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# Civil and Environmental Computations CEE 305

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This 32 page Class Notes was uploaded by Alejandra Gutkowski on Monday September 28, 2015. The Class Notes belongs to CEE 305 at Old Dominion University taught by Duc Nguyen in Fall. Since its upload, it has received 32 views. For similar materials see /class/215319/cee-305-old-dominion-university in Civil and Environmental Engineering at Old Dominion University.

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Date Created: 09/28/15

Selected answers for all customized versions of Numerical Methods Book Chapter 0101 Introduction to Numerical Methods Multiple Choice Test Answers 1 A meww DgtUIJOU 6 You can see complete solutions by taking the test online httn39 numru39 enouf I New rmquot Olaae39 I html Problem Set 2 006237758151 01463595047 004373708621 3 a 02904761905 b 1969047619 c 1085714286 4 5430420000 5 1 6 4225167110 7 y05 dydx04 y25o61563 dydx25053355 Chapter 0102 Measuring Errors Multiple Choice Test Answers 9959 UDgtUIJOOUZJ You can see complete solutions by taking the test online 1 1 ht m39 mum 139 enou f 39 aae rmquot Olaae mea urin eiTorhtml Problem Set 1 a 08679 b 08229 0 08257 d 004213 e 004213 1 5102 g 5102 h 004495 i 004495 j 5462 k 5462 1 0 m 0005 2 00221 or 2221 3 2 4 Hessup 5 a 24538 b 1 c 7 d mainly truncation but roundoff error is there also 6a3or4or5or6b3 c5d3e4f4g3h5i6 Chapter 0103 Sources of Error Multiple Choice Test Answers 6 9959 UODgtUUJ You can see complete solutions by taking the test online httn39 numru39 encu f I New rmquot Olaae r html Problem Set 1 000006666666 2 000003333333 3 616 4 035427560 105 5 5175 6 At T300F alpha3255E6 for part a and 30516E6 for part b Chapter 0104 Binary Representation of Numbers Multiple Choice Test Answers 9959 UUZJUZJUIJUJO You can see complete solutions by taking the test online httn39 numru39 encuf I MP rmquot Olaae I I html Problem Set 1 a 10011 1 b 1001011 2 a 55 2 b 25 3 a 0011 3 b 00001 3 b 0000100110011 4 a 0765625 4 b 04375 5 a 10011011 5 b 100101100010011 6 a 55765625 6 b 254375 Chapter 0105 Floating Point Representation of Numbers Multiple Choice Test Answers 39agt 9959 OUIJUJUIJUgt You can see complete solutions by taking the test online httn39 numru39 encuf 39 Wlaaenni Olaae 39 39 html Problem Set 1 0 0 0 1 1 0 0 1 2 775 31110101110 4 102 5 a01250125 b15 15 c0125 d0 0 0 1 010 e0 0 011101 046875 g 007142 This value is less than the machine epsilon of 0125 The relative difference between consecutive numbers is always going to be less than the machine epsilon Chapter 0106 Propagation of Errors Multiple Choice Test Answers 1 B 2 A 3 C 4 B 5 C 6 D You can see complete solutions by taking the test online httn39 numru39 encuf I qqem i Olaae I html Problem Set No problem set for this chapter Chapter 0107 Taylor Series Multiple Choice Test Answers 6 9959 DJgtUJOO You can see complete solutions by taking the test online httn39 mmm39 emu f 39 aae rmquot Olaae tavlor erie html Problem Set No problem set for this chapter Chapter 0201 Background on Differentiation Multiple Choice Test Answers 1 willbl gtDgtUIJOUUU You can see complete solutions by taking the test online ht m39 numru39 enuu f 39 erifnm39 dif html Problem Set 138 230 330 5 4 7 5x 32 5 0099174 632 78 8 0090158 2 2x 10y 474X444437 x 2yx2y y 7 2y2x4 6x3y 6x2y2 3x313 74y2 