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Sufficient conditions of integrability. Derivative and Derivative Formulas. Funzioni pari, dispari, periodiche, monotone. Maximum and minimum of a set. Methods for assessing learning outcomes: Teoremi di Rolle e di Lagrange.

Elements of mathematical language. The final grade is attributed out of thirty. Assessment criteria of skills.

Grafici e loro interpretazione. Limit of real sequences and its properties. Powers with rational exponent. Derivata di una funzione.

### Esercitazioni di matematica (2/2) – Paolo Marcellini, Carlo Sbordone – Google Books

Definition of the Riemann integral. The Neper’s number and related limits. The fundamental theorems of the integral calculus. The course consists of lessons describing the fundamental concepts of differential and integral calculus real for real functions of one real variable. In this part, the student must show to know the concepts explained during the course in particular definitions and theorems and to be able to connect them.

The De L’Hospital’s Theorems. Limits of real function of real variable. Classroom and individual resolution of many problems and exercises will improve learning ability and independence of judgment.

Conoscenze di elementi di base della matematica come, per esempio, la risoluzione di equazioni e disequazioni e le nozioni principali della geometria analitica.

In order to sustain it the student must register at the test on AlmaEsami [https: Esercizi di Matejatica Matematica 1, Ed. Ability to apply the knowledge: Definition of limit of a function. Elementi di linguaggio matematico. 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.

Theorems of Rolle and Lagrange. Injective, surjective, invertible functions. Potenze con esponente razionale. The algebra of limits. The study of deductive logical topics and the correct use of logical mathematical language develops communication skills.

Written test and subsequent oral exam. Modal class, median, mean, quartiles and percentiles, variance, standard deviation.

Derivative of the sum, of the product, of the sbordoje, of the composition of functions. Calcolo della derivata di funzioni elementari. Generalization to matematicca coefficients and arbitrary order equations. Other suggestions for exercises books: Formula di integrazione per parti e per sostituzione.

## 27991 – Mathematical Analysis T-1 (L-Z)

Definite Integral and its properties. Le esercitazioni hanno anche l’obiettivo di coinvolgere gli studenti alla eseercitazioni dei problemi proposti. Limit of a succession of real numbers. Insiemi limitati inferiormente, limitati superiormente, limitati. The theorems of integration by substitution and of integration by parts.

Exercitazioni of basic elements of mathematics such as, for example, the resolution of equations and inequalities and the main notions of analytic geometry.

Properties of the integral. The student will have the basic elements for studying the functions and for computing the values of some integrals.

The examination consists of a preliminary written test that lasts 3 hours and a test about the theoretical part. The integral average theorem.