#
Calculus and computer laboratory

A.Y. 2021/2022

Learning objectives

To provide the basic method and calculus tools of mathematical analysis and linear algebra which are propaedeutic to a full understanding and correct handling of biological data and information. These tools represent a mandatory cultural element for a modern biologist who wants to comprehend the life in its quantitative aspects.

To teach concepts and tools of Computer Science for an appropriate use of application software. Topics will concern basic introductory notions of informatics, data analysis and management, and introduction to Bioinformatics. The course is offered in e-learning through a dedicated online software platform, with the addition of two frontal lectures and two hands-on in computer laboratory.

To teach concepts and tools of Computer Science for an appropriate use of application software. Topics will concern basic introductory notions of informatics, data analysis and management, and introduction to Bioinformatics. The course is offered in e-learning through a dedicated online software platform, with the addition of two frontal lectures and two hands-on in computer laboratory.

Expected learning outcomes

At the end of the study the students will be able to use computational processes to analyze the biological phenomena. In particular the student: i) will be able to formalize elementary problems by mean of mathematical models; ii) will know the main basic results of differential and integral calculus (for real functions of one real variable) and of the linear algebra; iii) will be able to deal with such a theoretical part and related tools in order to solve problem in sciences of live for which a mathematical approach is suitable.

The students will benefit from this course since they will learn concepts of data representation, hardware, and software. In addition, they will acquire the ability to process data by using spreadsheets, databases, Internet and the web consultation related to biological databases.

The students will benefit from this course since they will learn concepts of data representation, hardware, and software. In addition, they will acquire the ability to process data by using spreadsheets, databases, Internet and the web consultation related to biological databases.

**Lesson period:**
First semester

**Assessment methods:** Esame

**Assessment result:** voto verbalizzato in trentesimi

Course syllabus and organization

### A - L

Responsible

Lesson period

First semester

More specific

information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation

information on the delivery modes of training activities for academic year 2021/22 will be provided over the coming months, based on the evolution of the public health situation

**Prerequisites for admission**

Elementary algebra, analytic geometry, plane trigonometry. Elementary functions and their graphs. Inequalities.

(see also the MiniMat course material available online at http://ariel.unimi.it/User/).

(see also the MiniMat course material available online at http://ariel.unimi.it/User/).

**Assessment methods and Criteria**

The exam consists of two parts, one for each of the two modulus of Matematica Generale (6 CFU) and of Laboratorio di Informatica (3 CFU).

To participate to the test of each modulus, the student must register through SIFA to the module itself.

The final grade is obtained after passing the tests related to the two modulus.

The two tests must be passed within the same academic year.

The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.

To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve the types of exercises illustrated during the exercises lectures.

The test of the modulus of Matematica Generale consists of exercises and some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.

There will be 7 tests distributed during the academic year, dates appearing on SIFA.

The written test can be replaced by passing two in itinere tests, the first indicatively in mid-November, the second in the same date of the January test.

The two in itinere tests are passed if in each one a score of at least 16 points is obtained out of a total of 30 and if the average of the two scores (approximated by excess to the unit) is greater or equal to 18.

Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph during which it is not allowed to consult any type of material, nor the use of calculators.

In case the student wants to improve the grade obtained in the written test or in the itinere tests or to obtain the Laude, the student must also pass an oral exam that will focus on the detailed program indicated on the website at the end of the semester (definitions, statements of theorems, proofs of theorems).

In the event of a negative evaluation of the oral exam, the mark obtained in the written test could be modified accordingly or even the written test will have to be repeated.

To participate to the test of each modulus, the student must register through SIFA to the module itself.

The final grade is obtained after passing the tests related to the two modulus.

The two tests must be passed within the same academic year.

The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.

To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve the types of exercises illustrated during the exercises lectures.

The test of the modulus of Matematica Generale consists of exercises and some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.

There will be 7 tests distributed during the academic year, dates appearing on SIFA.

The written test can be replaced by passing two in itinere tests, the first indicatively in mid-November, the second in the same date of the January test.

