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Università degli Studi di Parma Università degli Studi di Parma
Degree course in
Computer science
Università degli Studi di Parma
Department of Mathematical, Physical and Computer Sciences

MATHEMATICAL ANALYSIS
cod. 00013

Academic year 2013/14
1° year of course - First semester
Professor
Alessandro ZACCAGNINI
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione matematico-fisica
Type of training activity
Basic
72 hours
of face-to-face activities
9 credits
hub: PARMA
course unit
in - - -
lectures timetable unavailable
exam calls
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Learning objectives

Basic notions of calculus (limits, derivatives, integrals). The student should be able to plot the graph of a function, and to handle standard integration methods

Prerequisites

None

Course unit content

Limits for sequences. Differential and integral calculus for real functions of one real variable

Full programme

Sets and numbers. Basic set theory, operations between sets. Number systems: N, Z, Q, R, C. Representation of real numbers on a line; maximum, minimum, supremum, infimum of a set of real numbers; integer part and absolute value of real numbers; powers and roots. Complex numbers in various forms.

Functions: injective, surjective and bijective functions. Composition of functions; inverse function. Graphs. Real functions of one real variable. Monotonic functions. Powers with real exponent. Exponential and logarithmic functions. Angles; trigonometrical functions. Cardinality.

Sequences and series. Limits of sequences. Numeric series and convergence.

Limits and continuity. Limits of real functions of one real variable; properties. Continuity of real functions of one real variable; properties of continuous functions.

Differential calculus. Derivative and its geometric interpretation. Derivation rules (sum, product, ratio, inverse); chain rule; derivatives of the elementary functions. Relative and absolute maxima and minima; stationary points; monotony and the sign of the derivative. Main theorems (Fermat, Rolle, Lagrange aka mean-value, De l'Hopital); higher order derivatives; Taylor series development. Graphs.

Integral calculus. Primitive of a function defined in an interval; indefinite integrals. Geometric interpretation. Main properties. Fundamental theorem of the integral calculus. Integration techniques: by parts, by substitution; integration of rational functions.

Bibliography

M. Bertsch, R. Dal Passo, L. Giacomelli, Analisi Matematica, Mc Graw-Hill

Teaching methods

Traditional lecture. Detailed exercises

Assessment methods and criteria

Written and oral tests, that will confirm that the studenit is really able to deal with the basic notions of calculus (limits, derivatives and integrals of real functions of one real variable)

Other information

- - -

2030 agenda goals for sustainable development

- - -

Contacts

Toll-free number

800 904 084

Student registry office

E. segreteria.scienze@unipr.it
T. 0521 90 5116

Quality assurance office

Education manager
dr. Claudia Buga
T. 0521 90 2842
Office e-mail: smfi.didattica@unipr.it
Manager e-mail: claudia.buga@unipr.it

President of the degree course

Prof. Alessandro Dal Palù
E. alessandro.dalpalu@unipr.it

Faculty advisor

Prof. Vincenzo Arceri
E. vincenzo.arceri@unipr.it

Career guidance delegate

Prof. Roberto Alfieri
E. roberto.alfieri@unipr.it

Tutor Proffesors

Prof. Enea Zaffanella
E. enea.zaffanella@unipr.it

Erasmus Delegates

Prof. Roberto Bagnara
E. roberto.bagnara@unipr.it
Student tutor dr. Anna Macaluso
E. anna.macaluso@studenti.unipr.it

Quality assurance manager

Prof. Roberto Alfieri
E. roberto.alfieri@unipr.it

Internships

Prof. Roberto Alfieri
E. roberto.alfieri@unipr.it

Tutor students

Tutor a.a. 2021-2022 dr. Francesco Manfredi
E. francescosaverio.manfredi@studenti.unipr.it

Student representatives: 
Greta Dolcetti 
Massimo Frati
Davide Tarpini