Servizi per la didattica. Teaching Hours Lezioni 50 Esercitazioni in aula Teacher Status SSD h. Les h. Lab h. Date d'appello.
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To get theoretical knowledge and ability to solve problems in the field of metric spaces, numerical series, series of functions, differential calculus in several variables. Ability to present coherently the arguments of the course and to use properly the mathematical language and formalism. Differential and integral calculus in one variable.
It is necessary to have passed the exam of Analisi 1 before presenting to the oral test of Analisi 2. Metric spaces, normed spaces, inner product spaces. Euclidean spaces.
Limits and continuity for functions of several real variables. Uniformly continuous functions and contraction principle. Lower limit and upper limit for sequences. Series of real numbers. Sequences and series of functions, power series.
Differential calculus in several variables. Frontal lessons at the blackboard expaining the theory and presenting a consistent number of exercises. Student are strongly recommended to actively take part to the lessons, especially in solving exercises. Metric, normed and inner product spaces. Sequentially compact subsets and characterization in metric spaces and in Eucldean spaces. Topological properties and continuity of functions in metric spaces.
Uniformly continuous functions: definition and properties. Heine- Cantor theorem. Contraction principle. Connected sets, arcwise connected sets. Connectedness and continuity. Lower limit and upper limit for sequences: definitions and characterizations.
Series of real numbers: basic definitions. Convergence tests: comparison test, ratio test, root test, Cauchy's condensation test, integral test, alternating series test. The Riemann series theorem. Sequences and series of functions: pointwise, uniform and total convergence. Theorems concerning continuity, derivation and integration for sequences and series of functions. Power series. Partial derivatives and differentiability.
C1 functions. Taylor formula. Determination of the extreme values of functions of several variables. Differentiability of composite functions and applications. Implicit function theorem. Lagrange multipliers. The exam program coincides with the arguments of the lectures.
The written test consists in solving exercises usually modeled on those solved or assigned during the lectures. Calculators may be used, notes and books may not be used. Any written test substitutes a possible preceding one. Oral test consists in verifying the comprehension of the contents definitions and proofs and the ability in explaining the subject. The final score depends on both written and oral tests. Giusti, Analisi matematica 1, Bollati Boringhieri, Torino.
Giusti, Analisi matematica 2, Bollati Boringhieri, Torino. Pagani, S. Marcellini, C. Sbordone, Esercitazioni di matematica volume primo, parte seconda, volume secondo, parte prima e volume secondo, parte seconda, Liguori, Napoli. Back to list of courses. Piazzale Europa, 1 - - Trieste, Italia - Tel. IVA - C. Biblioteche Servizi online Webmail. Corsi di Studio Units. Toggle navigation. Academic Year Department student office. Student administration office. Online Guide. Course statistics - enrollment and graduations data.
Rosset Edi. Type of Learning Activity. Study Path. Teaching Material. Teaching language. Learning objectives. Teaching format. Extended Programme. End-of-course test. Other information.
Sbordone - Esercitazioni Di Matematica Volume 2 Parte Second
Published by Liguori editore,, Napoli Seller Rating:. About this Item: Liguori editore,, Napoli, Brossura editoriale, ottimo stato. Euro
Paolo Marcellini Carlo Sbordone
The main goal is to complete the introduction of the basic topics of mathematical analysis for functions of several variables. In particular, the theory of multiple integration and of curve and surface integration is developed. The problem of constrained maxima and minima is sketched. Furthermore, numerical series and series of functions power series and Fourier series in particular are studied.
ANALYSIS 2 (250SM)
Scuola Politecnica e delle Scienze di Base. DiArc Dipartimento di Architettura. Rss DiARC. Sinapsi Unina. Alma Laurea.
Paolo Marcellini, Carlo Sbordone - Esercitazioni Di Matematica Volume 2 Parte Prima
To get theoretical knowledge and ability to solve problems in the field of metric spaces, numerical series, series of functions, differential calculus in several variables. Ability to present coherently the arguments of the course and to use properly the mathematical language and formalism. Differential and integral calculus in one variable. It is necessary to have passed the exam of Analisi 1 before presenting to the oral test of Analisi 2. Metric spaces, normed spaces, inner product spaces.