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Course 2019-2020 a.y.

30122 - PRECORSO DI MATEMATICA / MATHEMATICS - PREPARATORY COURSE

Department of Decision Sciences

For the instruction language of the course see class group/s below

Go to class group/s: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 15 - 16 - 17 - 18 - 21 - 22 - 23 - 25

CLEAM (I sem. - P)
Course Director:
GUIDO OSIMO

Classi: 1 (I sem.) - 2 (I sem.) - 3 (I sem.) - 4 (I sem.) - 5 (I sem.) - 6 (I sem.) - 7 (I sem.) - 8 (I sem.)
Docenti responsabili delle classi:
Classe 1: ELIA BOMBARDELLI, Classe 2: FEDERICA ANDREANO, Classe 3: FEDERICO MARIO GIOVANNI VEGNI, Classe 4: MAURO D'AMICO, Classe 5: GUIDO OSIMO, Classe 6: MARCO UGO BOELLA, Classe 7: FABIO TONOLI, Classe 8: GIANPAOLO MONTI

Classe/i impartita/e in lingua italiana

Mission e Programma sintetico
MISSION

Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

PROGRAMMA SINTETICO

Parte online:

  • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
  • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
  • Calcolo letterale.
  • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
  • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
  • Elementi di trigonometria.
  • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

Parte in presenza:

  • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzioni suriettive, iniettive, biunivoche. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni trigonometriche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari.
  • Rapporto incrementale, derivata. Derivate delle funzioni elementari. Algebra delle derivate. Derivata della funzione composta. Equazione della retta tangente.
  • La matematica come sistema assiomatico: nozioni primitive e definizioni, assiomi e teoremi. Terminologia di base sui teoremi. Esempi di dimostrazioni e di tecniche dimostrative. Congetture: dimostrazioni e controesempi. Implicazione, equivalenza. Condizione sufficiente, condizione necessaria, condizione necessaria e sufficiente. La negazione di una proposizione. Esempi di dimostrazioni per assurdo.

Modalità didattiche
  • Lezioni frontali
  • Lezioni online
DETTAGLI

Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


Metodi di valutazione dell'apprendimento
  Accertamento in itinere Prove parziali Prova generale
  • Inserita all'interno della valutazione relativa al codice 30062
  • x x x

    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: viene utilizzata una dispensa, che è disponibile all’inizio di questa parte.
    Modificato il 25/07/2019 11:13

    CLEF (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classi: 9 (I sem.) - 10 (I sem.)
    Docenti responsabili delle classi:
    Classe 9: JACOPO GIUSEPPE DE TULLIO, Classe 10: FRANCESCA SIANESI

    Classe/i impartita/e in lingua italiana

    Mission e Programma sintetico
    MISSION

    Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

    PROGRAMMA SINTETICO

    Parte online:

    • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
    • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
    • Calcolo letterale.
    • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
    • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
    • Elementi di trigonometria.
    • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

    Parte in presenza:

    • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzioni suriettive, iniettive, biunivoche. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni trigonometriche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari.
    • Rapporto incrementale, derivata. Derivate delle funzioni elementari. Algebra delle derivate. Derivata della funzione composta. Equazione della retta tangente.
    • La matematica come sistema assiomatico: nozioni primitive e definizioni, assiomi e teoremi. Terminologia di base sui teoremi. Esempi di dimostrazioni e di tecniche dimostrative. Congetture: dimostrazioni e controesempi. Implicazione, equivalenza. Condizione sufficiente, condizione necessaria, condizione necessaria e sufficiente. La negazione di una proposizione. Esempi di dimostrazioni per assurdo.

    Modalità didattiche
    • Lezioni frontali
    • Lezioni online
    DETTAGLI

    Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


    Metodi di valutazione dell'apprendimento
      Accertamento in itinere Prove parziali Prova generale
  • Inserita all'interno della valutazione relativa al codice 30062
  • x x x

    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: viene utilizzata una dispensa, che è disponibile all’inizio di questa parte.
    Modificato il 27/05/2019 11:15

    CLEACC (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classi: 11 (I sem.)
    Docenti responsabili delle classi:
    Classe 11: ELISA CAPRARI

    Classe/i impartita/e in lingua italiana

    Mission e Programma sintetico
    MISSION

    Il precorso di matematica ha l’obiettivo di consolidare alcuni argomenti di matematica a livello pre-universitario, per permettere allo studente di iniziare gli studi universitari con serenità e competenza. Negli studi universitari questi argomenti sono dati per noti e non sono ripetuti. Il precorso è erogato in modalità blended learning, ovvero in parte on-line e in parte in presenza. La parte on-line è accessibile a partire dall’estate che precede il primo anno di studi universitari. La parte in presenza tratta argomenti diversi dalla parte on-line, si articola su 12 ore di corso e si svolge interamente durante la Welcome Week del primo anno. È preferibile che gli studenti fruiscano della parte on-line prima dell’inizio della parte in presenza. La conoscenza dei contenuti della parte on-line e della parte in presenza è un elemento importante per ottenere buoni risultati nei primi esami di matematica previsti nel piano di studi.

