MTH510-Midterm-F2010-Solns

MTH510-Midterm-F2010-Solns - RYERS ON UNIVERSITY DEPARTMENT...

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Unformatted text preview: RYERS ON UNIVERSITY DEPARTMENT OF MATHEMATICS MTH 501/510 - Numerical Analysis MIDTERM — FALL 2010 Last Name (print): First Name (print): Student ID Number: Signature: Course Section MTH 501 MTH 510 MTH 510 MTH 510 MTH 510 MTH 510 wearer-aw Date: October 25, 2010, 11:15 am INSTRUCTIONS: SOLUTIOMS Instructor: Course: Lab day / time Instructor Tues noon—1pm Dr. Ilie Fri 8-9am Dr. Ilie Wed noon-1pm Dr. Ilie Mon 9.10am Dr. Rohlf Tues 8—9am Dr. Rohlf Fn' 9~10am Dr. Rohlf -——-—.—_______ Time Allowed: 90 minutes Verify that the test contains all 8 pages, including this cover page. Use a pen or pencil and write leginy for full marks. The examination has two parts: Part A consists of full- solution questions with the mark for each full solution as indicated. Answer all questions in the space provided. Clearly explain your methods, and show all relevant steps in the solution. An answer consisting only of the final result will be given little or no credit. Part B contains Multiple Choice questions. Clearly write your answer in the space provided. No part marks will be given and no marks will be deducted for incorrect answers. If more than one answer is given, a mark of zero will be assigned to that question. This is a closed-book test. When not specified, six significant digits of accuracy is sufficient. The last page is for rough work. DO NOT SEPARATE THE PAGES Permitted Aids: i) One handwritten 8.5 x 11 inch Formula sheet (both sides), ii) Non-programmable scientific calculators. Question(s) Value For instructor’s use only. Mark MTH 501/510 — MIDTERM - Page 2 - FALL 2010 1. (a) (4 marks) Express the decimal number 43.34375 as a binary fraction. (b) (2 marks) Use 3—digit chopping to evaluate f($)=-1-§—-e’ atz=l.23. CM aflo .343?§xa: .58}? O 34% .bEFJflK: [639»? I C9 1&2) HHW A = .H’ o / 3&0 07'YA& ”(oY' \V (9 o .C )Q A “I K \ 9437‘ l 0 ° W W“ WMCéxoxA t3 ‘ W \\OOO\O.olOH LEVEQ. as)‘ : (WWW ~ mt X320933)thl\:((0837133CNP: (~85. 3% = blag—3T; {0.14a309...)wf : 0.143 @ 8‘: [anmlmywt : 30% (“1,333 3 O. (4; —— 3 4a: “(3 www (3M4) :2 «3.3? MTH 501/510 - MIDTERM - Page 3 - FALL 2010 2. (8 marks) Use the Secant method with 2:0 2 —1 and 11:1 the roots of f(:1:)= 45mm - a: —1 with at least jsignificant figure, = O to approximate one of XQ\:XL V XQ'KL'I Q)L:()alh' ‘PCXL ) "?<X(:-‘ h L XL XL" 35% 430cm \ lea! O v { 4 g, 365883‘13‘1 N44, 9‘ ‘4“ my”; 0 omfixstoaa 'l (09% 00 >o 1180mm Mafia 3 ,3m& 3» N r\ A— meg 30(wa I. Don me (043% raw/owe 1 § O Mode; Sm w SwMA 46 W3. 8 L9. wt ‘W’v 7< “X0 3% — (—L——-— X} ‘ WNW . w H014“) ‘7 ’\ \IARA,A AA 3’04“an MTH 501/510 — MIDTERM 3. (a) (2 marks) Show that f(2:)=3x4~—e’——1 has a root on the interval [0, 2]. error is less than 0.2. L03 19w): 4-4:”k ‘0 '5 .2 3mmo+ on {0,33 Lg G;- JQCM =~' 3%6\7O IkfinwdfifiQwaiThmw MW Ox“, CLH' Efir O O & <0 :cm: I l ‘3?er c1 @ >0 {$91 :.5 Q9 & 1 my (03’ @ >0 gas- 3 1 may My “U Q CC.\:§U\<O 0‘. W 13 0L VOG‘F Om CC‘ I ha] M beam/L21) Cat “9‘3, MTH 501/510 - MIDTERM - Page 5 — FALL 2010 4. Consider the matrix A given by \ 006) \ Aéx (:33; L: A \O andU: 03(9 (“KM O O a (b) (4 marks) Use the LU decomposition of A to find the third column of A‘l. (c) (2 marks) What is the determinant of A. 1 ex \ 1 Ex - “K O A? a tn R (0 1% ('R‘) L { l \) “l “I ‘15”)! ® @ MTH 501/510 — MIDTERM — Page 6 - FALL 2010 5. (8 marks) Use Gauss-Seidel iteration to solve Do three iterations iteration. H 6111 + 22724-2333 11:1 — 42:2 fxs 1, 0, 2:1 + 3x2 + 71:3 7. [I H N Wabaolute value of the approximate reiative error at each >w‘iw, fuldx'bl grub» CO 0 U1— b X ‘ lg (tzwbwi L4" {PF t : 2i);— (X‘Il +’)(3 ) fi ‘ ‘ L‘H LN LN (I, 9, “Mg ' i « . >< ‘ XB' :}(3"XI 31A\ W _ - 37/ ’ . L Gov L {a X% \ O o O \ N/A I €C\’O~&) , 5. 5be W§loo°éltobéfi1 3" aA” : qg4§a3509 21am i-olbézbb be; 'agoggssm ’° a zatcwasslt .{emgqgag .qgswzew wimfgi’fimzpj :&&,3k% 3 “altHbjrS .l8sfi’éflofi .iSObBH‘H whsmz/oag; 130/0. MTH 501 / 510 - MIDTERM - Page 7 - FALL 2010 MM Part B - Multiple Choice Questions 6. (2 marks) Let c be the machine epsilon in 3-digit chopping. Which of the following statements is true: (A) e + 0.1 = 0.0149, (B) g + g + g = e, (C) the value for e is impossible to determine, (D) None of (A)—(C) are true. ANSWER: 6. :D 7. (2 marks) To plot y = sina: for :z: e [0, 1], which of the following does not work: (A) x=linspace(0,1); y=sin(x); plot(x,y); (B) xalinspace(0,1); ploth,sin(x)); (C) x=linspace(0,1); plot(x,@(x) sin(x)); (D). x=linspace(0,1); y=@(x) sin(x); plot(x,y(x)) ANSWER: 7. C 8. (2 marks) The following commands have been entered in MATLAB: k=2; a=[1 2 3]; b=~[3 4 5]; The result of the command (a . *b) . *k is (A) [6 16 30] (B) 52 (C) ??? Error using ==> mtimes Inner matrix dimensions must agree. (D) None of the above ANSWER: 8. A 9. (2 marks) Typing the commands x=linspace(0,2,3); y=x. ‘2 gives the following result for y (A) y = [0 1 4} (B) y = 2 (C) y = [0 4/9 16/9 4] (D) None of the above A ...
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This note was uploaded on 03/07/2012 for the course MTH MTH510 taught by Professor Dr.silvanailie during the Winter '12 term at Ryerson.

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MTH510-Midterm-F2010-Solns - RYERS ON UNIVERSITY DEPARTMENT...

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