Academic year2016/17
CoursePHYSICS
Code240AA
Credits9
PeriodSemester 1 & 2
LanguageItalian
| Modules | Area | Type | Hours | Teacher(s) |
| GEOMETRIA 1 | MAT/03 | LEZIONI | 72 | |
Programma non disponibile nella lingua selezionata
Knowledge
Students are expected to acquire:
some knowledge of the basic theory of vector spaces, linear transformations, scalar products;
manipulation abilities with the main algorithms in linear algebra;
some geometric insight and geometric applications.
Assessment criteria of knowledge
In the oral exam, the student will be assessed on his/her demonstrated ability to discuss the main course contents using the appropriate terminology.
In the written exam (3 hours), the student must solve/answer a list of questions/problems by an appropriate use of the tools learned in the course.
Methods:
- Final oral exam
- Final written exam
- Periodic written tests
Teaching methods
Delivery: face to face
Learning activities:
- attending lectures
- individual study
- Other
Attendance: Advised
Teaching methods:
Syllabus
Geometric vectors, coordinates, lines and planes in the 3-space and their equations.
Canonical scalar product and vector product. Groups, fields, vector spaces; linear independence, bases, dimension.
Linear transformations; matrices associated to a linear transformation; change of bases.Invariant spaces, eigenvalues and eigenvectors, diagonalizable transformations; triangularizable transformations.
Bilinear forms, scalar products over the real and complex fields (related theorems).
Symmetric transformations (in an Euclidean space), spectral theorem.
Affine trasformations, affine spaces. Isometries.
Affine and isometric classification of conics and quadrics.
Bibliography
Recommended reading includes the following works:
S. Lang, "Linear Algebra";
S. Abeasis, "Algebra lineare e Geometria";
C. Ciliberto, "Algebra lineare"
Further bibliography will be indicated.
Updated: 14/11/2016 17:27