3y3 x2 2xy 2y3 11 So the critical points are x 5 x 15 x 1 The maximum is at x 5 minimum is at x l5 12 10667 13 4 Chapter 0202 Differentiation of Continuous Functions Multiple Choice Test Answers 1 D 2 B 9595 000C You can see complete solutions by taking the test online ht m39 numru39 emu f 39 eriFrmi dif cnntinum html Problem Set 1 14869 2 a 11657 01657 b 08207 01792 c 099334 00067 3 l0003 abs rel approx error 00271 4 a 07143 msz b 07174 msz FDD 071 11 ms2 BDD 07143 msz CDD c 00255 mszusing CDD 5 098327 6 01 Chapter 0203 Differentiation of Discrete Functions Multiple Choice Test Answers 1 D 9959 OUIJOOU You can see complete solutions by taking the test online httn39 numru39 emu f 39 eriF rmi dif di crete html Problem Set 1 a 55556 b 92 c Cannot be done 2 In ms2 22704 25370 25152 True errors 24814 018498 0032927 3 In ms2 22704 25370 25152 True errors 24814 018498 0032927 4 4533 ms from CDD 54 024ms if using third order polynomial interpolation 5 60442 ms2 ifusing 3rd order polynomial for location 60444 6 257437 kgms ifusing CDD ifusing 3rd order polynomial 300354 kgms Chapter 0301 Background of Nonlinear Equations Multiple Choice Test Answers 39agt 9959 GUJUUJUJ You can see complete solutions by taking the test online ht m39 numru39 encu f 39 quot quot html Problem Set 1 15 1 4 roots are 0062378 014636 0043737 Only X0062378 is acceptable as the root needs to lie between 0 and the diameter D011m 5 a 2 b 33149 s c 50175 s d Modeling of eqn must be wrong 04800000000 1010 Tf 0004973504000 03720000000 107 sz 6 000007200000000 Tf 0 Chapter 0303 Bisection Method Multiple Choice Test Answers 9959 OOOOUUJ You can see complete solutions by taking the test online ht m39 numru39 encu f 39 quot quot39 39 html Problem Set 1 I Iteration Root Approx True Rel Approx Rel True Estimate Error Error Error Error 1 205 005 25 2 1875 0175 0125 933 625 3 19625 00875 00375 445 1875 2 a 0055 00825 006875 b na 33333 2000 0 na 0 0 d Since the diameter is 011m initial guesses of0 and 011 are good 3 Iteration Estimated root Ea Vtms 1 4500 027221 2 2750 63663 053944 3 36250 24138 037247 4 See book 5 The equation has no real roots 6 125 Chapter 0304 Newton Raphson Method Multiple Choice Test Answers 9959 00030003 You can see complete solutions by taking the test online httn39 numru39 encl f 39 quot html Problem Set 1 Iteration Root Approx True Rel Approx Rel True Estimate Error Error Error Error 1 21667 01667 8335 2 20064 0 1603 00064 798 032 3 20002 00062 000002 031 0001 2 a 15236 16058 b 02260 3 a 006233 006237 006237 b na 006413 0 0 if only 4 signi cant digits were carried in the calculations c n a 2 4 as only 4 signi cant digits were carried in the calculations d Since the diameter is 011m a value of0 or 011 seems to be a good guess but these guesses give division by zero So 0055 is a good choice 4 024696 5 98012 6 Takes 6 iterations Root at end of 63911 iteration is 7100 with absolute relative approx error of 0014 Four signi cant digits were used in the calculations Chapter 0305 Secant Method Multiple Choice Test Answers 9959 GUJUIJDgtDgtO Chapter 0306 False Position Method Multiple Choice Test Answers 1 PPR59 00gt3gtUUJ Multiple Choice Test Answer 1 You can see complete solutions by taking the test online eweww wwgtgtgtc hnn mmm39 enm f Problem Set nwkp15 1 8 2 A 9 j 391862 9341 3A7 625 364 392400 4A23 90 0052 0036 3910000 01 000 M00 100 000 10 00001 6 A 7 A HAOOOROOCN NOOONWNO 