## 20810232 - ANALISI MATEMATICA I

Allow the acquisition of the method deductive logic and provide the basic mathematical tools of the calculation of differential and integral. Each topic will be introduced and strictly the treaty, carrying, sometimes, detailed demonstrations, and also doing large reference to physical meaning, geometric interpretation and application number. Proper methodology and a reasonable skill in the use of the concepts of calculation and its entirety and differential results will put in grade students in principle to face so easy application more topics that will take place in the following courses.

Curriculum

Canali

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria.
Complex numbers.
Solution of linear differential equations and separable differential equations.

Core Documentation

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill

Reference Bibliography

Marcellini, Sbordone - Analisi matematica uno Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2. Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill S. Lang, A First Course in Calculus, Springer Ed. L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Type of delivery of the course

Lectures on theory and exercises will be held.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Core Documentation

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill
Marcellini, Sbordone - Analisi matematica uno
Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.

Reference Bibliography

Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill S. Lang, A First Course in Calculus, Springer Ed. L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Type of delivery of the course

Lectures on theory and exercises will be held.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum. Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order. Limits of function, continuity, link with the limits of sequences, theorems on continuous functions. Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Core Documentation

Theory:
Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
S. Lang, A First Course in Calculus, Springer Ed.
L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Exercises:
Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
Marcellini, Sbordone - Analisi matematica uno Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.

Canali

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria.
Complex numbers.
Solution of linear differential equations and separable differential equations.

Core Documentation

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill

Reference Bibliography

Marcellini, Sbordone - Analisi matematica uno Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2. Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill S. Lang, A First Course in Calculus, Springer Ed. L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Type of delivery of the course

Lectures on theory and exercises will be held.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum.
Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order.
Limits of function, continuity, link with the limits of sequences, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Core Documentation

Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill
Marcellini, Sbordone - Analisi matematica uno
Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.

Reference Bibliography

Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica . McGraw Hill S. Lang, A First Course in Calculus, Springer Ed. L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Type of delivery of the course

Lectures on theory and exercises will be held.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.

teacher profile | teaching materials

Programme

Real numbers and functions, set theory, induction principle, infimum and supremum. Sequences, definition of limit, operations with limits, comparison theorems, infinitives of increasing order. Limits of function, continuity, link with the limits of sequences, theorems on continuous functions. Derivatives, geometric meaning, theorems on differentiable functions, relative maximums and minimums, applications to the study of functions. Indefinite integrals, integration by parts and by substitution, definite integrals, fundamental theorem of integral calculus, improper integrals. Numerical series, simple and absolute convergence, convergence criteria. Complex numbers.

Core Documentation

Theory:
Marcellini, Sbordone - Elementi di Analisi matematica 1. Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
S. Lang, A First Course in Calculus, Springer Ed.
L.Chierchia, Corso di Analisi - Prima parte, McGraw Hill (2019)

Exercises:
Bertsch, Dall'Aglio, Giacomelli - Epsilon 1, Primo corso di Analisi Matematica. McGraw Hill
Marcellini, Sbordone - Analisi matematica uno Marcellini, Sbordone - Esercitazioni di matematica Volume 1 Parte 1, 2.

Attendance

Attendance is not compulsory but is nevertheless strongly recommended.

Type of evaluation

Written test: 2 ongoing tests Written test for each session aimed at evaluating the student's ability to carry out exercises, including theoretical ones. Oral exam at the discretion of the teacher.