Advanced Engineering Mathematics: Lecture 2.1 - Fundamental Theorem of Linear ODEs

Advanced Engineering Mathematics, Lecture 2.1: The fundamental theorem of linear ODEs. In this lecture, we describe how a linear homogeneous ODE arises from a linear differential operator. Moreover, solutions to the ODE are precisely the functions in the kernel of the operator. A fundamental result is that every n'th order operator has an n-dimensional kernel. This means that every n'th order linear homogeneous ODE has a general solution involving exactly n linearly independent functions. We review how to find these functions for 1st order and certain 2nd order ODEs. Course webpage (with lecture notes, homework, worksheets, etc.): http://www.math.clemson.edu/~macaule/math4340-online.html Prerequisite: http://www.math.clemson.edu/~macaule/math2080-online.html