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.

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Knowledge: The course aims to introduce students to some theoretical, methodological and applicative elements of differential and integral calculus for real functions of one real variable and the basic elements of descriptive statistics frequency distribution, indicators of centrality, dispersion, covariance, linear regression. It aims to provide students with the elements necessary for the understanding of analytical models in use for describing the scientific phenomena and the correct interpretation of the experimental data.

Ability to apply the knowledge: The course aims to develop the ability to perform studies of functions, derivation, integration and solve simple differential equations.

It also develops the ability to perform graphical representations of data and relative statistical analysis. Soft Skills: Classroom and individual resolution of many problems and exercises will improve learning ability and independence of judgment. The study of deductive logical topics and the correct use of logical mathematical language develops communication skills.

Sets, Relations and Functions. Composition, invertibility. Natural, Integer, Rational and Real numbers. The Induction principle. Supremum, infimum, maximum, minimum. Modulus and powers. Exponential, logaritmic and angular functions. Limit of real sequences and its properties. Indeterminate forms.

Monotone sequences. The Neper's number and related limits. Asymptotic comparison. Limits of real function of real variable. Monotone functions. Derivative and Derivative Formulas. Successive Derivative. Derivative and monotonicity. The De L'Hospital's Theorems.

Asymptotes and the study of the graphs of functions. Definite Integral and its properties. Fundamental Theorem and Formula of the Integral Calculus. Indefinite Integral and integration methods: sum decomposition, by parts and substitution. General Integral for first order linear ordinary differential equations.

The Cauchy Problem. The Bernoulli's equations. The Malthus and Verhulst models for the population dynamics. Statistics: populations, characters and related typologies; Absolute and relative frequence.

Modal class, median, mean, quartiles and percentiles, variance, standard deviation. Frequency distribution and its graphical representations.

Multivariate distributions, covariance, correlation coefficient; linear regression and least squares method. Use of a spreadsheet with application to the descriptive analysis of a statistical population of data. Methods for assessing learning outcomes: The exam consists of a written and an oral test, the tests will concern the topics covered during the course offered in the same academic year. The list of the names of the students admitted to the oral test will be published by the teacher on his web page.

The oral test will contain mainly theoretical questions, some of which may be formulated in written form and contain exercises concerning course topics not covered in the written test or course topics in which the student may have shown weaknesses in the written test.

In case of a successful written test, the student may sit for the oral test either in the same session or the next available session, not later. All written tests have to be correctly and fluently written, well organized, easily readable and with a negligible presence of corrections which must anyway not mar the esthetics of the text. Particular attention will be given to evaluate the student's ability to justify rigorously his assertions and in the proper use of logical mathematical language.

In the statistic test the student must show knowledge of the statistical indicators used in his work and ability to interpret the results.

Criteria for measuring learning outcomes: The final grade is attributed out of thirty. The exam is passed when the rating is greater than or equal to It is possible the award of full marks with honors 30 e lode.

Criteria for conferring final mark: The final score will be given by the teacher on the basis of the score of the written test and of the level of knowledge and comprehension of the topics covered during the course. Marcellini - C. Sbordone, Elementi di Calcolo, Liguori editore. Sbordone, Esercitazioni di matematica vol. Con elementi di statistica, Mc Graw-Hill Editore.

Teacher's lecture notes. Economia "G. Medicina e Chirurgia.

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## Paolo Marcellini Carlo Sbordone

Servizi per la didattica. Teaching Hours Lezioni 50 Esercitazioni in aula Teacher Status SSD h. Les h. Lab h.

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## ANALYSIS 2 (250SM)

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. Finally, we show how to determine the general solution of a system of linear differential equations of order 2.

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## Sbordone - Esercitazioni Di Matematica Volume 2 Parte Second

Scuola Politecnica e delle Scienze di Base. DiArc Dipartimento di Architettura. Rss DiARC. Sinapsi Unina. Alma Laurea. Nome utente. Mathematical analysis and Geometry students M-Z annual course Prof.

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## Paolo Marcellini, Carlo Sbordone - Esercitazioni Di Matematica Volume 2 Parte Prima

Understanding of the proofs and ability to apply the theoretic knowledge in the solution of problems. Knowledge of basic arguments in mathematics; in particular: - geometry in the Cartesian plane - algebraic equations and inequalities I and II degree - systems of algebraic inequalities I degree - expressions containing the absolute value function - inequalities with fractional expressions - irrational, exponential and logarithmic equations and inequalities - trigonometry on the plane, trigonometric equations and inequalities. This site uses only proprietary and third party technical cookies. By continuing to browse the site you are agreeing to our use of cookies. I agree I want to find out more. Italian version.