8 None of them 37 10 9a 11 33 34 39 12 3 9b C 4 Kzntucky Sam um 10 Mechanical1168 11675 1209 McFat chholzs tml Civil 8937 8961 9319 Thus Burcholesterol is the cheapest for the mechanical department and McFat is the cheapest for the civil department 1994 2306 11 C 502 2094 582 2194 12 in nite solutions 13 14 Yes 15 No 1 1 1 J 2253453 0 1 3 C 0 16 006 008 011 D 19074057 06666 17 03333 0 0 025 0 0 0 0 020 525 19 X 4906 50072 1666 06666 0 20 21151 1333 03333 0 0 0 007692 Chapter 0406 Gauss Elimination Multiple Choice Test Answers 6 9959 USUUIJCDO You can see complete solutions by taking the test online hTTn39 numru39 enm f I quot4slequiz sle quot I I html Problem Set x1 3 1 x2 13 x3 1 x1 3000 2 x2 l300 x3 1000 3 15005 4 84 x1 3 5 x2 13 x3 1 1 2998 6 x2 1299 x 1000 Chapter 0407 LU Decomposition Multiple Choice Test Answers 9959 wwooagt0 You can see complete solutions by taking the test online httn39 mmm39 911911 f 39 041p rmi sle 39 quot html Problem Set 1 See book 1 0 0 4 1 l 2 LU 125 1 0 0 025 325 15 2 l 0 0 4 029310 0169379 0025862 3 A 1 01551 0060345 0043103 05 025 025 1 0 0 25 5 4 4 L 3 1 0 U 0 8 4 05 l1875 l 0 0 2475 5 Since the all 0 the rst step of Gaussian elimination will involve a division by zero 4 1 1 6 U 0 025 325 0 0 4 Chapter 0408 Gauss Seidel Multiple Choice Test Answers 9959 0303003003 You can see complete solutions by taking the test online httn39 mmm39 911911 f 39 14slequiz sle gau eidelhtml Problem Set x1 10380 1 x2 19377 x 30328 3 The absolute relative approximate error at the end of the third iteration is 10380 21383 10380 10599 19377 18791 19377 30216 30328 28700 3 3 30328 53676 The maximum absolute relative approximate error is 10599 a 1 x100 gtlt100 N gtlt100 2 At the end of the third iteration the estimate of the solution vector is x1 80180 x2 13340 x 65858 The absolute relative approximate error at the end of the third iteration is 80180 20276 80180 74712 13340 36550 13340 72601 65858 15 118 i 65858 77044 The maximum absolute relative approximate error is 77044 X 100 a 1 X 100 2 X100 3 3 At the end of the third iteration the estimate of the solution vector is x1 26982 x2 79861 x 013697 3 The absolute relative approximate error at the end of rst iteration is 26982 0027994 26982 10104 79861 35741 79861 55246 013697 21750 i 013697 16880 The maximum absolute relative approximate error is 16880 X 100 01 2 X 100 a gtlt100 a3 Chapter 0411 Cholesky and LDL Method Multiple Choice Test Answers 9959 OOUDgtUUZJ ADBDAA 0L2 789111 Chapter 0501 Background Multiple Choice Test Answers 6 9959 UdDgtUUU Chapter 0502 Direct Method Multiple Choice Test Answers 6 9959 gtDgtUOUJ You can see complete solutions by taking the test online httn39 numru39 encuf 39 05inn direrthtm Problem Set 1 2386 ms 2 2060 ms 3 1730 ms 4 18287s or 22028 s 5 24875 ms Intermediate answers a025008 a192636 a250770 arguments of sin are radians 6 a 39369 ms b 39219ms 038247 2 sig digits 0 39205 ms 0035561 3 sig digits d Exact 39208 ms True Interpolant Error El 1st order 161 2quotd order 011 3rd order 03 7 a 30914 msz b 29784 ms2 0 Method 1 26723 m by integrating 3rd order polynomial interpolant Method 2 27042 m by Trapezoidal rule with unequal segments Other methods are possible too 7 average method is unacceptable Chapter 0503 Newton s Divided Difference Polynomial Method Multiple Choice Test Answers 9959 gt00UJOUJ Chapter 0504 Lagrange Method of Interpolation Multiple