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Equazioni differenziali ordinarie di ordine n. Sistemi di equazioni differenziali del primo ordine, trasformata di Laplace e studi qualitativi. Applicazioni alla meccanica sistemi undimensionali, oscillatori accoppiati. Definition and convergence criteria for numerical series. Power series. Fourier series. Functions of several variables, vector fields.

Limits and continuity. Partial and directional derivatives, Jacobian matrix. Differentiability, gradient and tangent plane. Second derivatives, Hessian matrix. Taylor polynomial. Critical points, free and constrained extrema. Double and triple integrals, center of mass. Parametric curves and surfaces. Length of a curve and area of a surface. Line and surface integrals, circulation and flux of a vector field. Conservative vector fields. Green, Gauss and Stokes theorems.

## Maths Analysis

Ordinary differential equations of order n. First order systems, Laplace transform and qualitative studies. Applications to mechanics one-dimensional systems, coupled oscillators. Stability of stationary solutions. Note Additional information.

Organizzazione dell'insegnamento Course structure. Il corso consiste di 60 ore di lezione e 40 di esercitazione. Ogni argomento teorico trattato nelle lezioni viene arricchito da esempi introduttivi. Theoretical lessons: 60 hours.

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Exercise hours: 40 hours. Theoretical lessons are devoted to the presentation of the topics, with definitions, properties and the proofs which are believed to facilitate the learning process. Every theoretical aspect is associated with introductory examples. The exercise hours are devoted to the analysis and the methods required for solving exercises with the aim of preparing the student to the exam.

Bibliografia Reading materials. Canuto, A. Lang, Calculus of several variables, third edition, Springer, Pagani, S. The teacher of the course will suggest some textbooks among the following during the lectures: - C. Lang, Calculus of several variables, third edition, Springer, - C.

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Other material will be avalaible on the Portale della Didattica. Regole d'esame Assessment and grading criteria. L'esame consiste in una prova scritta di 8 esercizi a risposta chiusa e di un esercizio a risposta aperta sugli argomenti contenuti nel programma del corso.

Gli esercizi comprendono anche quesiti di tipo teorico. Ciascun esercizio a risposta chiusa vale: 3 punti se giusto, 0 punti se senza risposta, -1 punto se sbagliato. L'esercizio a risposta aperta vale 9 punti. The goal of the exam is to test the knowledge of the candidate on the topics included in the official program of the course and to verify the computational and theoretical skills in solving problems.

Marks range from 0 to 30 cum laude corresponding to 33 and the exam is succesful if the mark is at least High speed control, flux weakening. Mechanical loads, gearbox, control limits for oscillatory mechanical systems 6 hours. Position set point characteristic with speed and acceleration limits 6 hours.

Electric drives with induction motors 8 hours. Scalar control. Vector control of electric drives with induction motors: control of torque and flux components of stator current. Cascaded control of the stator current component generating the rotor flux and the rotor flux. Electric drives with synchronous reluctance motors 2 hours Sensorless control of syncronous and asynchronous drives. Electromagnetic compatibility issues in electric drives 4 hours Laboratory team-works: Rapid prototyping of control schemes for ac electric drives 6 hours. Grob, J.

Hamann, G. Legnani, M. Tiboni, R.

## Financial Markets and Institutions

Dispense fornite dal docente. It also describes the main features of SQL language and provides theoretical and practical knowledge about data storing within relational databases RDBs. Main languages for the Web and Web-based Information Systems are also introduced. The course also provides theoretical and practical knowledge about retrieval of unstructured information from the web.

Finally, it copes with emerging research issues, like the Semantic Web, by providing both theoretical and practical basic knowledge on such topics. Didactic Methods Course programme Recall of microwave and optical sources, microwave devices, Z,Y,S, parameters; radiating systems, radiating aperture. Microwave applicators [10 ore] Examples of microwave applicators. Bio-heat equation. Microwave thermotherapy and thermoablation [10] Optical sources and applicators: optical fibers, microstructured optical fiber PCFs; erbium, ytterbium, holmium fiber lasers.

Optical fiber and planar optics for sensing. Linac particle ccelerators. Diagnostics and therapy.

Collin, Foundations for microwave Engineering. Sorrentino, G. Wangler, RF Linear Accelerators, 2nd ed. Vespasiano Editore: Telecom Italia M. Transmission lines.

### Pre-requisites

Line parameters. Matched line, opened line loaded line. Single and double stub matching techniques. Recap on differential operators: div, grad, rot. Recap on differential equations for Electrostatics and Magnetostatics. Costitutive relations. Continuity of tangential fields and of normal fields at dielectric separation interfaces.

Poynting vector. Electromagnetic theorems of [9 ore] 3. Plane wave refraction and reflection. Campi Elettromagnetici e circuiti, G.