This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 310 Differential Equations Homework Exercises, Set 6 Summer 2011 Quiz on Wednesday, 26 October 2011 Course Information is on WebCT Textbook references are to: Boyce and DiPrima "Elementary Differential Equations and Boundary Value Problems" (9th edition). Reading: Sections 2.4, 2.5, 2.6 Problems to prepare for quiz (no need to hand in): Section 2.7, # 21 Euler's method (see also the additional problem); first read through #20. Recall limh0 (1 + h)t/h from calculus. . . # 8, 10, 15, 17, 20, 21, 23, 28 Second order linear DEs, real distinct roots of the characteristic equation # 12, 14, 15, 16 General theory Be sure you understand the ideas behind #1415 clearly (linearity!) For #16, one approach is to think about the values of y and y at t = 0 Section 3.1, Section 3.2, Additional problems 1. For the initialvalue problem y = 3 + t  y, y(0) = 1 : (a) Find the analytical solution y(t), and evaluate it at t = 0.1 and t = 0.2. (b) Compute approximate values of the solution at t = 0.1 and t = 0.2 "by hand" (you can use a calculator if needed!) using Euler's Method with step size h = 0.1, writing out the steps in the calculation. Compare with the exact solution from (a) to find the errors. (c) As in (b), compute "by hand" approximations to the solution at t = 0.1 and t = 0.2 using step size h = 0.05, and find the errors. How do the errors compare with those for h = 0.1? [This is a shortened version of Section 2.7 #1.] You are strongly encouraged to look at and work through other problems; the following is a suggested selection of other useful or interesting (optional) exercises: Section 2.7, Section 3.1, # 2, 12, 20 Numerical methods: Euler's method # 1, 4, 11, 12, 16, 22, 27 Second order linear DEs, real distinct roots Do as many of # 118 as needed # 9, 10, 13 General theory of linear equations: existence/uniqueness, linearity Section 3.2, ...
View
Full
Document
This note was uploaded on 01/30/2012 for the course MATH 310 303 taught by Professor Rwk during the Spring '11 term at Simon Fraser.
 Spring '11
 RWK
 Math, Differential Equations, Equations

Click to edit the document details