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The teacher will use, as far as possible, various technological tools to improve the learning and to let the students to have as much as possible education material to their disposal.

The oral part of the exam dwells upon the comprehension of the relevant concepts and on the knowledge of definitions and the statements of fundamental theorems.

The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit.

The evaluation of limits of one variable functions using both matekatica basic limits and Taylor’s formula. The commission may require an oral examination in case the written one has not been sufficient for a clear grading. The assessment consists in a written and an oral exam. Generalizations to triple integrals. Search Course unit catalogue.

Planned learning activities and teaching methods: The language of mathematics, basics of logics and set theory. The last one is of fundamental importance to develop the logic and practical abilities related with the topics covered in the course. My e-mail for students My e-mail for staff Close. Generalities on real and vector functions of several real variables.

An exercise book on functions of several real variables, such as, for example: The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function. Assessment methods The assessment consists in a written and an oral exam. Marco Bramanti, Carlo D.

The course consists of matematca describing the fundamental concepts of real and vector functions of several real variables. Interior and constrained local extrema for real functions of several variables.

### Elementi di analisi matematica – Michiel Bertsch, Roberta Dal Passo – Google Books

The oral part of the exam must be passed in the same session of the written part. Definition of Riemann double integral for functions defined on a bounded and measurable set. The detailed contents with the list of theorems and proofs, up to dated for each weak, can be found in the web course page. Textbooks and optional supplementary readings.

The divergence theorem and the Stokes theorem.

Conservative vector fields and their potentials. The students are required to attend the lectures and to devote a right amount of time analsii autonomous study. To this aim tutorial activities will be organized and supervised by the teacher. Partial and directional derivatives.

## MICHIEL BERTSCH

Definition of a convergent series. Absolute convergence of a series. Outline of double improper integrals.

The course will provide tools, like integral calculus, number series and functions of two variables, that are used for courses on Probability and Statistics.

The Cauchy problem for differential equations and systems. See the website of Annalisa Baldi. Marco Bramanti, Esercitazioni di Analisi Matematica matemativa. Taylor’s formula of the second order for functions of several variables. Elementi di Analisi Matematica, vol. Information on the course unit.