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Taylor’s formula of the second order for functions of several variables. Single cycle degree courses.

Lessons are completed with examples and counterexamples illuminating the theoretical content. The commission may require an oral examination in case the written one has not been sufficient for a clear grading. The integral of a vector field over an oriented curve. Planned learning activities and teaching methods: In the period jenuary-february the oral part may be passed in a subsequent session.

The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit. The language of mathematics, basics of logics and set theory. Give now Alma orienta Job placement. Assessment methods The assessment consists in a written and an oral exam. Double integrals on rectangular and normal domains computed by iterated integrals.

The mate,atica part of the exam dwells upon the comprehension of the relevant concepts and on the knowledge of definitions and the statements of fundamental theorems. Theorems on existence, uniqueness and continuation of solutions. Information on the course unit. Convergence criteria matematlca numerical series. An exercise book on functions of several real variables, such as, for example: The oral part of the exam must be passed in the same session of the written part.

The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for the evaluation. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables.

The Weierstrass theorem and the intermediate value theorem for functions of several variables. Teaching tools Tutorship if appointed.

## Analisi matematica

Interior and constrained local extrema for real functions of several variables. Generalizations to triple integrals.

Marco Bramanti, Esercitazioni di Analisi Matematica 1. The evaluation of limits of one variable functions using both notable basic limits and Taylor’s formula.

### Analisi matematica – Michiel Bertsch, Roberta Dal Passo, Lorenzo Giacomelli – Google Books

Textbooks and optional supplementary readings. Marco Bramanti, Carlo D. In the written part, lasting three hours, the solution of various exercises is required. Properties of the double integral. Department of Statistical Sciences. In the period june-july the oral part may be passed in a subsequent session.

The flux of a vector field through an oriented surface. Outline of double improper integrals.

## 27993 – ANALISI MATEMATICA T-2

Planned learning activities and teaching methods:. The course will provide tools, like integral calculus, number series and functions of two variables, that are used for courses on Probability and Statistics. My e-mail for students My e-mail for staff Close.

Smooth and piecewise smooth curves, length of a curve, integral of a function over a curve. Pagani e Sandro Salsa, Analisi Matematica 1. The teacher will use, as bfrtsch 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.

On-line material on IOL: The definition and the properties of the derivative of one variable functions.