The two in itinere tests are passed if in each one a score of at least 16 points is obtained out of a total of 30 and if the average of the two scores (approximated by excess to the unit) is greater or equal to 18.

Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph during which it is not allowed to consult any type of material, nor the use of calculators.

In case the student wants to improve the grade obtained in the written test or in the itinere tests or to obtain the Laude, the student must also pass an oral exam that will focus on the detailed program indicated on the website at the end of the semester (definitions, statements of theorems, proofs of theorems).

In the event of a negative evaluation of the oral exam, the mark obtained in the written test could be modified accordingly or even the written test will have to be repeated.

**Modulo: Matematica generale**

**Course syllabus**

· Natural, integer, rational, real numbers. The field of real numbers and its operations. The symbols + ∞ and -∞.

· Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.

· Elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.

· Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Inverse matrix. Rank of a matrix. Systems of linear equations and matrix representation. Cramer theorem and Rouchè-Capelli theorem. Eigenvectors and eigenvalues.

· Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.

· The number of Nepero e. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.

· Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Extreme points.

· Fermat's theorem. Rolle theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. De l'Hôpital theorem.

· Study of the graph of a function. Horizontal, vertical, oblique asymptotes.

· Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution. Integration of rational functions (outline).

· Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.

· Outline of linear differential equations of first and second order.

· Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.

· Elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.

· Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Inverse matrix. Rank of a matrix. Systems of linear equations and matrix representation. Cramer theorem and Rouchè-Capelli theorem. Eigenvectors and eigenvalues.

· Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.

· The number of Nepero e. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.

· Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Extreme points.

· Fermat's theorem. Rolle theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. De l'Hôpital theorem.

· Study of the graph of a function. Horizontal, vertical, oblique asymptotes.

· Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution. Integration of rational functions (outline).

· Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.

· Outline of linear differential equations of first and second order.

**Teaching methods**

Traditional. Tutoring activity for the preparation of the written tests.

**Teaching Resources**

· P. Marcellini, C. Sbordone, Calcolo - edizione aggiornata per i nuovi corsi di laurea, Liguori editore

· D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana

OPPURE

D. Benedetto, M. Degli Esposti, C. Maffei: Dalle funzioni ai modelli, Casa Editrice Ambrosiana

· Corso online "Matematica Assistita", http://ariel.unimi.it/User/

· D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana

OPPURE

D. Benedetto, M. Degli Esposti, C. Maffei: Dalle funzioni ai modelli, Casa Editrice Ambrosiana

· Corso online "Matematica Assistita", http://ariel.unimi.it/User/

**Modulo: Laboratorio di informatica**

**Course syllabus**

Risultati di apprendimento

Lo studente dovrà possedere un'adeguata misura di Conoscenze e Competenze.

Conoscenze: lo studente dovrà possedere conoscenze relative ai seguenti temi: fondamenti della disciplina informatica, fogli di calcolo, gestione delle informazioni, Internet e web. La parte di fondamenti include: nozioni storiche della disciplina informatica, struttura e organizzazione del calcolatore, codifica delle informazioni, unità di misura dell'informazione, definizioni di algoritmo e programma, rappresentazione digitale di testo, audio, immagini e video, classificazione del software di un calcolatore, sicurezza informatica e rischi connessi all'uso di tecnologie digitali. La parte di fogli di calcolo include: definizione e struttura di un foglio di calcolo, funzioni di calcolo nello strumento Microsoft Excel, funzioni statistiche e creazione di grafici in Microsoft Excel. La parte di gestione delle informazioni include: definizione di dato e informazione, basi di dati, modello relazionale delle basi di dati, sistemi di basi di dati, analogie e differenze tra fogli di calcolo e basi di dati relazionali, linguaggi per le basi di dati, composizione di query, basi di dati su web. La parte di Internet e web include: nozioni sulle reti di calcolatori, standard e protocolli delle reti di calcolatori, storia e struttura della rete Internet, architettura del web, linguaggio HTML, struttura e funzionamento dei motori di ricerca.

