Course Instructor: Alina Nita.

Basis and dimension of a vectorial space, evaluation of eigenvalues and eigenvectors, nature of conics and quadrics, solving elementary differential equations and linear differential equations of high order, using properties of Fourier and Laplace transforms.

Syllabus:

• Matrices and determinants.
• Linear systems.
• Vectorial spaces: base, dimansion, fundamental example Rn.
• Linear transformations, eigenvalues and eigenvectors.
• Algorithms of reducing to the canonical form.
• Euclidean vector space.
• Gramm-Schmidt method.
• Quadratic forms.
• Conics and quadrics.
• Surfaces generation.
• Elements of differential geometry.
• Elementary differential equations.
• Linear differential equations and systems.
• Non-linear differential equations; phase space, chaos, computation with MAPLE.
• Graphs; optimal paths.
• Fourier transform.
• Laplace transform and applications.