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: x ). Suppose we want to compute the derivative 1 at x = 0 using ﬁnite diﬀerences. Let D 1 ( h ) = f ( x + h )f ( x ) h and D 2 ( h ) = f ( x + h )f ( xh ) 2 h . Let D 3 ( h ) denote the method from Problem 8 of Section 2.2 in the textbook. Compute all of these for h = 10j , for j ∈ { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . Let e k ( h ) denote the error in D k ( h ) for k ∈ { 1 , 2 , 3 } . Plot log 10 ( e k ( h )) versus log 10 ( h ) for k ∈ { 1 , 2 , 3 } . What does the slope tell you? Can you say anything about the minimums of the curves? All the above problems (if graded) are worth 5 points each, except the ﬁnal two problems which are worth 10 points each. Study Problems (Will not be graded.) • Epperson, Section 2.1 problems: 1b, 4 (for 1b), 9 (for 1b). • Epperson, Section 2.2 problems: 2a, 2b, 3a, 3b, 9 (for 3a and 3b), 12, 14a. • Epperson, Section 2.3 problems: 1. 2...
View
Full
Document
This note was uploaded on 01/15/2012 for the course MAE 107 taught by Professor Rottman during the Spring '08 term at UCSD.
 Spring '08
 Rottman

Click to edit the document details