IN/0079/E - GEOMETRY AND ALGEBRA/E
Academic Year 2017/2018
Free text for the University
CARLO MEI (Tit.)
- Teaching style
- Lingua Insegnamento
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/46 - Ord. 2016] ELETTRICA ON LINE E IN PRESENZA (BLENDED)||7||42|
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/56 - Ord. 2016] ELETTRONICA ON LINE E IN PRESENZA (BLENDED)||7||42|
|[70/89] ELECTRICAL, ELECTRONIC AND COMPUTER ENGINEERING||[89/66 - Ord. 2016] INFORMATICA ON LINE E IN PRESENZA (BLENDED)||7||42|
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.
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.
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.
Basics on calculus, algebra, geometry and trigonometry according to the usual outcoms of the secondary school.
1 - Complex numbers: operations, Gaussian plane, trigonometric form, roots (4 hours lez. + 2 hours Fin.)
2 - The vectors of ordinary Euclidean space: vector operations, linear dependence and independence, bases and orthonormal bases, dot product, cross product, mixed product (7 hours lez. + 3 hours Fin.)
3 - Matrices and determinants: operations between matrices, determinants and their basic properties, Binet theorem, inverse of a matrix, the rank of a matrix, the theorem of Kronecker (7 hours lez. + 3 hours Fin.)
4 - Systems of linear equations: Cramer's rule, iI theorem Rouche-Capelli (7 hours lez. + 3 hours Fin.)
5 - Linear applications and matrices. Eigenvalues and eigenvectors: matrices associated, at change of base matrix and associated with an endomorphism, similar matrices, the characteristic polynomial of a matrix, algebraic and geometric multiplicity of an eigenvalue, diagonalized matrices. (7 hours lez. + 3 hours Fin.)
6 - Plane geometry: straight and conical (8 hours lez. + 3 hours Fin.)
7 - space geometry: lines, planes, quadrics (9 hours lez. + 4 hours Fin.)
The course with online delivery of teaching consists of a component of Education Grantmaking, consists of a set of "packages" pre-formed, and a component of Interactive Learning, where students interact with the teacher or the class tutor virtual with written or video mode, using tools such as e-mail, forums and virtual / video conference classroom.
The Education Grantmaking is divided into modules, which are further divided into teaching units lasting about 15 minutes each. Each teaching unit is organized in functional way to the specific training goal and can be constituted by: the recording of the teacher's lesson with the slide support, video and animation; from a set of slides and video faces to submit, primarily, examples of aspects of the subject application; for self-correction tests for self-assessment by the student.
The video lessons are accessible on the network asynchronously using the most common media (PC, smartphone, tablet) and the most common networking software (Explorer, Crome, Mozilla, etc).
You can also download to your multimedia support for off-line use, some specific content such as slides, tables, exercises proposed and carried out.
Verification of learning
The final examination consists in a written test, usually lasting two hours, including a test with true-false answers, questions on the theory and several exercises.
In case of a not sufficient mark for the true-false and theoretic part the exercises wont be considered for evaluation and the test is failed.
Bernardi, A. Gimigliano, Algebra Lineare e Geometria Analitica, Città Studi Edizioni
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
Notes, workbook with traces of the solutions, the exam papers with trace solutions.