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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 TraduttoreDisattiva traduzione istantaneaElements of logicreal numbers and functions.Numerical sets. Extremes of a numerical set. Topology of the line. General information onfunctions. 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 andinfinite (II CFU).continuous functions.Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theoremthe 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 ofelementary 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. functionszero 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 graphof 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 ofdefined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theoremof calculus. elementary methods to search for a primitive: immediate integration forbreak it down into the sum and by substitution. Integration by parts. of primitive search for some classes offunctions: 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 sequencemonotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonicageneralized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence ofserious. Series in terms of constant sign. Criterion of comparison, root and ratio. Seriesabsolutely 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 logicreal numbers and functions.Numerical sets. Extremes of a numerical set. Topology of the line. General information onfunctions. 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 andinfinite (II CFU).continuous functions.Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theoremthe 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 ofelementary 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. functionszero 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 graphof 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 ofdefined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theoremof calculus. elementary methods to search for a primitive: immediate integration forbreak it down into the sum and by substitution. Integration by parts. of primitive search for some classes offunctions: 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 sequencemonotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonicageneralized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence ofserious. Series in terms of constant sign. Criterion of comparison, root and ratio. Seriesabsolutely 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) No news posted
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## 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 TraduttoreDisattiva traduzione istantaneaElements of logicreal numbers and functions.Numerical sets. Extremes of a numerical set. Topology of the line. General information onfunctions. 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 andinfinite (II CFU).continuous functions.Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theoremthe 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 ofelementary 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. functionszero 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 graphof 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 ofdefined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theoremof calculus. elementary methods to search for a primitive: immediate integration forbreak it down into the sum and by substitution. Integration by parts. of primitive search for some classes offunctions: 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 sequencemonotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonicageneralized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence ofserious. Series in terms of constant sign. Criterion of comparison, root and ratio. Seriesabsolutely 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 logicreal numbers and functions.Numerical sets. Extremes of a numerical set. Topology of the line. General information onfunctions. 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 andinfinite (II CFU).continuous functions.Classification of points of discontinuity. Continuity of composite functions and inverse functions. Theoremthe 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 ofelementary 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. functionszero 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 graphof 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 ofdefined. Theorem average. Indefinite integral and its properties. integral functions. fundamental theoremof calculus. elementary methods to search for a primitive: immediate integration forbreak it down into the sum and by substitution. Integration by parts. of primitive search for some classes offunctions: 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 sequencemonotonous. Numerical series. key examples: the geometric series of Mengoli, harmonic and harmonicageneralized. Cauchy criterion for convergence of a serious. A necessary condition for the convergence ofserious. Series in terms of constant sign. Criterion of comparison, root and ratio. Seriesabsolutely 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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