and an oral examination and any tests in progress (optional).


The exam consists of a written test and an oral examination and any tests in progress (optional).
Books Reference documents:

• C. D. S. Pagani Salsa, Mathematical Analysis, Zanichelli, Bologna 2015
. Acerbi-Buttazzo, Mathematics ABC Analysis (op. 1 variable), Pythagoras publishing
• R. Adams Calculus 1 and 2. Edit. Ambrosiana
• James Stewart. Calculation "Func. a variable "and" more 'variables. "Edit. Apogee
• P. Marcellini, C. Sbordone, Esercuzi of Mathematics one (4 vol), Liguori Editore.
• Salsa-Squellati, Analysis Exercises Mathematics I, Zanichelli.
• A. Alvino, L. Carbone, G. Trombetti, The Practice of Mathematics, vol. I, Liguori Publishers, Naples.
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation Yes
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation No
Internship evaluation No
Evaluation in itinere Yes
Practice Test No

Further information

No document in this course
No news posted
No class timetable posted
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