Mathematical Analysis 1

Credits

Prerequisites

None

Scientific-disciplinary sector (SSD)

MAT/05 Mathematical Analysis

Examination method

Written exam (exercises and numerical problems, possibly multiple-choice) and oral exam

Learning
objectives

The course aims to provide an introduction to and a formalisation of the fundamental concepts of Mathematical Analysis and of differential and integral calculus.

Syllabus

Real numbers, elements of topology of the real line. Elementary functions. Sequences and limits of sequences. Real functions of one real variable. Limits and continuity. Differentiability and differential calculus. Concavity and convexity. Taylor’s formula and applications. Numerical series. The field of complex numbers. The concept of area, outline of the Peano-Jordan measure. The Riemann integral for functions of one real variable. Indefinite integration. Rules of integration. Integration by parts and by substitution. Improper integrals and summability.

Expected learning
outcomes

At the end of the course, students must demonstrate that they:

know and understand the language and basic concepts of mathematical analysis, with particular reference to the differential and integral calculus of functions of one variable;
are able to apply the knowledge acquired to the study of functions of one variable;
are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, clarity of presentation, rigour in the use of language, confidence in using the notions acquired.

Mathematical Analysis 1