Math 2214 - Third Test Review: Topics in Linear Differential Equations - Prof. Peter A. Li, Study notes of Differential Equations

Download Math 2214 - Third Test Review: Topics in Linear Differential Equations - Prof. Peter A. Li and more Study notes Differential Equations in PDF only on Docsity! Math 2214 Wednesday, November 12 Third Test Review The test will cover sections 3.11–4.7 and 4.9. Topics will include 1. Wronskian, fundamental set of solutions. If y1, . . . ,yn are solutions of the homo- geneous nth order linear differential equation y(n) + pn−1(t)y(n−1) + · · ·+ p1(t)y1 + p0(t)y0 = 0, where the pi are continuous functions on the open interval (a,b), then the Wronskian of y1, . . . ,yn is either identically zero, or it is never zero, on the interval (a,b). 2. Solving nth order homogeneous linear differential equations with constant coeffi- cients. 3. Writing an nth order linear differential equation as a system of first order linear dif- ferential equations. 4. The Wronskian of vector valued functions, fundamental set and fundamental matrix. 5. How to solve y′ = Ay, especially when A is a 2 by 2 matrix. Then there are three cases, namely A has real distinct roots, repeated roots, and complex roots. 6. The Euler method for a system of two first order differential equations. Test Friday, November 14. Review session 5:00 p.m. in McBryde 226, Thursday November 13.