    PROGRAMMA SINTETICO

    Parte online:

    • Insiemi. Operazioni tra insiemi. Insiemi numerici. Rappresentazione degli insiemi numerici sulla retta.
    • Potenze a esponente intero. Radici. Potenze a esponente razionale e a esponente reale.
    • Calcolo letterale.
    • Equazioni di primo e secondo grado. Equazioni di grado superiore al secondo. Equazioni frazionarie. Sistemi di equazioni.
    • Coordinate cartesiane nel piano. Rette. Parabole. Altre curve.
    • Disequazioni di primo e secondo grado. Disequazioni di grado superiore al secondo. Disequazioni frazionarie. Sistemi di disequazioni. Equazioni e disequazioni con termini in valore assoluto.

    Parte in presenza:

    • Funzioni reali di una variabile reale: definizione, grafico, esempi. Funzione composta. Funzione inversa. Funzioni potenza e loro grafici. Funzioni esponenziali e loro grafici. Introduzione ai logaritmi. Proprietà dei logaritmi. Funzioni logaritmiche e loro grafici. Funzioni definite a tratti. Funzione modulo. Trasformazioni di funzioni elementari.
    • Equazioni e disequazioni esponenziali/logaritmiche. Semplici equazioni e disequazioni irrazionali.

    Modalità didattiche
    • Lezioni frontali
    • Lezioni online
    DETTAGLI

    Lezioni online: la prima parte del precorso si svolge online, sulla piattaforma didattica Bboard.


    Metodi di valutazione dell'apprendimento
      Accertamento in itinere Prove parziali Prova generale
  • Inserita all'interno della valutazione relativa al codice 30268
  •   x x

    Materiali didattici
    STUDENTI FREQUENTANTI E NON FREQUENTANTI
    • Parte online: tutti i materiali didattici sono disponibili sulla piattaforma Bboard.
    • Parte in presenza: materiali didattici a cura del docente.
    Modificato il 27/05/2019 11:18

    Classes: 12 (I sem.)
    Instructors:
    Class 12: LAURA MARIANO

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions.
    • Exponential/logarithmic equations and inequalities. Simple irrational equations and inequalities.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30268
  •   x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 27/05/2019 11:20

    BESS-CLES (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 13 (I sem.)
    Instructors:
    Class 13: FABRIZIO IOZZI

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Elements of n-variable differential calculus: partial derivatives, unconstrained and constrained optimization.
    • Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Set axioms, number sets.
    • Elements of logic: propositions, quantifiers. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. The contrapositive proposition.
    • Basic terminology on theorems. Examples of proofs and demonstration techniques. Proofs by contradiction. The principle of mathematical induction; proofs by induction. Conjectures: proofs and counterexamples.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30448
  •   x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 27/05/2019 11:23

    BEMACS (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 25 (I sem.)
    Instructors:
    Class 25: MAURO D'AMICO

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Number systems.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Introduction to proofs. Connectives, quantifiers. Demonstration techniques: direct, contrapositive and indirect (or by contradiction). Principle of induction.
    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Bounded and unbounded functions. Increasing and decreasing functions. Global extrema of a function. Concave and convex functions. Operations with functions (sum, difference, product and quotient). Linear combination of functions. Odd and even functions. Periodic functions. Elementary functions and their graphs: constant, linear, affine linear, power, exponential and logarithm. Piecewise defined functions. Elementary notion of continuity.
    • Derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line. Stationary points. Second derivative.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30400
  •   x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 27/05/2019 11:26

    BIEM (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 15 (I sem.) - 16 (I sem.) - 17 (I sem.) - 18 (I sem.)
    Instructors:
    Class 15: GUIDO OSIMO, Class 16: FEDERICA ANDREANO, Class 17: MARIA BEATRICE ZAVELANI ROSSI, Class 18: FEDERICO MARIO GIOVANNI VEGNI

