Ordinary Differential Equations

First order equations, exact equations, integrating factors, separable equations, linear homogeneous and non-homogeneous equations, variation of parameters, Principle of superposition. Second order equations, Wronskian, Abel's formula, variation of parameters, exact equations, adjoint and self-adjoint equations, Lagrange and Green's identities, Sturm's comparison and separation theorems. First order linear systems, Wronskian, Abel's formula, variation of parameters, systems with constant coefficients. First order nonlinear equations, initial value problem. Use of ODE in simple modeling problems.