Choice Test Answers 9959 gt0UJUJUO Chapter 0505 Spline Interpolation Multiple Choice Test Answers 9959 00000031 You can see complete solutions by taking the test online httn39 numru39 encl f 39 lWinn nlinehtml Problem Set 4 2 1 0 0 0 a1 475 9 3 1 0 0 0 b1 525 0 0 0 9 3 1 CI 525 1a 0 0 0 36 6 1 a2 45 6 1 0 6 1 0 b2 0 1 0 0 0 0 0 c2 b 1 a b cl 1 0 5 375 2 425 25 42 yx05x375 2SxS3 425x2 25x42 3Sx 6 c708 2 a c08125 g 1625 h28125 j235 k 2285 l570 b linear4375 quadratic3955 3 g526391 4 023133 5 56965 Chapter 0601 Background Multiple Choice Test Answers CNUIkamr gtUIJUUUUJ You can see complete solutions by taking the test online httn39 mmm39 enuuf 39 Krennui reg html Chapter 0603 Linear Regression Multiple Choice Test Answers CNUIJkUJNt I gtOOUIJOO You can see complete solutions by taking the test online httn39 mmm39 enm f 39 W39Pn nm39 reg linearhtml Problem Set 1 l 2 30 Nm 3 006567177500 4 1655 Nm 5 0994 6 1828 GPa Chapter 0604 Nonlinear Regression Multiple Choice Test Answers 9959 OUUIJUJCDUJ You can see complete solutions by taking the test online httn39 mmm39 emu f 39 rm rmquot reg nonlinearhtml Problem Set 1 30213 p049101 2 097450 Nm2 3 Follow the hint 4 K158406 K2 4 9439xlO394 note the units for strain for which this K2 is valid is uinin 5 k112053 k2 013395 6 a 461851029069t b 31430 months 11 8p94136e0391199t 9 W003642t216659t77810 W36041102 10 A15502 11 5253 km Chapter 0605 Adequacy of Regression Models Problem Set 1 a 37306 ft3s 434 b 39496 ft3s 127 0 39322 ft3s 083 2 069441 3 C 4 All are in range 5 Check residual plot to reject it 6 Use Va1r020502 a 64082 ft3s b 24032 Zs 0 get 50266 by average method get 39322 by integrating formula 7 a 01219E10TA206313E8T06023E5 b 00137 not enough 0 00244 enough Chapter 0701 Background Multiple Choice Test Answers 1 A 2 D 3 B 4 C 5 C 6 D You can see complete solutions by taking the test online httn39 numru39 encuf Y39I html Problem Set 1 0 2 50404 3 027058 4 00031019 in 5 16391 0F 6 51750 Chapter 0702 Trapezoidal Rule Multiple Choice Test Answers 1 A 2 C 3 C 4 C 5 B 6 A You can see complete solutions by taking the test online httn39 numru39 encl f I Y39I 39 html Problem Set 1 14033 2 33875 3 a 94932 m b 10251 111 0 75790 m d 0073933 e 73933 1 10044 111 g 54865 h 0 4 042101 5 a 010075 b 012778 0 010719 d 0027028 000644 6 M 7 20280 m 8 47386 9 038887 10 1875 11 b3a33a2 Chapter 0703 Simpson s 13 Rule Multiple Choice Test Answers CNUIAUJNH 0303003030 Chapter 0704 Romberg Rule Multiple Choice Test Answers 9959 gtOOUJUUJ Chapter 0705 Gauss Quadrature Multiple Choice Test Answers 1 B 2 D 3 A 4 B 5 C 6 D You can see complete solutions by taking the test online hTTn39 numru39 encuf 39 Vr hfm Problem Set 1 a 035285 b 045812 2 a 10346 m b 10251 m 0 94458 m d 00092144 e 092144 f 10262 m 3 a 22049 0 b 652 m 0 4 clb ax1ba 2b2 a2 ab 3ba c 3b ab a2 1 4lbza2abl l ab b22a2 lczzab 2b2 ac1 a 62 6 a 6 b b 44750 by both formula and exact c 12976 by formula 10 exact x1 5 6 Chapter 0706 Discrete Data Integration Problem Set 1 2155 2 13923 by trapezoidal rule with unequal segments 3 9425 m3 4 97 m3 5 38477 ft3s by trapezoidal rule with unequal segments 6 a 014238quot b No needed contraction is 0015quot c Not a good assumption as the coefficient of thermal expansion is a function of temperature d trapezoidal rule with unequal segments012872quot polynomial regression0012897quot e cool in liquid nitrogen you will get an estimated contraction