EMCH_407_Topic_1_Part_1

EMCH_407_Topic_1_Part_1 - CHAPTER ONE Introduction Modeling...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER ONE . . Introduction Modeling, analysis, and control of dynamic. systems have interested engineers for a long time-Within recent years, the subject has increased in importance for three reasons. Before the invention of the digital computer, calculations required for meaningful applications of the subject were often too time consuming and error prone to be seriously considered. Thus, gross simplifications were made, and onlyrthe' simplest models of transient behavior were used, if at all. Now, of course, the widespread availability of computers, as well as pocket calculators, allows us to consider more detailed medels and more complex algorithms for analysis and design. - Second, with this increased computational-power, engineers have" correspond- ingly increased the performance specifications required of their designs to make—better use of limited materials and energy, for example, or to improve safety. This leads to the need for'more detailed models, especially with regard to predicting transient behavior. Finally, using computers as system elements-for measurement and control now ' 7 allows more complex algorithms to be employed for data analysis and decision making. For example, intelligent instruments with microprocessors can now calibrate themselves. This increased capability requires a better understanding of dynamic systems so that the full potential of these: devices can be realized. ' 1.1 SYSTEMS The term system has become widely used'today, and as a result,” its original meaning has been somewhat diluted. A system. is a combination of elements: intended to act together to accomplish on objective. For example; an electrical resistor is an element for impeding the flow of current, and it is usually not-considered to be a system in the sense of our definition. However, when it is used-in a network with other resistors, capacitors, inductors, etc, it becomes part of_-a system.“ Similarly, a car’s engine is a system whose'elements are the carburetor, the ignition, the Crankshaft, etc. On a higher level, the car itself can be regarded as a system with the engine as an element. 7 Since nothing in nature can be completely isolated from everything else, we see that our selection of the “boundaries” of the system depends on the purpose and the limitations of our study. This in part accounts for the widespread use of the term system, since almost everything can be considered a system at some level. ' The Systems Approach Automotive engineers interested in analyzing the car’s overall performance would not have the need nor the time to study in detail the design of the gear train. They most likely would need to know only its gear ratio. Given this information, they