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The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for the evaluation.

Taylor’s formula of the second order for functions of several variables. Alternate series and Leibnitz criterion. Smooth and piecewise smooth curves, length of a curve, integral of a function over a curve.


In the period jenuary-february the oral part may be passed in a subsequent session. Teaching tools Tutorship if appointed. Proofs of some theorems, clearly detailed, may be required. Generalized integrals and convergence criteria.

The students are required to attend the lectures and to devote a right amount of time to autonomous study. Futhermore a lot of exercises are solved in the classroom.

Generalizations to triple integrals. Lessons are completed with examples and counterexamples illuminating the theoretical content.


The assessment consists in a written and an oral exam. Office hours See the website of Annalisa Baldi See the website of. Dal Passo e L. The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of mmatematica function.


Target skills and knowledge: In the written part, lasting three hours, the solution of various exercises is required. See the website of Annalisa Baldi. The divergence theorem and the Stokes theorem.

The change of variables theorem for a double integral. The oral part of the exam must be passed in the same session of the written part. Properties of the double integral. Single cycle degree courses. Access to the oral part is allowed only to the students passing the written part. Elementi di Analisi Matematica, vol. On-line material on IOL: The fundamental notions of mathematical analysis related with the properties of real numbers and to the definition of limit.

Marco Bramanti, Esercitazioni di Analisi Matematica 1. Information on the course unit. The Cauchy problem for mstematica equations and systems.

ANALISI MATEMATICA T-2 / — University of Bologna

Absolute convergence of a series. Interior and constrained local extrema for real functions of several variables. The commission may require an oral examination in case the written one has not been sufficient for a clear grading. The teacher will use, as far as possible, various technological tools to improve the learning and to let the students to have as much brrtsch possible education material to their disposal.


Personal page of Michiel Bertsch

Partial derivatives of higher order. Theorems on existence, uniqueness and continuation of solutions. Textbooks and optional supplementary readings M. Search Course unit catalogue. The Weierstrass theorem and the intermediate value theorem for functions of several variables. Geometric, harmonic and generalized harmonic series.

Planned bettsch activities and teaching methods:.

Definition of a continuous function and of limit of a function. Give now Alma orienta Job placement. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables. The evaluation of limits of one variable functions using both notable basic limits and Taylor’s formula. Marco Bramanti, Carlo D. First cycle degree courses. Textbooks and optional supplementary readings.