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MTH-103.4 Theory of Ordinary Differential Equations

Methods of solving 1st and second order, linear ODE by variation of parameters and Wronskian, solutions by series of some special 2nd order ODE.

1st order non-linear ODE, Cauchy-Picard theorem,two point boundary value problem and Sturm-Liouville theory, Weyl-Titschmarsh theorem for unbounded interval - limit cycle, limit point cases.

Linear systems with constant coefficients, Fundamental Matrix, Linear Systems with periodic coefficients. Nonlinear Autonomous system, critical points. Phase plane analysis, stability, Periodic solutions.