Euclidean vectorial spaces. |
1. Introduction to euclidean spaces.
1.1 Scalar product.
1.2 Norm of a vector. Properties.
1.3 Angle between two vectors.
2. Orthogonality.
2.1 Orthogonal vectors.
2.2 Orthogonal systems. Gram-Schmidt method.
2.3 Singularties of orthonormal basis.
2.4 Orthogonal projection.
2.5 Symmetric endomorphisms.
3. Orthogonal maps.
3.1 Definition.
3.2 Properties.
3.3 Eigenvalues and eigenvectors of an orthogonal map.
3.4 Orientation of a basis
3.5 Inverse and direct orthogonal maps.
3.6 Classiication of orthogonal maps in two and three dimensions.
4. Vectorial product and triple product.
4.1 Definition.
4.2 Properties. |
Conics and quadric surfaces. |
1. Conics.
1.1 Definition and equations.
1.2 Intersections of a conic and a line.
1.3 Polarity.
1.4 Important potins and lines of a conic.
1.5 Description of nondegenerated conics: ellipse, parabola e hyperbola.
1.6 Change of reference.
1.7 Classification of conics. Reduced equation.
1.8. Pencils of conics.
2. Quadric surfaces.
2.1 Definition and equations.
2.2 Intersections of a quadric surface and a line.
2.3 Polarity.
2.4 Change of reference.
2.5 Important potins, lines and planes of a quadric surface.
2.6 Classification of quadric surfaces. Reduced equation.
2.7 Description of quadric surfaces of rank 3 and 4. |