Reading Assignment: Today we covered Section 6.1. You should read it, as well as Section 6.2 which we will cover on Friday. When reading: Section 6.1: 1) How is the Laplace transform defined? 2) When does it exist? 3) Basic examples are numbered 4,5 & 6 Section 6.2: How do we use the Laplace transform to solve an IVP? In particular, what is the importance of Theorem 6.2.1? Additionally, start building a list of properties of the Laplace transform; all we know up to this point is 1) it is linear 2) Theorem 6.2.1 concerning derivatives Problems (due Monday 2/23): Section 7.9 : Consider the system (page 412 #10) dx (-3 root{2}) (1) -- = ( )x + ( )e^{-t} dt (root{2} -2 ) (1) 1) Solve the associated homogeneous system 2) Solve given non-homogeneous system using the method of variation of parameters 3) Solve given non-homogeneous system using the method of undetermined coeffecients 4) Make sure the answers you got in 2) and 3) agree. Section 6.1 : 5ab,6,7,15,16