Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

Topics include orthogonal and unitary matrices and transformations; orthogonal projections; the Gram-Schmidt procedure; and best approximations and the method of least squares. Inner products; angles and orthogonality; orthogonal diagonalization; singular value decomposition; and other applications will also be explored.

Topics include systems of linear equations, matrix algebra, elementary matrices, and computational issues. Other areas of the course focus on the real n-space, vector spaces and subspaces, basis and dimension, rank of a matrix, linear transformations and matrix representations. Determinants, eigenvalues and diagonalization, and their applications are also explored.

This course gives an introduction to numerical methods and their applications in computational science and engineering. It presents various numerical methods, discusses their mathematical properties, and provides practice in scientific computer programming. The main topics include computer arithmetic, nonlinear algebraic equations, polynomial interpolation, numerical differentiation and integration, initial-value problems for ordinary differential equations, and direct methods for solving linear systems.