Applied Mathematics I

Matrices in engineering. Linear transforms and their matrices. Approximation of
differential operators by matrices. Matrix algebra. Eigenvectors, eigenvalues
and invariants. Scalar product, orthogonal and unitary matrices. Elements of
matrix computation. Givens rotations and Hausholder transforms, QR
decomposition, Gauss transformation and LU decomposition. Finite solution of
systems of linear equations. Polar decomposition, singular decomposition,
pseudoinverse, least squares. Matrix functions. Localization of eigenvalues,
algorithms for eigenvalue problems. Canonic forms, application to ODE.
Generalizations to infinite dimensional spaces.