Linear algebra and solutions of linear systems. Linear geometry in euclidean 3d-space. Vectors in 3d-space and operations between them. Eigenvectors and eigenvalues. Diagonal form of endomorphisms.
Course Content - Last names E-N
Elementary geometry in the plane and in the space.
Course Content - Last names O-Z
Vector spaces; linear systems of equations; affine geometry; inner products and Hermitian products; eigenvectors; conics.
- Notes by the teacher.
- C. Petronio, "Geometria e Algebra Lineare," Esculapio.
- G. Anichini, G. Conti, "Geometria analitica e algebra lineare", Ed. Pearson.
- G. Anichini, G. Conti, R. Paoletti, "Algebra lineare e geometria analitica - Eserciziario", Ed. Pearson.
- E. Abbena, A. M. Fino, G. M. Gianella, Algebra lineare e geometria analitica. Volume I, Aracne, 2012.
- E. Abbena, A. M. Fino, G. M. Gianella, Algebra lineare e geometria analitica. Volume II, Aracne, 2012.
- E. Schlesinger, Algebra lineare e geometria, Zanichelli, 2011.
- L. Mari, E. Schlesinger, Esercizi di algebra lineare e geometria, Zanichelli, 2013.
- M. Abate, C. De Fabritiis, "
Geometria analitica con elementi di algebra lineare", McGraw-Hill.
- M. Zedda, Note per il corso di Geometria e Algebra, Universit`a del Salento, https://sites.
google.com/site/michelazedda/.
- A. Bernardi, A. Gimigliano, Algebra lineare e geometria analitica, Citt`a Studi, 2017.
Learning Objectives - Last names A-D
Basic notions about analytic geometry (geometric interpretation of equations) and linear algebre (linear sistems, linearity, eigenvectors).
Learning Objectives - Last names E-N
Basic notions about analytic geometry (geometric interpretation of equations) and linear algebre (linear sistems, linearity, eigenvectors).
Learning Objectives - Last names O-Z
Students are expected to manage the basic tools in analytic geometry (geometric interpretation of systems of equations) and linear algebra (analytic solution of systems of equations; notions of linearity and eigenvectors). They are expected to use the language of linear algebra to descrive linear phenomena in analytic geometry.
Knowledge and understanding of both mathematical principles and the role of mathematical sciences as a tool for the analysis and the problem solving of mechanical engineering problems. Knowledge of the principles of computer science and the algorithmic and numerical approach to problems.
Applying knowledge and understanding related to mathematical methods - with particular reference to differential and integral calculation, geometry, linear algebra, numerical calculation, linear programming and probability and statistical calculation - to model, analyze and solve engineering problems, also with the help of IT tools.
Prerequisites - Last names A-D
Elementary geometry in the plane and n the space. Algebraic calculus.
Prerequisites - Last names E-N
Elementary geometry in the plane and n the space. Algebraic calculus.
Prerequisites - Last names O-Z
Basic mathematics.
Teaching Methods - Last names A-D
Class teaching (lessons and exercises) according to the given timetable.
Teaching Methods - Last names E-N
Class teaching (lessons and exercises) according to the given timetable.
Teaching Methods - Last names O-Z
Lessons and exercise classes.
Further information - Last names A-D
See the personal web page.
Further information - Last names E-N
See the personal web page.
Further information - Last names O-Z
For further information, feel free to contact the lecturer.
Type of Assessment - Last names A-D
Written test. A couple of written tests during the course (to be confirmed).
Type of Assessment - Last names E-N
Written test and eventually oral examination.
Type of Assessment - Last names O-Z
Written exam, and optional oral exam. Intermediate exams. Each written exam consists of 11 multiple-choice questions.
Course program - Last names A-D
Free and applied vectors. Sum, multiplication with numbers and related
properties. Linear dependence, parallelism and complanarity. Generated
subspaces and bases. Scalar, wedge and mixed products. Ortogonal
projections.
The vector spaces R^2, R^3, R^n.
Matrices: elementary operations and their properties. Vector space of
matrices.
Special matrices. Determinant and invertible matrices.
Linear systems: generality, structure of the space of solutions. Gauss
elimination method.
Analytic geometry on the plane and in the space: straight lines and planes;
parallelism and orthogonality conditions; relative positions. Distances.
Linear applications: definition, kernel and image; associated matrix.
Eigenvalues and eigenvectors. Diagonalization of linear applications.
Course program - Last names E-N
Free and applied vectors. Sum, multiplication with numbers and related
properties. Linear dependence, parallelism and complanarity. Generated
subspaces and bases. Scalar, wedge and mixed products. Ortogonal
projections.
The vector spaces R^2, R^3, R^n.
Matrices: elementary operations and their properties. Vector space of
matrices.
Special matrices. Determinant and invertible matrices.
Linear systems: generality, structure of the space of solutions. Gauss
elimination method.
Analytic geometry on the plane and in the space: straight lines and planes;
parallelism and orthogonality conditions; relative positions. Distances.
Linear applications: definition, kernel and image; associated matrix.
Eigenvalues and eigenvectors. Diagonalization of linear applications.
Conics and quadrics.
Course program - Last names O-Z
0 - Introduction and preliminaries. Complex numbers.
1 - Vector spaces: Vectors, operations on vectors. Generated subspaces, linear dependence, basis, dimension. Numerical vector spaces. Scalar product, vector product, triple product.
2 - Linear systems: Matrices. Operations on matrices and properties, special matrices. Determinant, rank. Linear systems of equations. Solutions of linear systems. Gauss Elimination Method.
3 - Linear analytic geometry: Parametric and Cartesian equations for subspaces. Lines, planes. Parallelism and perpendicularity.
4 - Linear metric geometry: Scalar products. Distance, angle, area, volume. Ortoghonal projection.
5 - Linear maps: Linear transformations. Kernel and image. Matrices associated to linear maps. Change of basis. Eigenvectors and eigenvalues. Diagonalization. Diagonalization of symmetric matrices and spectral theorem. Conics and quadrics.