|SCIENTIFIC DISCIPLINARY SECTOR||MAT/03|
Prerequisites (for future units)
The course aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry
The student must learn the concept of number of solutions of a mathematical problem, must know how to work with complex numbers vectors and matrices, including their diagonalization, must be able to solve equations and linear systems, must know how to make a change of coordinates in the plane and in space, as well as knowing how to solve simple problems concerning lines, planes, spheres, circles and conic sections
Complex numbers and representation in the Gauss plane: powers and solution of particular equations.
Real / complex coefficient polynomials: factor breakdown, fundamental theorem of Algebra and Ruffini's theorem.
Geometric vectors: equivalence, module, versorem operations and properties. Scalar and vottorial product and property. Mixed product of carriers.
Linear systems: elementary operations on equations and Gauss theorem-algorithm
Matrices: various definitions, operations and properties. Reverse matrix. Definition of characteristic and Rouchè Capelli Theorem with method for determining the solutions of a linear system. Determinant definitions e
Finitely generated vector spaces: basic definitions of size and relative theorems, subspaces.
Definition of linear application.
Changes of coordinates in the plane and in space, formulas of rotations and translations. Orthogonal matrices.
Matrix diagonalization: definition of eigenvalue, eigenvector and relative theorems. Spectral theorem for symmetric matrices.
Lines in the plane and lines and planes in space: parametric and Cartesian equations. Various formulas of analytic geometry.
Spheres and circumferences in space.
Quadratic forms and Conic sectionss: associated matrices and defining character.
Conic sections classification: parabolic, elliptic and hyperbolic type (canonical equations and theorems on canonical form reduction.
Algebra: factor decomposition: binomial and trinomial square, equation and inequalities of first, second degree and fractional.
Trigonometry: definitions of the sine, cosine, tangent, their graphical representations and main formulas.
Euclidean geometry: similitudes and equality of triangles, theorems of Pythagoras and Euclid, circles.
The course (four-months) consists of 3 hours of theory + 2 hours of exercises a week for 12 weeks.
There are also two optional afternoon hours of guided exercises in the presence of tutors and lecturers.
Notes and exercises can be found on the website AulaWeb of the web classroom
Odetti-Raimondo Elementi di Algebra lineare e geometria analitica (ECIG)
All class schedules are posted on the EasyAcademy portal.
The exam consists of a written test and an oral test.
Knowledge of the statements and demonstrations of the most important theorems is required, as well as the ability to use these tools in a critical way, also for the resolution of new problems for the student.