Competenze: lo studente acquisirà le seguenti competenze:

· creazione e organizzazione dei dati in un foglio di calcolo

· trascinamento di formule in un foglio di calcolo

· formattazione di celle in un foglio di calcolo

· uso di funzioni generali e statistiche in Microsoft Excel

· creazione di grafici in Microsoft Excel

Il programma dell'insegnamento prevede la trattazione dei seguenti argomenti:

· Fondamenti della disciplina informatica

o Introduzione all'informatica

o Codifica dell'informazione

o Struttura del calcolatore

o Programmi e software

o I rischi della "Infosfera"

· Fogli di calcolo

o Introduzione ai fogli di calcolo

o Funzioni di calcolo in Excel

o Funzioni statistiche in Excel

o Creazione di grafici in Excel

· Gestione delle informazioni

o Introduzione alla gestione delle informazioni

o Memorizzazione di dati e basi di dati

o Basi di dati relazionali

o Creazione di una base di dati

o Composizione di query

o Basi di dati sul web

· Internet e web

o Reti di calcolatori

o La rete Internet

o Architettura del web

o Standard per il web

o Contenuti sul web

o Motori di ricerca

o Evoluzione del web

Lo studente dovrà possedere un'adeguata misura di Conoscenze e Competenze.

Conoscenze: lo studente dovrà possedere conoscenze relative ai seguenti temi: fondamenti della disciplina informatica, fogli di calcolo, gestione delle informazioni, Internet e web. La parte di fondamenti include: nozioni storiche della disciplina informatica, struttura e organizzazione del calcolatore, codifica delle informazioni, unità di misura dell'informazione, definizioni di algoritmo e programma, rappresentazione digitale di testo, audio, immagini e video, classificazione del software di un calcolatore, sicurezza informatica e rischi connessi all'uso di tecnologie digitali. La parte di fogli di calcolo include: definizione e struttura di un foglio di calcolo, funzioni di calcolo nello strumento Microsoft Excel, funzioni statistiche e creazione di grafici in Microsoft Excel. La parte di gestione delle informazioni include: definizione di dato e informazione, basi di dati, modello relazionale delle basi di dati, sistemi di basi di dati, analogie e differenze tra fogli di calcolo e basi di dati relazionali, linguaggi per le basi di dati, composizione di query, basi di dati su web. La parte di Internet e web include: nozioni sulle reti di calcolatori, standard e protocolli delle reti di calcolatori, storia e struttura della rete Internet, architettura del web, linguaggio HTML, struttura e funzionamento dei motori di ricerca.

Competenze: lo studente acquisirà le seguenti competenze:

· creazione e organizzazione dei dati in un foglio di calcolo

· trascinamento di formule in un foglio di calcolo

· formattazione di celle in un foglio di calcolo

· uso di funzioni generali e statistiche in Microsoft Excel

· creazione di grafici in Microsoft Excel

Il programma dell'insegnamento prevede la trattazione dei seguenti argomenti:

· Fondamenti della disciplina informatica

o Introduzione all'informatica

o Codifica dell'informazione

o Struttura del calcolatore

o Programmi e software

o I rischi della "Infosfera"

· Fogli di calcolo

o Introduzione ai fogli di calcolo

o Funzioni di calcolo in Excel

o Funzioni statistiche in Excel

o Creazione di grafici in Excel

· Gestione delle informazioni

o Introduzione alla gestione delle informazioni

o Memorizzazione di dati e basi di dati

o Basi di dati relazionali

o Creazione di una base di dati

o Composizione di query

o Basi di dati sul web

· Internet e web

o Reti di calcolatori

o La rete Internet

o Architettura del web

o Standard per il web

o Contenuti sul web

o Motori di ricerca

o Evoluzione del web

**Teaching methods**

The Course provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.

The Course is provided as a blended-learning course.

For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.

Examination modality and evaluation criteria

The examination is articulated in two distinct evaluation steps.