of 0023627quot Chapter 0707 Improper Integrals Problem Set 1 Answers will be different We broke the integral into two limits of integration 22 210 Approximated upper limit as 10 Used 2pt rule on each integral Answer 75330 Exact is 73890 2 Answers will be different Imade y1x3 change of variables Got answer as 059716 3 18415 exact17683 4 Answers will be different We made y1x change of variables Got 045455 Exact is 046210 5 Errata Lower limit is 2 Use 2pt rule and got value as 49520 Exact 6 6 Answers will be different y11t change of variables Broke integral into two limits of integration inf1nity0 0inf1nity Applied 2 pt rule for both Got 059695 Chapter 0708 Simpson 38 rule Multiple Choice Test Answers 9959 03gt0w03gt Chapter 0801 Background of ODEs Multiple Choice Test Answers ONUIkamr UUIJJgtOODgt You can see complete solutions by taking the test online httn39 numru39 encuf 39 Rode ode html Problem Set 1 y 687560 1875equot 2 a 5 b 7 c 014699 1 020872 3 y 316 2425e 3 025e 4 y e 0 75 5292237cos x 6859588sin x 0 109589 sin x 0292237 cos x 5 y e 69986cos3x 83403sin3x 0038462x2 0023669x 00013655 6 580431n6 26963 70370 111612 239646 65478 X106 a 2104tan 1 198786 300 t 51921 19 11982 b 13696 K c 1 2500K ii 22072 Ks iii 13913 W iv 13823 W V 27736 W d No as the rate of heat lost due to convection and radiation is of the same order Chapter 0802 Euler s Method Multiple Choice Test Answers ONUIlkUJNH USODgtUIJDgtUJ You can see complete solutions by taking the test online m ethnd htm httn39 numru39 encl f Problem Set 1 32945 2 a 3371 b 50539 c 014699 d 21976 e 020872 1 23214 3 a 16581 true error21906 b 25842 true error12645 4 16581 same as LRAM 5 a 27737 In b 15182 minutes c part a exact 29371m 55623 part b exact 19415 minutes 21802 6 a 2500 K 22072 Ks 13913 W 13823 W 27736 W b 12523 K 54568 Ks 87344 W 59838 W 68572 W c No as rate of heat lost due to convection and radiation is of same order d 22654 s Chapter 0803 Runge Kutta 2quotd order method Multiple Choice Test Answers CNUIbUJNt I gtUJDgtODgtUJ You can see complete solutions by taking the test online httn39 numru39 encu f 39 2nd method htm Problem Set 1 y6 m 23684 2 a y25m 35433 b 53031 c 014699 d 23106 e 020872 f 24408 3 a 45446 18083 b 40274 46441 4 45446 MRAM 5 a 29282 m b 19248 min c part a h29371 029795 partb t1 164 87 s 6 a 2500 K 22072 Ks 13913 W 13823 W 27736 W b 13819 K 6441Ks 12963 W 67978 W 80941 W c No as rate of heat lost due to convection and radiation is of same order d 31591 s Chapter 0804 Runge Kutta 4th order method Multiple Choice Test Answers CNUIbl Nt I gtUJODgtOUJ Chapter 0805 Higher OrderCoupled ODEs Problem Set 3 a 3 2 2 b 38750 081970 32685 0 36958 069213 30893 4 37067 In 067811 ms 31001ms2 Chapter 0806 Shooting Method Multiple Choice Test Answers 1 A 2 A 3 B 4 C 5 A 6 B Chapter 0807 Finite Difference Method Multiple Choice Test Answers 1 A 2 B 3 D 4 D 5 A 6 B You can see complete solutions by taking the test online enonsf J 39 08ode nite dif mPThnd hT m httn39 mlmru39 39 quot J Chapter 1102 Continuous Fourier Series Multiple Choice Test Chapter 1103 Fourier Transform Pair Frequency and Time Domain Multiple Choice Test Answers 9959 GUJUUJOU Chapter 1104 Discrete Fourier Transform Multiple Choice Test Answers 1 B 9959 UUJDgtU0 Chapter 1105 Informal Development of Fast Fourier Transform Multiple Choice Test Answers 1 D 9959 CDUUIJCDO

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