|Diary of lessons of the part of this course concerning linear algebra and geometry|
Prerequisites: Linear algebra: matrices, linear systems,
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)
Lessons of geometric and algebraic part (prof. F.Odetti)
|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|
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