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Analisi Matematica 2 (ELE)
Mathematics 2
Matteo Franca

Seat Ingegneria
A.A. 2015/2016
Credits 9
Hours 72
Period II
Language ENG

Prerequisites
None

Learning outcomes
Know the tools and techniques of integration in several variables: line integrals, surface and volume. Know the methods for solving differential equations. Know the tools and techniques of complex analysis and the operational calculus (Fourier and Laplace). Ability to apply them in solving scientific and technological problems.

Program
Functions from R^n to R: continuity, differentiability. Partial and directional derivative. Schwartz theorem. Necessary and sufficient conditions to find max and min. Curves and line integrals. Smooth curves and length of a curve. Abscissa on a curve. Line integral of a function. Vector fields: work along a curve, conservative and irrotational fields. Characterization of conservative fields by means of potentials. Poincare’s Theorem. Green formulas and applications. Surface integrals: evaluation of areas and of the flow of a vector field through a surface. Volume integrals: normal domains, reduction formulas, change of variables. The real Laplace transform: definition and basic properties. Use of Laplace transform to solve linear differential equations. Hints on Fourier seiries.

Development of the examination
LEARNING EVALUATION METHODS
The exam consists of a written and an oral part.

LEARNING EVALUATION CRITERIA
The exam is meant to verify the capability of solving exercise and the knowledge of theorical instrument for them useful, and to evaluate the skill in connecting the objects described in the course, and to use an appropriate technical language.

LEARNING MEASUREMENT CRITERIA
To access the oral part it is necessary to pass the written one. To pass the written test is necessary to get an evaluation equal or superior to 15 and equal or superior to 18 for the oral test. To pass the tests the student needs to have understood the

FINAL MARK ALLOCATION CRITERIA
The final mark is the result of written tests, modified by the evaluation of the oral test. If the student fails this latter test he has to redo the exam, and if the evaluation is negative the final mark could decrease, while if it is positive it could increase at most of 7 points.

Recommended reading
G. C. Barozzi, “Matematica per l'Ingegneria dell'Informazione“, Zanichelli, Bologna, 2001. M. R. Spiegel, “Trasformate di Laplace“, McGraw-Hill (collana Schaum's). M. R. Spiegel, “Variabili complesse“, McGraw-Hill (collana Schaum's).

Courses

• Ingegneria Elettronica (Corso di Laurea Triennale (DM 270/04))