Vai al contenuto principale Vai al footer
Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Mathematics
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

CALCULUS 1 (UNIT 2)
cod. 1004541

Academic year 2011/12
1° year of course - Second semester
Professor
Stefano PANIZZI
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione matematica di base
Type of training activity
Basic
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -
lectures timetable unavailable
exam calls

Integrated course unit module: CALCULUS 1

Print

Learning objectives

Provide the basic tools of Mathematical Analysis

Prerequisites

No

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

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Student registry office

E. segreteria.scienze@unipr.it
T. +39 0521 905116

Quality assurance office

Education manager
dott.ssa Giulia Bonamartini
T. +39 0521 906968
E. servizio smfi.didattica@unipr.it
E. del manager giulia.bonamartini@unipr.it

President of the degree course

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Faculty advisor

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Career guidance delegate

Prof. Francesco Morandin
E. francesco.morandin@unipr.it

Tutor Professors

Prof. Emilio Acerbi
E. emilio.acerbi@unipr.it

Prof. Marino Belloni
E. marino.belloni@unipr.it

Prof.ssa Maria Groppi
E. maria.groppi@unipr.it

Prof.ssa Chiara Guardasoni
E. chiara.guardasoni@unipr.it

Prof. Luca Lorenzi
E. luca.lorenzi@unipr.it

Prof. Costantino Medori
E. costantino.medori@unipr.it

Prof. Adriano Tomassini
E. adriano.tomassini@unipr.it

Erasmus delegates

Prof.ssa Fiorenza Morini
E. fiorenza.morini@unipr.it

Quality assurance manager

Prof.ssa Maria Groppi
E. maria.groppi@unipr.it

Tutor students

Dott. Matteo Mezzadri
E. matteo.mezzadri@studenti.unipr.it