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Department of Statistical Sciences. Marco Bramanti, Carlo D.
ANALISI MATEMATICA T-2 / — University of Bologna
The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for the evaluation. Interior and constrained local extrema for real functions of several variables. Convergence criteria for numerical series.
Assessment methods The assessment consists in a written wnalisi an oral exam. Absolute convergence of a series. Teaching methods The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables. Generalities on real and vector functions of several real variables.
Single cycle degree courses. The divergence theorem and the Stokes anapisi. The assessment consists in a written and an oral exam. The change of variables theorem for a double integral.
Properties of the double integral. Proofs of some theorems, clearly detailed, may be required. The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function. Definition of a convergent series. See the website of Annalisa Baldi. Taylor’s formula of the second order for functions of several variables.
Futhermore a lot of exercises are solved in the classroom. Course Timetable from Feb 21, to May 03, Smooth and piecewise smooth curves, length of a curve, integral of a function over a curve. The integral of a vector field over an oriented curve.
The evaluation of limits of one variable functions using both notable basic limits and Taylor’s formula. In the written part, lasting three hours, the solution of various exercises is required. Elementi di Analisi Matematica, vol. Target skills and knowledge: Dal Passo e L.
In the period jenuary-february the oral part may be passed in a subsequent session. 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 commission may require an oral examination in case the written one has not been sufficient for a matematoca grading.
Outline of double improper integrals. The last one is of fundamental importance to develop the logic and practical abilities related with the topics covered in the course. The detailed contents with the list of theorems and proofs, up to dated for each weak, can be found in the matematicx course page. An exercise book on functions of several real variables, such as, for example: Partial derivatives of higher order.
Educational offer – University of Padova
Generalized integrals and convergence criteria. Marco Bramanti, Esercitazioni di Analisi Matematica 1. Double integrals on rectangular and normal domains computed by iterated integrals. The oral part of the bersch dwells upon the comprehension of the relevant concepts and on the knowledge of definitions and the statements of fundamental theorems. Textbooks and optional supplementary readings M. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables.