First order differential equations: integrating factor, separation equations, exact equations.
General theory for differential equations: nth order ODE in IR^m are equivalent to 1st order ODE in IR^{nm}, Banach fixed point theorem, existence and uniqueness results for differential equations.
2nd and nth order differential equations: homogeneous
equations with constant coefficients, Wronskian, nonhomogeneous
equations - method of undetermined coefficients and variation of
parameters.
General theory for linear differential equations: existence, uniqueness of global solutions, fundamental matrix, equations with constant coefficients.
Material
Related to Exam 1:
Sample Problems for Exam 1
- Please turn solutions to this list of problems in a neat and very
organized way, by Wednesday, Feb. 23rd. Depending upon your
performance, you may earn up to 10 extra points to Exam 1.