MATH 263 Lecture 8: Lecture 8
14 Feb 2019
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Document Summary
In today"s lecture we introduce and discuss the theory of higher order linear homogenous equations. Recall that second order equations can be written generally as, As before we will work with equations in normal form (semilinear equations) which can be written as, y (t) = f (t, y, y ) (1. 1) (1. 2) Moreover as before the above equation is linear if the function f is linear in the y and y variables. We will be primarily concerned with linear second order equations. Their is a rich theory for such equations and we will spend some time trying to understand the fundamental results and their applications to problems in science and engineering. When studying linear second order equations we will look at equations where the coe cients are constant and when the coe cients are variable. For constant cone cient equations we have a uni ed method to understand solutions in closed form.