would then consider the gear train as a “black box." This term is used to convey the fact that the details of the gear train are not important to the study (or at least constitute a luxury 1 N EHwOUCQHHOZ 80% 0803 0.3.0005. .H.H.HOHH 20:8 00 meHmHHQH 00 80m 0.0 HHH0HH 0008 008008 80 83:0 000 00000 H: HHH0 8:0. @800 80 8300 .80 0000.0 0H 90 00:0 0H8? H00 EmanHoHH 000009 H0 0000520: 8 firmH H80 H000: 00:00 HHH0 205.880 0008000.. 8 08208 0078,”. EHHHH HHHHH 0000000? 000: 0H0HHH0HHH H0 80 $20.0 Hm H3200 00 0 200w H0000, 000 80 HHHHHHHuHmHm 80:000.. 0.: H52 008002000 00800: HHH0 0H0HHHH0HHH0 HHHHHHH0000 80 088: 00:05.80. 2. 80.. $209. :0 <H0H<H00HHHH 88:00 0 00:08:00.0 8 00002.. HH H000 008:3 00000880 0H,. HHH0 0008300 0H. HHH0 HHHHHHHHHHHHHHHH 0H0B0HHH0. H: 9.000 8 003040 HHHHm 0008: 0000380018. .H.HHH0 103083 000 H00 80:00 H0 80 080% 08:09. maHHHHnHmH 00 008me $2080. .HH H.0HHH00H0 HHH0 G0HH0H HEHH HHHO 0070280 0m 0008an $3880 H0 H0000 £0 00 0me0 0000500 002030 HHHHHH 30 00038500 3 000: 05802 mum 00.0 H00 mHHHHHH0nH 0:0 0H m :80. .000 0000300 0% m HuHmansHuoHH 0H080HHH H0 0000500 315 8080288 108200.. >8 HEB: H0 0 002.8 00 0088. H0 HHHH $.02 80 8 HHH0 HHHHHHHH. .HHHHHH 80 80510085 H.0H0HH0HH 08000000 HHH0 0800-80-032 005280 0H. HHH0 0H0HHH0HHH. HH.0H. 08810. n <0HH0W0 0 38:00 8 0. H.058” Ha 000000 0 00203 H. 8 H82. .20 HHHHHHHHIOHHHHHHHH 0H. 00:me 0080.0: H0 H.“ 35. :0 HHHHHHHH H0 0. HHH 0085 H0 H. 0:8 :0 805.0088 008:0: H0 80 9.000005 0nHHHHHHH0HH. wan—n UHHHNHHHHSHH .20 200803 HH.0HHHHHH.0HHH 00 00 0H0HHH0HHH 0»: H00 08000000 mHmHuHHHomHHHH. 00 0:02: HHH H0850 H .H. .30 00a 000000003 :0 08802. HHH0 05.02 0=H0H.H=m HHH0 00» 000000003 HHH0 HHHHHHHH. H80 90 000 H0m<HHHm HHH0 00x 08000 «0.. 8.0 0085. 8080 80 00x. 20 H0800 HHH0 803080203 080009.00 HrmH 00880 :5. 0:65 8 H70. :85. Hm HHHHm 0800008: H0 :2 80. 0080000080 000. H0 H8055. .H.H.HH0 mHmHHHHHomH 000000008200 H0.» 20an $0.088. .25 HHHmmEB HHH . HuHmHHHd :0 000000030 80 n00H08H. HH..HHHH HHHHHHHH 0 000. 008.: H. H03 000 00880 E HHH0 000082 HEN. HuHmHHHd :0 0:020 H00 000000008300 Om m HEHHHm 2:000 H00H0HH0m H0HHmHH0 H.900 H0 Hm 080000000: 8 HH... 00200080 x 00 HHHHHH RH Hen. mHmHHHd :0 0003.0 :02 0 H080 .H. 80:00 8 0 H0000 E 000000 HHHH 0000H0Hr 0:0: 0. .90 m0<0HHHHHHm H0HHHHH0HH H0 20880.0 Hmfixfl .30. H0 0088 0 H.008 .H.. 000 803 BcHHHuHHH 80 HHHHHHHH H. 3 80 000. mHmHHH CS. .380. HHH0 05.:on HHH HHH0 00% 000000008 80 000830: HHHHHH HHEmH 00 H000- 80800 0: H00 HHHHUHHH 8 0888.80 0:82. 22 m: £090-00» 0000000083000 HHHHHmH 00mg 8 manmH 00mean 208030. MES 80% 080000 0050-08-03.02 H.0Hm- HHH0 HHHHH0 H3003: 3. 00012330. 3 3000 80% 000 00 0000 H0 aHmEmHH 08000000 501000503 00 :5 HHS... H3003: 0H. 0.... 20: 00 008000008. H20 080800 00 H0505. 0.2.0 8.0 0855 8 HHmHHHdHH HHHH 000 :0. ill. .llvfilfH. HIV—w]... . . l-lv End—"H uh .chan $0535 0.. H505! 0:85 . 