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Matematics and Operation research, first module: "Mathematics"

Corso di laurea magistrale in

Academic year 2014-15                 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)  
 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:


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Lessons of geometric and algebraic part (prof. F.Odetti)

Tuesday 09/23/2014

Tuesday 9/30/2014 Wednesday 10/1/2014

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 answers)

Exercises on Orthonormal bases, norms and condition number 2 pages Oct 7, 2013
Answers to Orthonormal bases, norms and condition number 6 pages Oct 7, 2013
Exercises on Changes of coordinates, curves, surfaces 2 pages Oct 24, 2013
Answers to Changes of coordinates, curves, surfaces 5 pages Oct 24, 2013
Exercises on quadrics 3 pages Nov 4, 2013
Answers to quadrics 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.

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