The Gram-Schmidt process; similarity and orthogonal diagonalization; abstract vector spaces and linear transformations over arbitrary fields; change of basis; inner product spaces; norms and distance; least squares and Fourier approximation; singular value decomposition. Applications to differential equations and other topics will be emphasized throughout the course.

Antirequisite(s): Mathematics 2211A/B, the former Applied Mathematics 2811A/B, the former Mathematics 2120A/B, the former Mathematics 3121A/B.

Prerequisite(s): One of Mathematics 1700A/B (recommended), Mathematics 1600A/B, Numerical and Mathematical Methods 1411A/B, or the former Applied Mathematics 1411A/B; plus one of Calculus 1301A/B, Calculus 1501A/B, Numerical and Mathematical Methods 1414A/B, the former Applied Mathematics 1413, or the former Applied Mathematics 1414A/B. Integrated Science 1001X with a minimum mark of 60% can be used in place of Calculus 1301A/B.

Extra Information: 3 lecture hours, 1 tutorial hour.