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Access to the oral part is allowed only to the students passing the written part. My e-mail for students My e-mail for staff Close. Theorems on existence, uniqueness and continuation of solutions. Convergence criteria for numerical series. Outline of double improper integrals.

## 27993 – ANALISI MATEMATICA T-2

The definition and the properties of the derivative of one variable functions. Smooth and piecewise smooth curves, length of a curve, integral of a function over a curve. Proofs of some theorems, clearly detailed, may be required.

Marco Bramanti, Esercitazioni di Analisi Matematica 1. In the period jenuary-february the oral part may be passed in a subsequent session. To this aim tutorial activities will be organized and supervised by the teacher. The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables.

Teaching tools Tutorship if appointed. Give now Alma orienta Job placement. The last one is of fundamental importance to develop the logic and practical abilities related with the topics covered in the course. The Weierstrass theorem and the intermediate value theorem for functions of several variables. Pagani e Sandro Salsa, Analisi Matematica 1.

The divergence theorem and the Stokes theorem. Course Timetable bbertsch May 06, to Jun 07, The vector space structure, the dot product and the euclidean norm.

On-line material on IOL: The correctness, clarity of exposition and completeness of the answers given to the different exercises are the criteria for the evaluation. Teaching methods The course consists of lessons describing the fundamental concepts of real and vector functions of several real variables. The language of mathematics, basics of logics and set theory.

## MICHIEL BERTSCH

The flux of a vector field through an oriented surface. Geometric, harmonic and generalized harmonic series. 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. Information on the course unit.

### Michiel Bertsch (Author of Analisi matematica)

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.

Definition of a convergent series. Target skills and knowledge: Generalizations to triple integrals.

The students are required to attend the lectures and to devote a right amount of time to autonomous study. The evaluation of limits of one variable functions using both notable basic limits and Taylor’s formula.

### Analisi matematica : Bertsch :

In the written part, lasting three hours, the solution of various exercises is required. The Cauchy problem for differential equations and systems.

Absolute convergence of a series. Taylor’s formula of the second order for functions of several variables.

The ability of calculate derivatives and to use them to solve problems depending on parameters and to draw the graph of a function.