Programme

Real numbers and functions, finite and infinite sets, the principle of induction, upper and lower bounds.
Definition of limit, limit operations, comparison theorems, notable limits, connection with the limits of sequences, continuity, theorems on continuous functions.
Derivatives, geometric meaning, theorems on differentiable functions, relative maxima and minima, concavity, applications to the study of functions.
Indefinite integrals, integration by parts and by substitution, definite integrals.
Differential equations, first-order linear equations, linear equations with constant coefficients, equations with separable variables.

Core Documentation

Luigi Chierchia: Corso di analisi. Prima parte. Una introduzione rigorosa all'analisi matematica su R
McGraw-Hill Education Collana: Collana di istruzione scientifica
Data di Pubblicazione: giugno 2019
EAN: 9788838695438 ISBN: 8838695431
Pagine: XI-374 Formato: brossura
https://www.mheducation.it/9788838695438-italy-corso-di-analisi-prima-parte

Testi di esercizi:
Giusti, E.: Esercizi e complementi di Analisi Matematica, Volume Primo, Bollati Boringhieri, 2000
Demidovich, B.P., Esercizi e problemi di Analisi Matematica, Editori Riuniti, 2010

Type of delivery of the course

Lectures and exercises in class. All the material of the program will be explained in class. The lessons / exercises will include a continuous dialogue with the students: the feedback from the students during the course is a fundamental tool for the success of the course itself. In the event of an extension of the health emergency from COVID-19, all the provisions (of the State and of the Roma Tre University) governing the methods of carrying out educational activities will be implemented. In particular, distance learning may be necessary.

Attendance

Attendance is optional and the understanding of the text adopted is sufficient for the full use of the course. Of course, attendance is desirable and STRONGLY recommended, as the interaction between teacher and students is a fundamental and unrepeatable teaching tool.

Type of evaluation

The evaluation is based on a written test and an oral exam. There are two written tests "in progress" which, in the event of a positive outcome, replace the final written test. Examples of tests of past years will be available on the web site dedicated to the course which will be constantly updated by the teacher.

Programme

Real numbers and real-valued functions; finite and infinite sets; the principle of mathematical induction; supremum and infimum.

Definition of a limit; operations with limits; comparison theorems; notable limits; the relationship with limits of sequences; continuity; theorems on continuous functions.

Derivatives; geometric interpretation; theorems on differentiable functions; relative maxima and minima; concavity; applications to function analysis.

Indefinite integrals; integration by parts and by substitution; definite integrals.

Differential equations; first-order linear equations; linear equations with constant coefficients; separable equations.

Core Documentation

W. Rudin, Principles of Mathematical Analysis, 3rd Edition, McGraw Hill

Attendance

Attendance recommended

Type of evaluation

Midterm tests, written exams, and oral examination.