4.00 Credits
Linear systems, abstract vector spaces, matrices through eigenvalues and eigenvectors, solution of ode's Laplace transform, first order systems. For Engineer majors. Covers the following methods of solving ordinary differential equations (along with applications of such): separation of variables, homogenous and non-homogeneous, exact, first-order and higher, integrating factors, substitution methods, linear and non-linear, complex characteristics, variation of parameters, undetermined coefficients (superposition and annihilator approach), and Euler-Cauchy. Will introduce power series solutions, and the Laplace transform. Covers matrix and vector analysis, linear dependence and independence, matrix algebra, diagonalization, eigenvalues and eigenvectors, linear transformations (kernel and range), and vector spaces and subspaces (including null, column, and bases). **COURSE LEARNING OUTCOMES (CLOs) At the successful conclusion of this course, students will be able to: 1. Solve ordinary differential equations via the use of the following solution types: exact, implicit, series, and discrete application. 2. Solve systems of linear ordinary differential equations via the use of differential operators, Laplace transformations, and matrix methods. 3. Utilize ordinary differential equations as well as systems thereof to obtain solutions to related application problems. Course fee required. Prerequisites: Math 1220 (Grade C or higher). SP