Physics | University of Parma

Professor
Academic discipline: Analisi matematica (MAT/05)
Field: Discipline matematiche e informatiche
Type of training activity: Basic

48 hours
of face-to-face activities

6 credits

hub:

course unit
in

lectures timetable unavailable

exam calls

Integrated course unit module: CALCULUS 1

Learning objectives

Provide the basic tools of Mathematical Analysis

Prerequisites

Course unit content

Real analysis, functions of one variable, sequences, series

Full programme

Complex numbers. Definitions, operations, complex plain, polar form, root extraction.

Sequences. Mathematical induction; real and complex sequences;
limit of a sequence; subsequences; Cauchy sequences; monotonic sequences;
Neper's number; sequences defined by recurrence relation; upper and lower limits;
Bolzano-Weirstrass theorem, compactness in the real line. Uniform continuity.

Series. Convergence criteria: comparison tests, ratio test, root test; absolute convergence;
rearrangements; alternating series; examples: geometric series, harmonic series, power series.

Improper integrals; convergence of the integral, absolute convergence,
comparison tests. Integral test for positive valued series.

Bibliography

E. Acerbi, G. Buttazzo: Primo corso di Analisi Matematica, Ed. Pitagora, 1997.

E. Acerbi, G. Buttazzo: Analisi matematica ABC, Ed. Pitagora, 2000.

M. Bramanti, C.D. Pagani, S. Salsa: Analisi Matematica 1, Ed. Zanichelli, 2008.

M. Giaquinta, L. Modica, Analisi Matematica 1, vol. 1 & 2, Ed. Pitagora, 1998.

E. Giusti, Analisi matematica vol.1, Ed. Boringhieri, 2002

Teaching methods

classroom lectures and classroom exercises

Assessment methods and criteria

written and oral examination

Other information

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CALCULUS 1 (UNIT 2) cod. 1004541