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Trigonometric functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions.
    • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line.
    • Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Basic terminology on theorems. Examples of proofs and demonstration techniques. Conjectures: proofs and counterexamples. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. Examples of proofs by contradiction.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30062
  • x x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: we use a booklet, which is available at the beginning of this part.
    Last change 27/05/2019 11:28

    BIEF (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 21 (I sem.) - 22 (I sem.)
    Instructors:
    Class 21: JACOPO GIUSEPPE DE TULLIO, Class 22: ANDREA GIUSSANI

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 12 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • Elements of trigonometry.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Real functions of one real variable: definition, graph, examples. Surjective, injective, bijective functions. Composite function. Inverse function. Power functions and their graphs. Exponential functions and their graphs. Introduction to logarithms. Properties of logarithms. Logarithmic functions and their graphs. Trigonometric functions and their graphs. Piecewise defined functions. Absolute value function. Transformation of elementary functions. 
    • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line.
    • Mathematics as an axiomatic system: primitive notions and definitions, axioms and theorems. Basic terminology on theorems. Examples of proofs and demonstration techniques. Conjectures: proofs and counterexamples. Implication, equivalence. Sufficient condition, necessary condition, necessary and sufficient condition. The negation of a proposition. Examples of proofs by contradiction.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30062
  • x x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: we use a booklet, which is available at the beginning of this part.
    Last change 27/05/2019 11:29

    BIG (I sem. - P)
    Course Director:
    GUIDO OSIMO

    Classes: 23 (I sem.)
    Instructors:
    Class 23: BARBARA GATTI

    Class group/s taught in English

    Mission & Content Summary
    MISSION

    The aim of the preparatory course in mathematics is to consolidate some topics in pre-undergraduate mathematics, in order to help students begin their university studies with comfort and competence. In university courses, these topics are considered as known and are not repeated. The preparatory course is a blended learning course, that is it is partly online and partly in person. The online part is accessible from the summer that precedes the first year of university studies. The classroom part deals with different topics with respect to the online part, consists of a 15 hours course and it is entirely delivered during the Welcome Week of the first year. It is preferable that students complete the online part before the beginning of the classroom part. The knowledge of the content delivered in both the online and classroom parts are integral in helping students earn high marks on the first exams in mathematics, which are part of their plan of study.

    CONTENT SUMMARY

    Online part:

    • Sets. Operations with sets. Number sets. Representation of number sets on the line.
    • Powers with integer exponents. Roots. Powers with rational exponents and with real exponents.
    • Polynomial algebra.
    • First and second degree equations. Higher degree equations. Fractional equations. Systems of equations.
    • Cartesian coordinates in the plane. Straight lines. Parabolas. Other curves.
    • First and second degree inequalities. Higher degree inequalities. Fractional inequalities. Systems of inequalities. Equations and inequalities with terms in absolute value.

    Classroom part:

    • Summation symbol and remarkable sums.
    • Real functions of one real variable: definition, graph, examples. Composite function. Inverse function. Elementary functions and their graphs: linear, affine linear, quadratic, power, exponential, logarithmic functions. Piecewise defined functions. Transformation of elementary functions.
    • Behaviour of elementary functions at the boundary of their domain. Hierarchy of infinite functions.
    • Exponential equations and inequalities. Properties of logarithms. Logarithmic equations and inequalities. Solution to equations and inequalities by graphical methods.
    • Difference quotient, derivative. Derivatives of elementary functions. Algebra of derivatives. Chain rule. Equation of the tangent line. Stationary points. Derivative and monotonicity. Second derivative. Convex and concave functions.
    • Graph of a function: domain, behaviour at the boundary, zeros (or x-intercepts), y-intercept, sign, monotonicity, points of maximum and minimum, concavity and convexity.
    • Antiderivatives of elementary functions. Integration methods: decomposition, substitution, by parts.

    Teaching methods
    • Face-to-face lectures
    • Online lectures
    DETAILS

    Online lectures: the first part of the preparatory course takes place online, on the Bboard teaching platform.


    Assessment methods
      Continuous assessment Partial exams General exam
  • Included in the assessment procedures for code 30319
  •   x x

    Teaching materials
    ATTENDING AND NOT ATTENDING STUDENTS
    • Online part: all teaching materials are available on the Bboard platform.
    • Classroom part: teaching materials prepared by the instructor.
    Last change 27/05/2019 11:32