The course introduces fundamental notions and tools of linear algebra, before giving their representation and applications to analytic geometry. The elements given here are crucial for many disciplines of mathematics and physics, including functional analysis, differential geometry, classical and quantum mechanics, relativity, field theory, dynamical systems, to name but a few.
To give fundamental tools in Linear algebra and basic applications in analytic geometry;
Each chapter introduces a specific topic of linear algebra, before giving the representation or application in geometry. For instance, the student will therefore discover the links between vector and affine spaces, duality and covariant coordinates, multinearity and wedge product, determinant and volume of an automorphism, metric and orthogonality, length and its invariance under isometries. One last chapter on vector calculus and the geometry of curves and surface in 3D euclidean space closes the lecture.
Crucial for developping computational skills, for both mathematicians and physicists.
The evaluation is twofold. One oral exam on theory, without notes, including notably definitions and demonstrations of important results. One written exam based on computation skills obtained from the exercises.
Lecture notes for theory and exercises.