The first part held by prof. F. Odetti deals with Linear Algebra and Analytic
Geometry.

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
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:

- Complements of linear algebra: non-finitely generated vector spaces
- Oorthonormal bases, projections, condition number of a matrix.
- Complements of analytic geometry: curves and surfaces.
- Changes of coordinates.
- Quadrics.

References:

- for linear algebra and geometry
**Odetti-Raimondo**- Elementi di algebra lineare e geometria analitica (in italian)

**Gilbert Strang**- Linear algebra (in english) - for calculus
**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)

**Theory notes **

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, normscondition number |
Text | 2 pages
| Oct 7, 2013 |

Answers | 6 pages
| Oct 7, 2013 |

**Exercises on Changes of coordinates, curves, surfaces**

Changes of coordinatescurves, surfaces |
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.

**Some past exams**

January 2014 | February 2014 | April 2014 |

June 2014 | July 2014 | September 2014 |