### Teachings

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

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[70/77]  CHEMICAL ENGINEERING [77/00 - Ord. 2020]  PERCORSO COMUNE 7 70
[70/78]  MECHANICAL ENGINEERING [78/00 - Ord. 2019]  PERCORSO COMUNE 7 70

### Objectives

Knowledge and Comprehension:

- adequate knowledge and interpretation of the problemes related to linear algebra and geometry;
- ability of solving mathematical problems by the correct use of the methods tools of the linear algebra and ability of an their adequate geometric interpretation;

- correct interpretation and use of the obtained results.

Judgement ability:

the student will be able to recognize the different problem of geometric nature appearing in different fields and to chose their correct and simpler solution.

Communication skills:

correct use of the scientific linguage both in the oral and written form.

Ability of autonomous study:

The course solicites the students to study and work autonomously in order to be able to use various fonts in the scientific literature, different from the material provided by the teacher.

### Prerequisites

Basics on calculus, algebra, geometry and trigonometry according to the usual outcoms of the secondary school.

### Contents

1 - Complex numbers: operators, Gauss plane, trigonometric form, roots.
(lectures 4 hours, exercises 2 hours).

2 - Vectors in a Euclidean space: operators on vectors, condition of linear independence, base of a Euclidean space, horthonormal base, scalar and vectorial product between vectors, mexed product.
(lectures 7 hours, exercises 3 hours).

3 - Matrices and determinants: operators between matrices, determinant of a matrix and their properties, Binet theorem, inverse matrix, matrix rank, Kronecker theorem.
(lectures 7 ore, exercises 3 hours).

4 - Linear systems: Cramer formula, Rouché-Capelli theorem.
(lectures 7 ore, exercises 3 hours).

5 - Applications in a linear space: Eigenvalues and eigenvectors, base transformations, endomorphism, similar matrices, characteristic polynomial of a matrix, algebraic and goemetric molteplicity of an eigenvalue, diagonalizable matrices.
(lectures 7 ore, exercises 3 hours).

6 - Geometry on a plane: lines and conic curves.
(lectures 8 ore, exercises 3 hours).

7 - Geometry in a space: lines, planes and hypersurfaces.
(lectures 9 ore, exercises 4 hours).

### Teaching Methods

Traditional teaching by means of the blackboard; cooperative approach to the exercises involving the students.

### Verification of learning

The final examination consists in a written test, usually lasting one hour, including several exercises.

### Verification of learning

The final examination consists in a written test, usually lasting one hour, including several exercises.

### Texts

E. Schlesinger, Algebra Lineare e Geometria, Zanichelli
G.Anichini, G.Conti, Geometria analitica e Algebra Lineare, Prentice Hall
M. Abate, Geometria, Ed. McGraw-Hill
M. Abate – C. De Fabritiis, Esercizi di Geometria, Ed. McGraw-Hill