008:3? To <0HHmn0|0=H.H.0HHH 88:0: 80 a H.00H08H.. n3 GHQ—00050:? “0000 00—08: H.0H. a 011.55 02.8008? 0.03ch "0.38: H.0H. H 50%. AS «H0805. 00 H.H 000.0030 u HH. :0 8.8me8 .80 000083.300 0 9.00 HHHHH0. E0 0088 80 <0H00HHHH 0. HHHHHH Hm. 0H.... 00.0. .280. 0.0008820: H0 H50 00.000 OH. 889%. mHHHHHHmHHF HHHHOmBHHdm <0H00HQ 080.0000 $880082: H0 HI T28 .90 H=H0mBHHoHH 20000.80 EHHHHHHH own—H cox HHH Emma... :0. 0.8 :0 08000000 8000 H.003. $0009.00 00 0085 H0 80 HHHHH0 HHHH0mH.HHH 0H. HHH0 HHHHHHHH. 80 06803 H0 008 8 $38: HHHHmmEH 005.023.. 20 EH: 000 83 HHHH0mBH omcmmHHHuH noanHHHHSm m HummHo H.008 0H. anHmmHHHHH H.0H. 0.: 0?mean $0880. .25 HHHHUHHHIOHHHHHHHH HOHmHHoHHm MB. 0000 08303 08500 m B080. 2. H800HQHHHm :0 00803800 008.000 :0 $0803.... 2000 00000200 8m0HHH0H. 8 H.050 m @308. 80 HHHHHHHHHH H0 0030 0H0HHH0HHH0 SH: 00 80 00806 H.008 0HHH0H. 0H0HHH0HHH0. H000 08520. 80 domHHHoHH on 0 0000008080 000%... H0 000000— HHHH 80 03.0 8000. .280. 8H. 80 000305080. 08805. :6 000.0. 800m H0 0.: H098 $023.00. HHH0 .8000 H0 H00 H.000: 0.. 00:00 0m 80 0H.H<0 HEHHH 0H0HHH0HHH. .90 805008.: Him—H80 0H5 0080HHHHH00 H00 00.000000 EH. EH 0H0HHH0HHH. 9: .02 03.30. 20 000 030; 0. 000002 00 HH.HH0_.HH 8 m H.00H08H. 000 0000800 HHH0 8.5000 080 8 00.30 0085. O: HHH0 0HHH0H. HHHHHHHH. 80 08:80 0H. 80 0000008080 002:0 anH HHH so 23 HuHHHHmHomHHHH H0m00000 H30 00000 0H. :8 03.. HHH0 $038 HHO0HH.. .08 HHm<0 HHHHEHm. mam 008:8. H0000 0.00 00808800 g :8. 00H00HH0HH 0H. HHH0 $308.0 00000030 >3 000000 0.28m 0: H30 @085 H.H.0HHH 80 (<0an 0HHH0HHHHHH H0 HHHHm 000.08% 08 000080000 8 00 $02.08 HHHHHHHHHH. mHHHHHHmmHHH. 0 $083 0 00850 0.0: H00 HHHO 0080.3 H.003 0.3. 000 9. 8000 0H. 2.0 108030. $020.0. 5 HumHHHnHHHmH. H.008 05080 80 0.2088. 0 00000030 HH. £0 88 HHHO 000. 2580 8 H00 HHH0 $038.» $308 HHHHHHHH H88 H00 :0 H0830 womHHHop 00830800 3H 80 00003008: 000%. 08 0 020.88 0085 €0ch H00 80 8500 0030000 8 HHH0 03.0 0002:: HHH0 0010 HHHHSHH 8 H00 .HHH0.0HH0H0H.HH.HHHHH0EH. :8 H005 €008 mHHHH H00 HHHO H0003 HuomHHHcHH. HHHHH HHH0 oHHHHHHHHm HHHHmHHH H00 HES: 8 a0 :5 000.0 H000HHH0HH. H0805. 80 00000880. C0005. 0H: 0HHoH000 8.. @an8 0085.0 000 0. 080$ 0m HHHO H0000HH0H0 0:850. 000 000 :5 81880 HHH EHHHoHH 50 0:0 HHHH0H00H0HH. .012. 08830. 0. 09.8an000 mamemHm 0m 80 000 0808 000803 H.005 0: 8.... 0.0020830: 00 <0H00HH.<. 00H 00H 00 HHH0 000.0 00330:. . > 2.810 08:60 0H. 0 $300.. nHHmmBHHH Hm 081000 HHH Emma Hb. 9600.00 .0. H0000 H3 H0 0000023 8 000 000 2. m munHHHm. HHH0 082 000 0a 80 885 Hm 080000 8 m HHmHHH .8283. H0 8050: 8 80 0010..“ 8000 H... 000801.080 H... 00$ 0H. 80 8009681080 Hm 000080000 8 H00 0.00 8 H50 0xH0HHHHHH £010 000 0on 008mm 80 8208 000835? . HHHHHH. .0. HH H0 02 m0HH0HfiH0nH SH 03‘ 028: SHHHHHHH H00 $208 H80; HH 0.0me H00 0:0 8 mamas: 8H. 08810. .25 00:00- 000. 