CALCULUS 2 PART. 1
cod. 1003931

Academic year 2016/17
2° year of course - First semester
Professor
Emilio Daniele Giovanni ACERBI
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione teorica
Type of training activity
Characterising
56 hours
of face-to-face activities
6 credits
hub: PARMA
course unit
in - - -

Integrated course unit module: CALCULUS 2

Learning objectives

To learn about the subjects of the course, and to be able to solve problems.

Prerequisites

Good knowledge of the theory of functions of one real variable and of the geometry of Euclidean spaces.

Course unit content

Normed and metric spaces. Norms, distances, equivalent norms and equivalent distances.

Limits and continuity of functions of several real variables.

Differential calculus for functions of several real variables: directional derivatives and their geometric meaning, partial derivatives, gradients, differentiation rules, tangent hyperplanes and their geometric meanings, Schwarz Theorem, Taylor formula, quadratic forms, local maxima and minima.

Regular curves, simple curves, equivalences among curves, paths, unit tangent vector to regular paths, curve lenghts, integrals of continuous functions along paths.

Implicit Function Theorem, Inverse Function Theorem, Lagrange Theorem.

Linear differential forms, integrals along oriented paths, primitives, equivalent conditions for the existence of primitives, primitives on starshaped sets, simply connected sets.

Elementary notions about multiple integrals: definitions, reduction theorem, changes of variables, Gauss-Green formulae in dimension 2.

Full programme

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Bibliography

E. Acerbi, G. Buttazzo: Secondo corso di Analisi Matematica. Pitagora, Bologna, 2016;

G. Prodi: Lezioni di Analisi Matematica II. ETS Pisa (1974);

M. Bramanti, C.D. Pagani, S. Salsa: Analisi Matematica 2. Zanichelli (2009);

N. Fusco, P. Marcellini, C. Sbordone: Analisi matematica due. Liguori (1996).

Teaching methods

Lectures are held in the classroom, that concern both theoretical and applicative aspects. Moreover, exercises are solved by students with the guidance of the teacher, in such a way that it is possible to verify the degree of comprehension and knowledge of the students.

Assessment methods and criteria

The examinations consist of a written and an oral session. The students are allowed to the oral sessions only if they pass the written examination. In the written examination 3 or 4 questions are asked. The students should exhibit calculus skills and master of different subjects taught in the course. Marks are given to each question.
The oral examination consists of a discussion about the written examination and of questions to verify the level of comprehension of the theoretical parts of the course.

Other information

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2030 agenda goals for sustainable development

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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