The course is a bridge between three dimensional geometry and linear algebra, with an extension to non linearity through the study of the curves and surfaces, in particular the quadratic ones. The metric part leads to the introduction of contravariant and covariant coordinates, opening a door on the tensorrial formulation.
To give fundamental tools in Linear algebra and basic applications in three dimensional geometry;
The course starts with a study of lines and planes, in parametric and cartesian representations. The metric part and the scalar product allow to introduce covariance and contravariance concepts, linked to orthogonality.
A general introduction of curves and surfaces follows, with Frenet-Serret frame and tangent planes. The case of the conics and quadrics is analyzed in details.
Some more sophisticated properties of the surfaces are then described, as regularity, development, planarity, with examples of generic cones or cylinders.
the vector product and its properties, the cylindric and spheric coordinates are rapidly explained.
Crucial for the understanding of the course.
The exam is only written with several questions (applications or exercises). A question about the TG could be included (precised during the year).
syllabus