The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).

The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.

The Course is provided as a blended-learning course.

For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.

Examination modality and evaluation criteria

The examination is articulated in two distinct evaluation steps.

The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).

The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.

**Teaching Resources**

Teaching stuff

The teaching stuff is online at https://3cfuinformatica.unimi.it

The teaching stuff is online at https://3cfuinformatica.unimi.it

Modulo: Laboratorio di informatica

INF/01 - INFORMATICS - University credits: 3

Basic computer skills: 18 hours

Modulo: Matematica generale

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Practicals: 48 hours

Lessons: 24 hours

Lessons: 24 hours

Professors:
Carone Fabiani Filippo, Penati Tiziano

### M - Z

Responsible

Lesson period

First semester

Videos with lessons and exercises collections will be made available at the official web space of this course and they will cover the topic of each week. Live meetings during the classes hours may be scheduled by using Zoom.us. The details of these meetings will be available in the course web page of the Ariel platform, as well as the videos and every kind of material needed for the course.

The exams will be done by following the ways suggested on the web page of the university. The written exam will have the same structure as the one done in presence, possibly reduced in time and number of exercises.

The exams will be done by following the ways suggested on the web page of the university. The written exam will have the same structure as the one done in presence, possibly reduced in time and number of exercises.

**Prerequisites for admission**

Elementary algebra, analytic geometry, plane trigonometry. Elementary functions and their graphs. Inequalities.

See also the MiniMat course material available online at http://ariel.unimi.it/User/

See also the MiniMat course material available online at http://ariel.unimi.it/User/

**Assessment methods and Criteria**

The exam consists of two parts, one for each of the two modulus of Matematica Generale (6 CFU) and of Laboratorio di Informatica (3 CFU).

To participate to the test of each modulus, the student must register through SIFA to the module itself.

The final grade is obtained after passing the tests related to the two modulus.

The two tests must be passed within the same academic year.

The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.

To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve the types of exercises illustrated during the exercises lectures.

The test of the modulus of Matematica Generale consists of exercises and some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.

There will be 7 tests distributed during the academic year, dates appearing on SIFA.

The written test can be replaced by passing two in itinere tests, the first indicatively in mid-November, the second in the same date of the January test.

The two in itinere tests are passed if in each one a score of at least 16 points is obtained out of a total of 30 and if the average of the two scores (approximated by excess to the unit) is greater or equal to 18.

Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph during which it is not allowed to consult any type of material, nor the use of calculators.

In case the student wants to improve the grade obtained in the written test or in the itinere tests or to obtain the Laude, the student must also pass an oral exam that will focus on the detailed program indicated on the website at the end of the semester (definitions, statements of theorems, proofs of theorems).

In the event of a negative evaluation of the oral exam, the mark obtained in the written test could be modified accordingly or even the written test will have to be repeated.

To participate to the test of each modulus, the student must register through SIFA to the module itself.

The final grade is obtained after passing the tests related to the two modulus.

The two tests must be passed within the same academic year.

The grade resulting from the weighted average of the grades reported in the two modulus (approximated to the unit by default / excess depending on the decimal number 0-4 / 5-9) will be registered by the professor of the modulus of Matematica Generale.

To pass the exam relating to the modulus of Matematica Generale it is necessary to know the theory (definitions, theorem statements) presented during the lectures and to be able to solve the types of exercises illustrated during the exercises lectures.

The test of the modulus of Matematica Generale consists of exercises and some multiple choice questions on the contents of the theory. The test is considered passed if at least 18 points are obtained out of a total of 30.

There will be 7 tests distributed during the academic year, dates appearing on SIFA.

The written test can be replaced by passing two in itinere tests, the first indicatively in mid-November, the second in the same date of the January test.

The two in itinere tests are passed if in each one a score of at least 16 points is obtained out of a total of 30 and if the average of the two scores (approximated by excess to the unit) is greater or equal to 18.

