### Teachings

Select Academic Year:     2016/2017 2017/2018 2018/2019 2019/2020 2020/2021 2021/2022
Professor
STELLA PIRO (Tit.)
Period
Second Semester
Teaching style
Convenzionale
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/10 - Ord. 2016]  ELETTRICA 5 50
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/20 - Ord. 2016]  ELETTRONICA 5 50
[70/89]  ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING [89/30 - Ord. 2016]  INFORMATICA 5 50

### Objectives

Introducing students in solving mathematical problems to be applied to engineering problems. In particular the students will be able to apply
differential and integral calculus for functions of several variable.

### Prerequisites

Good knowledge of Calculus 1 subjects

### Contents

Functions in RN . Sets in RN : accumulation, isolated, internal , external, boundary points; bounded, open, closed, compact, connected sets.Functions of several variables in RN , domain, image; definition and properties of limits. Limit theorems. Continuity. Partial derivatives. Higher derivatives. The total differential. Tangent plane. Taylor formula. The chain rule. Implicit functions.
-Maxima and minima.
Local maximum and minimum. Critical points of a smooth function. The second derivative test. Maximum principle for harmonic functions. Maxima and minima with constraints.

-Curves and surfaces.
Plane Curves: parametric equations, implicit form, smooth, piecewise, simple, closed, oriented curves.Length of arc in parametric, Cartesian, polar form. Curves in R3 .Surfaces in R3: parametric and Cartesian form, normal vector to a surface.

-Multiple integrals.
Double integral. Integration over normal regions. Normal regions in polar coordinates. Triple integral: Integration over normal regions, cylindrical coordinates and applications. Volume.

-Line and surface integrals. Line integrals, applications. Area of smooth surfaces, of a surface of revolution. Surfaces Integrals. Flux.

-Green’s theorem, Stokes’ theorem and their applications.

### Teaching Methods

Frontal lectures (theory): 31 hours
Frontal lectures (exercises): 19 hours

Tutor activity is scheduled.

### Verification of learning

Final exam: a test exam, consisting on solving several exercises and proving some theorems. An eventual discussion.

### Texts

Marco Bramanti, Carlo D. Pagani, Sandro Salsa: Analisi matematica 2. Zanichelli,
Sandro Salsa, Annamaria Squellati: Esercizi di Analisi matematica 2, Zanichelli