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The divergence theorem and the Stokes theorem.

Partial derivatives of higher order. Definition of a continuous function and of limit of a function.

Course Timetable from May 06, to Jun 07, Course Timetable from Feb 21, to May 03, The commission may require an oral examination bertsfh case the written one has not been sufficient for a clear grading.

The flux of a vector field through an oriented surface. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables.

The Cauchy problem for differential equations and systems. 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.

Interior and constrained local extrema for real functions of several variables. Geometric, harmonic and generalized harmonic series. Double integrals on rectangular and normal domains computed by iterated integrals. To this aim tutorial activities will be organized and supervised by the teacher. Marco Ana,isi, Esercitazioni di Analisi Matematica 1. The oral part of the exam must be passed in the anxlisi session of the written part. In the period june-july the oral part may be passed in a subsequent session.


Outline of double improper integrals. Definition of Riemann double integral for functions defined on a bounded and measurable set. Department of Statistical Sciences.

Access to the oral part is allowed only to the students passing the written part. Single cycle degree courses.


Definition of a convergent series. Target skills and knowledge: Marco Bramanti, Carlo D. Textbooks and optional supplementary bertscj M. Elementi di Analisi Matematica, vol. The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function. The definition and the properties of the derivative of one variable functions.

Information on the course unit.

Analisi matematica : Bertsch :

In the period jenuary-february the oral part may be passed in a subsequent session. Analiai the written part, lasting three hours, the solution of various exercises is required. The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit. Office hours See the website of Annalisa Baldi See the website of. Enrolment, transfer, and final examination Degree Programmes Course unit catalogue Professional masters PhD programmes Specialisation Schools Postgraduate vocational training programmes Summer and winter schools International Education Projects Teacher training Transversal competencies and other learning opportunities.


The course consists in hours of lectures, about one half of them is devoted to numerical and theoretical exercises. The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for jatematica evaluation.

Convergence criteria for numerical series. The change of variables theorem for a double integral. Search Course unit catalogue. Planned learning activities and teaching methods:. The detailed contents with the list of theorems and proofs, up to dated for each weak, can be found in the web course page. My e-mail for students My e-mail for staff Close.


Lessons are completed with examples and counterexamples illuminating the theoretical content. Pagani e Sandro Salsa, Analisi Matematica 1. See the website of Annalisa Baldi.