0R00H H.0H0.HHOHHm 00: .00 008801000 3 HHH0 02085 HHHmmEHHH. HHH 30.800 H. EH. HHH.0 00H 880 00 25 8000 H: 80 0:00:00 0m 000HHH<0 HHHmHHHHHoQHHQHH a Hm N... we...” % 3000 00...._HHO: EOCWH H.“ 90 3000-001...“ 3035 EHHHH a: 9088...: 880% . EH 50% 08000:. cm HHH0 00:9: 00:585.. HS A 020.000.00.052 01 a i a... 00000 000 .610m (3: 00: 00 00 000 0.000. m. 000 00000 000000 00 00000. :00 000" 000.300 On V 9. H00 000300 000 00020000: 0m 0.00000 00 00.00000 "00 0000 0.00.00 0.00 000000000000 0% 0 000. £00000. :0 0050000000.}:0 000000 80000 0055 mm .000 05000 0000 0—. 50 000000. H00 0001i 0M0 000000000 90. h. 0.. 00. 00 00000“ 000 00000 HIV 0% 00000080 0.00 05.. 0 8 00 000200000 0.0 00.00000 000 001.0000. H00 0000000 0000.” 00 b“ :0 00000” 0005 00 00% 00. 0:00a 90 0000200 000000000 2500 :00 0000000.. 0.4 5.0 0000 0000000000 00 000% 90 0010003000 x. 500 :0 0:00. 00 0005.0 _00<Em 90 350000. . $00000 0000000000 0000 00 :00 000 0 000003 000000 000.00qu 00. 000 00003000 . 002.000 000 000000 000 000 00.005. «<0 00: 000 00000 0200.. 30.000 050 c.0509? 3.00050 H0 W000000. ”00 0000000 £000 00 00 000000000 0065 mm 000 0.000: 00. 0.000 000 00000000 00 00 0000000» 00 90 00mm 00 0.0: 00 0.000 00 00.000003 00.00000 0. 0000 0008000. 90 00.00000 0000000 on 0 00—. 00—0000 00 $000.0 0 000100 000 £000 :0 4.000000 000 0000 @000 000 000:. $0 00000 0 35050.0 $000000 3 00 000 0.0000 0000000 00900 0000000. 00 0000 000000. 0000000000. 0 .0000 000000.” 00 000 30000 000000 00 00% «0.00 900 . 0000000 00 0.0; 30 0002.: 0... 90" 0.000. 000.. 30 000 000,009.00 0m 00 00000000 SE» 00 000000000000 00000 0000300 00 0000» 000 000. 0000000 00 00.305. :00 00000005 000000000 00080 .90 00000000 8 00 0000200. 00 E0 0300. 0000. 0.0 000 00000000 0 000080 8 00 0 00000 00000000. 0000000 :0 000000» 002.00.... 0000000 00 00; :00 40:0m0 0000000 .0” 000000». 00" 00 000" <0:0m0m. . H.000 00 00 0000000300000. 0”. 000000. 0000000 .0000 0.000080 00000» 0.000000 00000000- 00000? 8 5:000 0000000. H00 00 :00 00. 0: 030000. 00000005. 000 0.0 00000300 00000000 0000 0 .3000 0000000” 00 00 0000000000000. 2000300000. 0 00 0000? 0000. 0000000 w 0.00500 00 0 00.00000. 0003030000_ 0000000000000. . H0 0000000 =m0m0. :00 00000 0000.0 0.00 0050300 0000050000 00800000 00 00000 00 000000 00002 0.300 00000 :00” 000 003.000 8 0000000 00.00 00.0. Ham 0000.0 0000.00.80 00 00 000000000 000000000 0“ 00000 "0000 m :00 00.0000 0000000000000 00 5000. > 00000 0000000; 00005 000 0000m0 00:0 0000 00:. 0. 50 0000.” 0000W00 000 .00: 00» 0000m0 .0. 0.0 00000 00 00000000 00. 0—0000". $0000.00. 0. 90 0000.0 00 00000000 9. 00,009.00 #05 0 0000300 00000000. :0 00:00" 000 00: 0000.00. 0000 0000.030. mm "0.0 000.0 00%00 mm 0.0.000 00.. :00 000.0 00000: 00: 0000000 00 0000m0 0000000 00. 000 000.0 0.0000me $000000 00. 0000 00003. > 0000000. 0008.00.00 000000 00 3000 m0... 000 0000300 0000080... H0 30 000.00 0.0%. 20 0000 000000 00. 