Candidates must attend the written tests or in itinere tests with a valid identity document with a photograph during which it is not allowed to consult any type of material, nor the use of calculators.

In case the student wants to improve the grade obtained in the written test or in the itinere tests or to obtain the Laude, the student must also pass an oral exam that will focus on the detailed program indicated on the website at the end of the semester (definitions, statements of theorems, proofs of theorems).

In the event of a negative evaluation of the oral exam, the mark obtained in the written test could be modified accordingly or even the written test will have to be repeated.

**Modulo: Matematica generale**

**Course syllabus**

·Natural, integer, rational, real numbers. The field of real numbers and its operations. The symbols + ∞ and -∞.

·Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.

·Elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.

·Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Eigenvalues and eigenvectors. Inverse matrix. Rank of a matrix. Systems of linear equations and matrix representation. Cramer theorem and Rouchè-Capelli theorem.

·Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.

·The number of Nepero e. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.

·Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Extreme points.

·Fermat's theorem. Rolle theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. De l'Hôpital theorem.

·Study of the graph of a function. Horizontal, vertical, oblique asymptotes.

·Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution. Integration of rational functions (outline).

·Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.

·Outline of linear differential equations of first and second order.

·Real functions of real variable. Properties: injectivity, surjectivity, biunivocity, monotony. Inverse functions. Composition of functions. Cartesian representation of the graph of a function.

·Elementary functions: powers, logarithms, exponentials, trigonometric functions, absolute value.

·Linear algebra: vectors, matrices and their operations. Determinant of a square matrix. Eigenvalues and eigenvectors. Inverse matrix. Rank of a matrix. Systems of linear equations and matrix representation. Cramer theorem and Rouchè-Capelli theorem.

·Limits of functions: definitions and first properties. Uniqueness of the limit. Limits of monotone functions. Limits of elementary functions. Operations with limits. Indeterminate forms. Asymptotic functions. Comparison theorems.

·The number of Nepero e. Special limits. Hierarchy of infinities and infinitesimals. Continuous functions and their properties: zeros theorem and Weierstrass theorem.

·Differential calculus: definition of derivative; geometrical meaning; tangent line. Derivability and continuity. Operations with derivatives. Derivatives of composition of functions and inverse functions. Derivatives of elementary functions. Applications of derivatives. Extreme points.

·Fermat's theorem. Rolle theorem and Lagrange theorem. Increasing and decreasing functions. Convexity. De l'Hôpital theorem.

·Study of the graph of a function. Horizontal, vertical, oblique asymptotes.

·Indefinite integral. Calculus of primitives: integration by sum decomposition, integration by parts, integration by substitution. Integration of rational functions (outline).

·Definite integral. Definition, geometric interpretation, properties. The integral mean value theorem. The fundamental theorem of integral calculus. The formula of integral calculus theorem. Area of plane regions.

·Outline of linear differential equations of first and second order.

**Teaching methods**

Teaching Methods: Traditional.

Tutoring activity for the preparation of the written tests.

Frequency: Strongly recommended.

Tutoring activity for the preparation of the written tests.

Frequency: Strongly recommended.

**Teaching Resources**

·P. Marcellini, C. Sbordone, Calcolo - edizione aggiornata per i nuovi corsi di laurea, Liguori editore

·D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana

OR

D. Benedetto, M. Degli Esposti, C. Maffei: Dalle funzioni ai modelli, Casa Editrice Ambrosiana

·Corso online "Matematica Assistita", http://ariel.unimi.it/User/

·D. Benedetto, M. Degli Esposti, C. Maffei: Matematica per le scienze della vita, Casa Editrice Ambrosiana

OR

D. Benedetto, M. Degli Esposti, C. Maffei: Dalle funzioni ai modelli, Casa Editrice Ambrosiana

·Corso online "Matematica Assistita", http://ariel.unimi.it/User/

**Modulo: Laboratorio di informatica**

**Course syllabus**

The Course program is focused on the following topics:

