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# GEOMETRY

 Degree course Information and Communication Technologies (ICT) Engineering Curriculum Curriculum unico Learnings Orientamento unico Academic Year 2016/2017 ECTS 6 Scientific Disciplinary Sector MAT/03 Year First year Time unit First semester Class hours 48 Educational activity Basic training activities

## Single group

 Professor VITTORIA BONANZINGA Objectives Knowledge of the basic notions of linear algebra (matrices, determinants, systems of linear equations, vector spaces, linear maps, eigenvalues and eigenvectors, diagonalization of a matrix, scalar products) and analytical geometry in dimension two and three (equations of lines and plans and analytical study of their mutual positions; equations and study of curves and surfaces, with particular reference to conics and quadrics). Knowledge of the tools and techniques of Linear Algebra for the study of Analytic Geometry. Ability to understand and use mathematical instruments to solve geometric problems of plane and space. Ability to communicate the knowledge acquired through appropriate scientific-technical language. Programme Systems of linear equations. Matrices. Reduction for rows of a matrix. Solving systems of linear equations. Product of matrices. Properties. Invertible matrices. Transposed matrix. Symmetric and antisymmetric matrices. Uniqueness of the inverse with demonstration. Inverse matrix of the matrix product A · B.Rank of a matrix. Determinants. Laplace theorem. Determinants and properties. Determinants and invertible matrices. Inverse of a matrix. Complements and Applications: Cramer's Rule, Theorem of Kronecher, Rouchè-Capelli theorem. Vector spaces, scalar product. Definition and examples of vector spaces. Cancellation law of product in vector spaces. Subspaces. Systems of linearly independent vectors. Vector spaces of finite dimension. Generators and bases of a vector space. Method of completion and the discard method for the determination of a base. Canonical bases. Components of a vector and base changes. Linear maps: definitions and examples. Kernel and image of a linear map. Linear applications and matrices. Similar matrices. Diagonalization. Eigenvalues and eigenvectors. Theorem on the linear independence of the eigenvectors. Characteristic polynomial. Scalar products. Angle between two vectors. Orthonormal bases. Plane geometry . Cartesian coordinates. Lines in the plane. Angle between two lines. Parameters directors and direction cosines. Intersections. Parallelism and orthogonality. Circumferences. Conics. Classification of affine conics. Canonical forms. Reduction to canonical form of conics. Geometry in the space. Points, lines and planes of Cartesian space. Angle between two lines. Angle between two planes. Intersections. Parallelism and perpendicularity conditions. Spheres. Quadrics: definition. canonical forms. Reduction to Canonical forms. Books 1. S. Greco, P. Valabrega,  Algebra lineare , Levrotto& Bella, Torino.2. S. Greco, P. Valabrega,  Geometria Analitica,Levrotto& Bella, Torino.3. N. Chiarli, S. Greco, P. Valabrega, 100 Pagine di...Algebra lineare Levrotto& Bella, Torino.4. N. Chiarli, S. Greco, P. Valabrega, 100 Esercizi di...Algebra lineare Levrotto& Bella, Torino.Volume 1 includes theory and exercises of volumes 3 and 4 Traditional teaching method Yes Distance teaching method No Mandatory attendance No Written examination evaluation Yes Oral examination evaluation Yes Aptitude test evaluation No Project evaluation No Internship evaluation No Evaluation in itinere No Practice Test No

## Further information

Description Document
Compito 31 gennaio 2017 (esercitazioni) Compito 6 giugno 2017 (esercitazioni) I Compito gennaio 2017 (esercitazioni) Prova d'esame (esercitazioni) prova d'esame (esercitazioni) prova d'esame (esercitazioni) prova d'esame (esercitazioni) No news posted
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