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Matematics and Operation research, first module: "Mathematics"

Corso di laurea magistrale in

Academic year 2013-14                 Prof F. Odetti - Prof. E. Mainini

The module of "Mathematics" of this course is divided into two parts:

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

 Program    Texts (theory and exercises)    Some past exams  

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:


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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, norms
condition number
Text 2 pages Oct 7, 2013
Answers 6 pages Oct 7, 2013

Exercises on Changes of coordinates, curves, surfaces

Changes of coordinates
curves, 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
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