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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 |

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 |

No news posted

No class timetable posted

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 |

No document in this course

No news posted

No class timetable posted

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