State which of the following matrices are stochastic and which are not. Explain why a matrix is not stochastic. (a) [i ] (b) [! -] [i !J [ 0 ] (c) (d) 1 0 [! 3 !] [l 1 _j]

FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS I: Introduction and Analytic Methods David Levermore Department of Mathematics University of Maryland 22 January 2012 Because the presentation of this material in lecture will diﬀer from that in the book, I felt that notes that closely follow the lecture presentation might be appreciated. Contents 1. Introduction: Classiﬁcation and Overview 1.1. Classiﬁcation 2 1.2. Course Overview 4 2. First-Order Equat