Vector fields, surface integrals, line integrals, independence of path, conservative fields, divergence, curl. Green's theorem. Divergence theorem of Gauss, Stokes' theorem and applications of these theorems. Transformations of coordinate systems and vector components. Invariance of divergence and curl. Curvilinear coordinates.
Vector spaces. Inner products. Matrices and determinants, linear transformations. Systems of linear equations. Gauss elimination, rank of a matrix. Inverse of a matrix. Bilinear and quadratic forms. Eigenvalues and eigenvectors. Similarity transformations. Diagonalization of Hermitian matrices.
Numerical methods for solving systems of linear
equations. Ill-conditioning. Methods of Gauss and least squares. Inclusion of matrix
eigenvalues. Finding eigenvalues by iteration.