00000 000 00.00000 3000030. > 00000 0200000 00000000 0: 00000 00030000. >00 8000000 0000 00000000 0.10000 000 0000000 0000000” 00. 0 0000000 83003. . , g.- C . 030000040. 02000000. 020 002.5000 «<0 :00 00 0 000000.00 0.00" mm 0000nmow0m 00000000 000000. H000 00000.0 00 0.00 000.000 000.0000" 0% :0 0000 00000 mm 0000 000000. 0000 00 0.00 0050 m0000m0 000000000. 00" 00 00%00000. 0.0 0000” 00.000 00...: 0.00 000000000 0.0000 000000000005 00.003 000 000002.000. 0.00 00000000. 000000000. Em000000 08000000 8030.030 0000 00.0000 00000000 00000000 90 000000000. 300000 000 3 Em: 000000000000 no 00 050: 00 H.» EOUMHHZA“. >2>F4mumu EU DOZHWOH m 0000:0000 .000 000 00.0. 0.005%. €000.00. 0000000000000 0000500. 0". P00 000. 000 0000 000000.00 9.0000000 00000000000 00.090 2.00 000050 0m :00 «0.00000 0.. 0 000000000 00.00000. 9.00 0 0.000000; :fi000005x. 03000. 0000 00 0 010m? B000 00 0005000 "0 0000000000000 :00 0000000 000 0.00.000 00000000 .3. 0 0005. .0500 0000. Seaman—N . 00 00.000. 00 0000 m0 0 0000000000 000 00.000000 €000 2:0 00.050000 03.07000 E00. 0000000000 0000300.. 20 5000 000.0 0 000010000 0a 00 00.00000 00 000000.000 00067.00. 20 00: 00.00 0 000000000 0 300.00 > 000000 0.00 000000000 000. 00008000000m 00. 0.0 00300000. 000.0000 0000000 0.0300. > 030000 0.00000. ES 0. 00000 000000. 00:00 00 00 5000000 002 :00 000000000000 0% 0.00 00050 0.: nomflrfl. 000 000 000100 000me5 03 0000000000 0.0.00.0 E00000” Hfirmnr m0 000.900 000000 0.023. 000000 00. E03 000 00: 0000000 .500 0m 000000. H000 000 940.0 30000» 0000000000002 0000000000 0 000000 £00. 000 won 300 000000.00 $0: 0.0;... 00 00000 0005; 000000.003 $00 0000* H00 50000 @000 0.0 00: 000 00000 0.800.005 mm 50 Satainmnnw 08000. 00000 00 0 00001000.: .00 00300 00. 0000000000000 005.0000. H0000 0.0000000 00: 000mm: 05 050000000 00. 05.00.0000 00000000 m 000 000000 mm 8 0000000 0 0000000 $00000. H00 0000000 0m 0 0000000000000 8000— 00 00000300? 300500. 0.0.00.0 000000303. . 0000000. 0000.000 0003000 0000.00 5.0 0.3000000300300008 0.00 0 0.00080. 0 H E. 000 30 3200000000: 0.000000 0.00. 0 000$ a.” 00.. 000 00. DE. 00000 000.0 mm 8 00000000 0 0.05.00.00.00 00.00 0:020 0000 000000000000 00 000900000000 0000000 m9. 000000.000m :00 0300000000? 00000000. 0». 0.000% 3600 0m 0000000000“ 0000 moi. "0020.00 000000000. 800000000 000000000. 000 00005000 $000.00.. 00 E0: 00 0000 0000300000 0000000000. H0 :00 000000.: 00 0.000300” 3 0000000000 0000 000 000000 00050 on 0 000300000000 ”00000 0000000 00 :0 000.0000. H.100. 00000000. 00 00005000 0000030 000 00 00.00080 8 00000000000 00300000000 : :0. 00000000.. 00000 0.. 000000000 8 1.000000. 00 :00 0000. E0 “0000-00000000 00000 000000 00.00 00 0000 8 0000000 00 000000} 0000000000 0000.000 H000. 80 000 0000 000 00050 00. 00% 0.00.000 000 0.000% .0003” 000000. 0000000000. 000030000. 000 00 0.020. 20 000900000000 000000 000 000: 005 0: 00000 “00000. 