Course catalogue | University of Parma

Learning objectives

The course provides the basic notion of calculus

Prerequisites

Prerequisites are basic facts on theory of sets, functions, trigonometry, analytic geometry.

Course unit content

Elementary algebraic properties of the real numbers (standard types of 
equations and inequations); maximum and supremum of a set or a function; 
algebraic properties and n-th roots of the complex numbers. 
Graphs of the elementary fonctions and geometric transformations of the 
same; properties of continuous functions (including mean value, existence of 
a maximum, lipschitz continuity); limits of functions and of sequences of 
real numbers; infinitesimals. 
Properties of differentiable functions (including Rolle, Lagrange, Hopital 
theorems); Taylor expansion (with Peano and Lagrange remainder); graphing a 
function. 
Indefinite and definite integral: definition and computation 
(straightforward, by parts, by change of variables); integral mean and 
fundamental theorems; Torricelli theorem; generalised integrals: definition 
and comparison principles. 
Numerical series: definition, convergence criteria, Leibniz and integral 
criteria.

Full programme

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Bibliography

E. Acerbi - G. Buttazzo: Analisi Matematica ABC vol.1, Pitagora, Bologna, 2003; 
D. Mucci: Analisi Matematica - Esercizi 1, Pitagora, Bologna, 2004.

Teaching methods

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Assessment methods and criteria

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MATHEMATICAL ANALYSIS AB
cod. 13100

Learning objectives

Prerequisites

Course unit content

Full programme

Bibliography

Teaching methods

Assessment methods and criteria

Other information

MATHEMATICAL ANALYSIS AB cod. 13100

Learning objectives

Prerequisites

Course unit content

Full programme

Bibliography

Teaching methods

Assessment methods and criteria

Other information

MATHEMATICAL ANALYSIS AB
cod. 13100