Linear Algebra and Differential Equations

Catalog description

Term hours: 90 lecture. This course is an introduction to linear algebra and ordinary differential equations. Linear algebra includes matrix algebra, solutions of linear systems of equations, augmented matrices with Gauss-Jordan elimination, inverse matrices, determinants, vector spaces, linear independence, basis, dimension, subspace, row space, column space, null space, inner product space, the Gram-Schmidt procedure, linear transformations (proofs, kernel and range), eigenvalues, eigenvectors, diagonalization and orthogonal diagonalization of symmetric matrices. Differential equations includes applications and solutions to first-order differential equations (separable, linear, homogeneous, Bernoulli, and exact), higher order differential equations (reducible to first order, Cauchy-Euler, undetermined coefficients, variation of parameters, power series, and the Laplace Transform), and systems of linear differential equations (fundamental solutions, variation of parameters, and solutions by eigenvalues and eigenvectors). (UC/CSU, AA GE, IGETC, CSU GE, C-ID: MATH 240, MATH 250, MATH 910S)