9.00 a. 0 000—0. 0 0.0000 00 0000000. 0000000 :0 0.00% 000.00me 800.0 0.00000. 0 000000000000. 20 000 0.00. 00 0003mm $000 00000. > E400 00%00 000 .00 00001000 3. 0 0.000 500. 0 002000 00040000 300. 0 000000.00 000000.000 0.000. 0 000000000 00005 0000. 000 00 00. > 00003 0.000 0000000000 0: :00 003300.000 0.0000 00 30:00.00 000 00000800 000000. 500000. 5.0 00000" :00 000000000 3:00 on 0000 000000.00 0.00 000 0000000 00 0000. H0 90 00000 5.00.. 0.0 0000.9 00 0000200” 0 000900000000 30000 8 00: :00 0000000000000 0% 000 030%. H00 000.0000 00 :00 0.00000 0000:... @000 90 00000000 0H 30 0000010 .0000 00000. :0 00m? 0000. 000 :00 000000000. 0.000.» 00q 000 03.00? 000000 8 00 00000000 9003000 00000000000. 00005000. 0.000. H00 0000 00000 00: 00 0.0.0 0000:0000 2000000 00 000 0.00. 00000000. 00.0000 000000 00 00000000. AH008000 200 000000 0000008000 0000- 0000000000 00000000 00 0 00000000 0000 00000 .00” 0.050 000 00 0000000000 3 00 00%002 0000m0m0m 0 010%; $8003.. 000 .0000: 0000 000.5 0000080 0.00.0 020:0 000000 00 000000 00» .00 000—0000. H00 0.0000000. 0005.000m 90 00.000000 0m 50000000 0000000030 00m? 0.000 0 000000000” 00 0 0000." 00000. 0.000.000 9: 00030000000 m0 0000000 8 0 3000:5005 00000000 00000000 000000.000 0H 90 000000000. 00000. 0 04600000052 .. E000 000.0530 00.0 0300 0000 8 0000000 50 0000000000000— 000000 00 0 0.050 0000 0:000 0.0 ”.0 0000000000 30 0000000000000 000.05% 00300.0 0000 33008.0 00000000. 0.00. 90000000v :0 00000000000000 000000 0m 90 300000100 $00000 0000.0 00 3050 _.N0 .00 brhusa _ ....DH..~AX. 270." 00“. M000 0000000 000000000 0 00.000-000-050" 00000000000 3000.0 00: 0m 90 300000. . H00 0.0%.000 0.0 0 000000000. 000. .05 0340 $000 8 0020 mo” 90 0000000000000 03. .00 0000 :00 0.000050 00000000 0000.0. Hm. .00 0500000000 E0 500 $40 0.0000000 20 0.00000 0- g... . . 00.... . . 00 I0 . .00. 0 I 0000 . 1: haw. . mcqmfiwfigm $00 000 0.00 000000 200.000. 008 90 0an W700 . 000 . b .| 00 H 5.0.0.0: . . ARV: .200 050000.000 00000.00 00. 0 0000000020 000010000 00. 90 00.00000. @0400 b. F 00“ 000 90 00:00— 0000000 .028 000 0.000000% 0A9. 00 000 :00 "00 30.0500 00. 00000 0000003 .8 0020 E0 0000.000 mom .03. 5.03300 > 00050300000. 000000 0000000005 0 0000000 200000.00» .00 05. 0060000000 0000000000.“, ”"00 00:03.50. 00. 30 000.000 00000 030%. $0 000 0000 2:0 30 403000000 0m 30 000000 00 000 £000. $010800: 3 000000000. 00 30.000 00 00000000000 00000000 00. 0: 000000 00am.“ 03.00000. .25 mm 00” 00.205 0000 00.. "00 05000 on 0 000.0% 000000.00u 000000050 0. 00 000.000000m 005 00500000» 3600 000000 00004000. 00 W002; 00 .00 30: 00000000 3 0 000030 000000 00 90 000.00 0». 0000 006010000. #000 00050000 20 00.0 00 0040 @3000 00 0005. 90, 0.00080 00.0000 0 H 0.0» 2:000» 0.0100000: 00 000m 00 000 0000.000m 000000.000 9000.000 004000, 880000000.an 08.0 mi 000 000.050.. .200 00 0:00 :0 0000 0.00 30 £000 0m 00020000 00 00: 00 0000000100. 