### Teachings

Select Academic Year:     2017/2018 2018/2019 2019/2020 2020/2021 2021/2022 2022/2023
Professor
MONICA MARRAS (Tit.)
Period
First Semester
Teaching style
Convenzionale
Lingua Insegnamento
ITALIANO

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/77]  CHEMICAL ENGINEERING [77/00 - Ord. 2017]  PERCORSO COMUNE 8 80
[70/78]  MECHANICAL ENGINEERING [78/00 - Ord. 2017]  PERCORSO COMUNE 8 80

### Objectives

1. Knowledge and understanding. At the end of the course the student will have knowledge of topics concerning real sequences, the infinitesimal calculus of real functions of a real variable.
2. Applying knowledge and understanding. The student will be introduced to the main applications of the theoretical notions of the course, concerning both the solution of mathematical problems and the study of physical problems.
3. Autonomy of judgment. The student will learn how to classify single problems of differential and integral calculus.
4. Communicative Skills. Students will acquire the ability to communicate what they learn and elaborate and also to express and argue the choice of methodology with respect to another to solve a mathematical problem.
5. Learning skills. Thanks to the notions acquired in this course, the student will be able to perfect his knowledge of higher mathematics and its applications to engineering.

### Prerequisites

Good knowledge of algebra, trigonometry and elementary analytic geometry.

### Contents

Functions in R^N . Sets in R^N : 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.
- Sequences of functions, Series of real numbers and functions. Convergence.
Comparison tests. Positive series. Alternating series.

### Teaching Methods

Frontal lectures (theory): 50 hours
Frontal lectures (exercises): 30 hours

### Verification of learning

A test, consisting on solving several exercises and proving some theorems. An eventual discussion.

### Texts

-Analisi Matematica 2.
casa editrice Zanichelli,
autori Paolo Marcellini, Carlo Sbordone.

- Esercitazioni di Matematica Due. Prima e Seconda parte.
casa editrice Zanichelli.
autori Paolo Marcellini, Carlo Sbordone.

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