Program | Texts |
Diary of lessons of the part of this course concerning linear algebra and geometry |
Prerequisites: Linear algebra: matrices, linear systems,
gaussian elimination.
Vector spaces: Subspaces, linearly independent vectors, generators (spanning sets),
bases, dimension.
Diagonal form of a matrix: eigenvalues, eigenvectors, eigenspaces.
Scalar products. Orthogonal vectors. Orthonormal bases. Orthogonal matrices.
Spectral theorem (symmetric matrices are diagonalizable). Quadratic forms.
Analytic geometry of plane: conic sections.
Analytic geometry of space: lines, planes, distances, circles, spheres.
An outline of the program is the following:
References:
Odetti-Raimondo - Elementi di algebra lineare e geometria
analitica (in italian)
Gilbert Strang - Linear algebra (in english)
R. A. Adams - Calcolo Differenziale 1 (numerical integration,
series) both in italian and english
R. A. Adams - Calcolo Differenziale 2 (triple ntegrals and surface
integrals) both in italian and english
C.D. Pagan - S. Salsa - Analisi Matematica 2 (in italian)
Lessons of geometric and algebraic part (prof. F.Odetti)
Thursday 09/27/2012
Theory notes
Outline of theory. First part: Orthonormal bases, norms and condition number: | 7 pages | Sep 27, 2013 |
Outline of theory. Second part: Changes of coordinates, curves, surfaces, quadrics | 8 pages | Nov 5, 2012 |
Exercises (with many answers)
Warning: These
notes are under further development:
A new version will be ready in a few weeks
Exercises on Orthonormal bases, norms and condition number | 2 pages | Dec 23, 2012 |
Answers to Orthonormal bases, norms and condition number | 3 pages (for now) | Dec 23, 2012 |
Exercises on Changes of coordinates, curves, surfaces, quadrics | 5 pages | Dec 23, 2012 |
Answers to Changes of coordinates, curves, surfaces, quadric | 6 pages (for now) | Dec 23, 2012 |