· Foundations of Computer Science

o Introduction to Computer Science

o Information coding

o Computer structure

o Programs and software

o The "Infosphera" risks

· Spreadsheets

o Introduction to spreadsheets

o General functions in Excel

o Statistical functions in Excel

o Chart creation in Excel

· Information management

o Introduction to information management

o Data storing and databases

o Relational databases

o Database creation

o Query composition

o Web databases

· Internet and web

o Computer networks

o The Internet network

o Web architecture

o Web standards

o Web contents

o Search engines

o Web evolutions

· Foundations of Computer Science

o Introduction to Computer Science

o Information coding

o Computer structure

o Programs and software

o The "Infosphera" risks

· Spreadsheets

o Introduction to spreadsheets

o General functions in Excel

o Statistical functions in Excel

o Chart creation in Excel

· Information management

o Introduction to information management

o Data storing and databases

o Relational databases

o Database creation

o Query composition

o Web databases

· Internet and web

o Computer networks

o The Internet network

o Web architecture

o Web standards

o Web contents

o Search engines

o Web evolutions

**Teaching methods**

The Course provides the basic notions of the computer-science discipline with focus on i) foundations of Computer Science, ii) spreadsheets, iii) information management, and iv) Internet and web. Furthermore, the Course provides skills about the main functionalities of spreadsheet software tools, with focus on the use of formulae, functions, and chart creation.

The Course is provided as a blended-learning course.

For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.

Examination modality and evaluation criteria

The examination is articulated in two distinct evaluation steps.

The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).

The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.

The Course is provided as a blended-learning course.

For acquisition of expected knowledge, a student has to browse the program contents on the online course according to an e-learning modality. Contents are organized into the following training courses: G) Foundations of Computer Science, F) Spreadsheets, B) Information management, and I) Internet and web. A training course is then articulated into thematic modules. Students have to pass a self-evaluation test at the end of each thematic module. Initially, a student can access just an introductory module. The access to subsequent modules is progressively enabled when the test of available modules is successfully passed. For acquisition of expected skills, a student can attend two exercise sessions in a computer-science room. Each exercise session is three hours long. The attendance to exercise sessions is not a mandatory requirement for successfully pass the Course and obtain the credits, however students are strongly encouraged to attend the exercise sessions.

Examination modality and evaluation criteria

The examination is articulated in two distinct evaluation steps.

The first evaluation step consists in the successful completion of self-evaluation tests related to all the thematic modules that constitute the training courses. The tests are composed of choice questions on the whole Course program. The completion of all the expected self-evaluation tests is a mandatory requirement for accessing to the subsequent evaluation step (final exam).

The second evaluation step (final exam) consists successfully pass a test in a computer-science room. The test one hour long and it is based on choice questions on the whole Course program. The questions aim to evaluate the expected acquisition of both knowledge and skills. During the test, it is not possible to use paper stuff and to access web resources that are not explicitly authorized. The final exam result is expressed in thirtieths. The Academic Exam System (SIFA) is exploited by students for subscription to the final exam.

**Teaching Resources**

The teaching stuff is online at https://3cfuinformatica.unimi.it

Modulo: Laboratorio di informatica

INF/01 - INFORMATICS - University credits: 3

Basic computer skills: 18 hours

Modulo: Matematica generale

MAT/01 - MATHEMATICAL LOGIC - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

MAT/02 - ALGEBRA - University credits: 0

MAT/03 - GEOMETRY - University credits: 0

MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0

MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0

MAT/06 - PROBABILITY AND STATISTICS - University credits: 0

MAT/07 - MATHEMATICAL PHYSICS - University credits: 0

MAT/08 - NUMERICAL ANALYSIS - University credits: 0

MAT/09 - OPERATIONS RESEARCH - University credits: 0

Practicals: 48 hours

Lessons: 24 hours

Lessons: 24 hours

Professors:
Ballerio Augusto Carlo, Panozzo Simone

Educational website(s)

Professor(s)

Reception:

to be fixed by email

office num. 1039, first floor, Dep. Mathematics, via Saldini 50