00000 0.0 00: 00 00000300 200 90 000030000. 00.000000 000000000 00. 0000000008 $0000 000700000 00005010 00.000 20: . 000030000. . . 0000 S0 000 0000000 000.. 000 (00:05 0a 000 000000 0000000000 0000000v 000% 000 00 0000 .00 000000” 90 0003200000 0m 90 $0800 00 0000000. 30000000 90 000.503.0000 @000. 0 00000. 0.. 00:00 00030.00. 0000 0008000. 000 002.00.” 9.000000 00 0 0000030. 30 00 000000 05:00.0 0 000 00 00.00.0080 8 00 Mn 0% .3 00700m .00 0000000 . PM ZOUMHHZD. 0540:5055. EU DOZHWOH .N 000000 0.00 000 00W00€0 $00.20 0. 00 00.000 0m :5 0700 00000.02 0.000 m. 3000 00. 20. 0000000000000 000006 00: 00000000 300000 0000000.. 000 <1: .0000 0000000 0m 05.030000 00. 000.0308 3000000. @0000 00: 00.” .00 00 000030 00:0 00 000 Emmanfio . 000005.000 0000. 20402000000“ “00 000003000 30 000E§0m 0000 050000 000 300000. .. 0.020000. 0.0000 00.0 000300000 00 0000000. m. . HEW” 00 000 0000000 0050000 002G 0000000000 :0 300g 00 0000 0000 £00 05080. 00000000 000 $600 on 0000030000 000005000 0000 no 000000» 90 $0000.00 000.0300 0.0 mm 00” 00000040 0000000 9000 000000000 2:0 90 000000 0000080. 00.0000. 0000000 08 0000000 00, 00 000000. $0,000.00 20 .00: 00 090000005 0.000% 0600 00. 0000000000 ”0000500020000 000:000EQ 0000000 00 .000 000.0000 0.. 90 00000000. 20H 0: 0w 9000 000005000 0.0: 00 9.95030 .0000 00 000 000 00000000. 00» E0 00000000. 000000. 000 “000:": 000.. 0: 00.9000. H00“ 000 E0 "0000 00 90 0.000.|0 30000 00 00 000. ¢<0 SE 000 000000 5000. 00 0 00000030000000 05000u 0.9 .000: 0000000” 0080000 $00000u 00 00.: ”0000 00 090. 0.00. 000 0000 00 00.00000 .50 0003050000 0m. 0 0800000000000. 000.000 00 0000000 4.0002000 000 .055 0 500-00.000.30. 00000000. 1:00 0. 0000905 0.000303 .8000q 0500.00.00» 50003 000300.005 00000003 000 8.0 @3200 000 00000020 8 0:00. 305 .8 .00 000: 009050 "003000 0000500 0000000000. 000.0000 .. .200 00000000: 00000000 00. 0 3.0.0000 00000 0000m00m 00003000 0000 00000.00 0 0009.00 $000000. 009. 0.0000050 0.0000000 00.000000 00.00000 0.000000 0 ”000800900 .8 0:0 .00 00003 00080000. 00 9. 0m 00 E0 800. "0000000050 0000 000 3:0 $00008 0.3. 2000 0.00» .20 00<0 000 0000.00 0000 00000000000 00 000 00000.00". 0000000 0 00m 340 00000000” 3. 8..B0000H0 30 30090030000050 000 00000000 x .0000 :00 0000.00 00.00000nfid 000 A3 00 00000 $020030 00.0 .00 00.0000 00 0,. 0m. H00 4000.000 00 .90 0000000. 003000800. 00 90 0100000 0.00000 0.00 H00 0000000000000 0000m0 00 E0 00000 ”0000000050.. m. :00 005000 0000000000 2030000300. $0.00. 0000100000000. 08.0 0.00.0 000000000000 20 00.00 00050 0 00000100» 20000 0000000, 00000000000 00 000—0; 0000 0.0 0. 0000080400000 0.08 .0000 #0000 00000.0 "0 800000.90. 0.00» 0000 .5 “00 00.3000 00000000000 2.0 00000009. 20000 00 000000030. 00. 09.0.00.“ :00 0,000 0.5100000 000...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern