| Content: |
First order equations: separable, linear, homogeneous exact equations, orthogonal and oblique trajectories, applications. Higher order linear differential equations: Reduction of order, method of undetermine coefficients, method of variation of parameters, Cauchy-Euler equations, operator methods, applications. Power series solutions: ordinary points, regular singular points. The Laplace Transform: basic properties, solution of initial value problems, convolution integral, solution of various equations. Systems of linear differential epuations: Brief discussion of theory of linear systems, solving linear systems; by operator method, by Laplace transform. Introduction to Partial Differential equations: Separation of variables. |