LEARNING OUTCOMES

The course aims to provide basic technical notions and tools on complex numbers, linear algebra and analytical geometry.

AIMS AND LEARNING OUTCOMES

The student must know how to work with complex numbers, vectors and matrices, including their diagonalization,  must be able to solve linear systems and to find their number of solutions depending on a real parameter, must know how to work with vector spaces, vector subspaces and linear maps, as well as knowing how to solve simple problems concerning lines, planes and spheres in the space.

PREREQUISITES

• Algebra: factor decomposition, equations and inequalities (first, second degree and fractional);
• Trigonometry: definitions of sine, cosine, tangent, their graphical representations and main formulas;
• Euclidean geometry: basic concepts related to lines and circles, and their graphical representations.

TEACHING METHODS

The course has a duration of 12 weeks (4 months in total) and consists of 5 hours a week (dedicated to theory and exercises).

Working students and students with certified SLD (Specific Learning Disorders), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination arrangements so to take into account individual learning patterns, while respecting the teaching objectives.

SYLLABUS/CONTENT

• Complex Numbers and operations; algebraic, goniometric ed exponential form; representation in the Gauss plane: solution of particular equations.
• Geometric vectors and operations.
• Matrices: definitions, operations and properties; determinant of a square matrix; invertible matrices and  inverse matrix; rank of a matrix; diagonalization.
• Linear Systems; Rouché-Capelli’s theorem.
• Vector Spaces and Subvector spaces: basis, dimension, sum, intersection; definitions and theorems.
• Linear maps; properties and theorems.
• Lines and planes in the space: relative positions, parallelism and orthogonality conditions, distances, orthogonal projections and symmetries, lines and planes satisfying some given conditions.
• Spheres  in the space

RECOMMENDED READING/BIBLIOGRAPHY

Notes and exercises can be found on the website AulaWeb. Suggested books:

• E. Sernesi, Geometria vol. 1, Bollati-Boringhieri;
• V. Bertella-A. Damiano, Esercizi su spazi vettoriali e applicazioni lineari, con svolgimento e commenti, Esculapio 
• D. Gallarati, Appunti di Geometria, Di Stefano Editore-Genova;
• F. Odetti - M. Raimondo, Elementi di Algebra Lineare e Geometria Analitica, ECIG Universitas;
• M. Abate, Algebra Lineare, McGraw-Hill.