The first part held by prof. F. Odetti deals with Linear Algebra and Analytic
The second part held by prof. E. Mainini deals with Analysis and Calculus.
In this web page we deal with the first part of Linear Algebra and Analytic Geometry
Prerequisites: Linear algebra: matrices, linear systems, gaussian
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:
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)
|First part: Orthonormal bases, norms and condition number:||7 pages||Sep 27, 2013|
|Second part: Changes of coordinates, curves, surfaces, quadrics||8 pages||Nov 5, 2012|
Exercises on Orthonormal bases, norms and condition number
|Orthonormal bases, norms
|Text||2 pages||Oct 7, 2013|
|Answers||6 pages||Oct 7, 2013|
Exercises on Changes of coordinates, curves, surfaces
|Changes of coordinates
|Text||2 pages||Oct 24, 2013|
|Answers||5 pages||Oct 24, 2013|
Exercises on Quadrics
|Quadrics||Text||3 pages||Nov 4, 2013|
|Answers||10 pages||Nov 4, 2013|
Remark: Possibly there are errors
in these exercises.
Comments and notifications of errors shall be welcome.
At the bottom of each page you'll find the date of release.