(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 93117, 2284]*) (*NotebookOutlinePosition[ 93790, 2307]*) (* CellTagsIndexPosition[ 93746, 2303]*) (*WindowFrame->Normal*) Notebook[{ Cell["\<\ 12.010 Lecture 13 (Fall, 2005)\ \>", "Title"], Cell[CellGroupData[{ Cell["Slide 03: Flow control statement forms:", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(If[7 > 8, x, y]\)\(\ \)\( (*\ Here\ true\ or\ false\ is\ clear*) \)\)\)], "Input"], Cell[BoxData[ \(y\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(If[x == y, a, b]\)\(\ \)\( (*Here\ the\ answer\ is\ neither\ true\ nor\ false\ so\ \ nothing\ is\ output*) \)\)\)], "Input"], Cell[BoxData[ \(If[x \[Equal] y, a, b]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(If[x == y, a, b, c]\)\(\ \)\( (*\ Now\ there\ is\ the\ neither\ true\ nor\ false\ option\ and\ so\ c\ is\ \ output*) \)\)\)], "Input"], Cell[BoxData[ \(c\)], "Output"] }, Open ]], Cell["\<\ Demonstration of using the Which Function. Here a the function is \ linear for values less than 0, Sin[x] for values greater then 0\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[ Which[x < 0, x, x \[GreaterEqual] 0, Sin[x]], {x, \(-2\) \[Pi], 2 \[Pi]}];\)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.0757881 0.485367 0.117953 [ [.04527 .47287 -6 -9 ] [.04527 .47287 6 0 ] [.19685 .47287 -6 -9 ] [.19685 .47287 6 0 ] [.34842 .47287 -6 -9 ] [.34842 .47287 6 0 ] [.65158 .47287 -3 -9 ] [.65158 .47287 3 0 ] [.80315 .47287 -3 -9 ] [.80315 .47287 3 0 ] [.95473 .47287 -3 -9 ] [.95473 .47287 3 0 ] [.4875 .01356 -12 -4.5 ] [.4875 .01356 0 4.5 ] [.4875 .13151 -12 -4.5 ] [.4875 .13151 0 4.5 ] [.4875 .24946 -12 -4.5 ] [.4875 .24946 0 4.5 ] [.4875 .36741 -12 -4.5 ] [.4875 .36741 0 4.5 ] [.4875 .60332 -6 -4.5 ] [.4875 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .04527 .48537 m .04527 .49162 L s [(-6)] .04527 .47287 0 1 Mshowa .19685 .48537 m .19685 .49162 L s [(-4)] .19685 .47287 0 1 Mshowa .34842 .48537 m .34842 .49162 L s [(-2)] .34842 .47287 0 1 Mshowa .65158 .48537 m .65158 .49162 L s [(2)] .65158 .47287 0 1 Mshowa .80315 .48537 m .80315 .49162 L s [(4)] .80315 .47287 0 1 Mshowa .95473 .48537 m .95473 .49162 L s [(6)] .95473 .47287 0 1 Mshowa .125 Mabswid .08317 .48537 m .08317 .48912 L s .12106 .48537 m .12106 .48912 L s .15895 .48537 m .15895 .48912 L s .23474 .48537 m .23474 .48912 L s .27264 .48537 m .27264 .48912 L s .31053 .48537 m .31053 .48912 L s .38632 .48537 m .38632 .48912 L s .42421 .48537 m .42421 .48912 L s .46211 .48537 m .46211 .48912 L s .53789 .48537 m .53789 .48912 L s .57579 .48537 m .57579 .48912 L s .61368 .48537 m .61368 .48912 L s .68947 .48537 m .68947 .48912 L s .72736 .48537 m .72736 .48912 L s .76526 .48537 m .76526 .48912 L s .84105 .48537 m .84105 .48912 L s .87894 .48537 m .87894 .48912 L s .91683 .48537 m .91683 .48912 L s .00738 .48537 m .00738 .48912 L s .99262 .48537 m .99262 .48912 L s .25 Mabswid 0 .48537 m 1 .48537 L s .5 .01356 m .50625 .01356 L s [(-4)] .4875 .01356 1 0 Mshowa .5 .13151 m .50625 .13151 L s [(-3)] .4875 .13151 1 0 Mshowa .5 .24946 m .50625 .24946 L s [(-2)] .4875 .24946 1 0 Mshowa .5 .36741 m .50625 .36741 L s [(-1)] .4875 .36741 1 0 Mshowa .5 .60332 m .50625 .60332 L s [(1)] .4875 .60332 1 0 Mshowa .125 Mabswid .5 .03715 m .50375 .03715 L s .5 .06074 m .50375 .06074 L s .5 .08433 m .50375 .08433 L s .5 .10792 m .50375 .10792 L s .5 .1551 m .50375 .1551 L s .5 .17869 m .50375 .17869 L s .5 .20228 m .50375 .20228 L s .5 .22587 m .50375 .22587 L s .5 .27305 m .50375 .27305 L s .5 .29664 m .50375 .29664 L s .5 .32023 m .50375 .32023 L s .5 .34382 m .50375 .34382 L s .5 .391 m .50375 .391 L s .5 .41459 m .50375 .41459 L s .5 .43819 m .50375 .43819 L s .5 .46178 m .50375 .46178 L s .5 .50896 m .50375 .50896 L s .5 .53255 m .50375 .53255 L s .5 .55614 m .50375 .55614 L s .5 .57973 m .50375 .57973 L s .25 Mabswid .5 0 m .5 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .18814 0 m .22272 .05382 L .26171 .1145 L .30316 .17901 L .34309 .24115 L .3815 .30094 L .42237 .36454 L .46172 .42578 L .49955 .48467 L .53984 .54455 L .55838 .5675 L .57861 .58692 L .58957 .59451 L .59491 .59739 L .59975 .59951 L .60475 .60123 L .60705 .60184 L .60947 .60238 L .61071 .60261 L .61206 .60282 L .61331 .60298 L .61445 .6031 L .61579 .60321 L .61653 .60325 L .61723 .60329 L .61848 .60332 L .61918 .60332 L .61984 .60331 L .62101 .60328 L .62225 .60321 L .62331 .60313 L .62447 .60302 L .62706 .60266 L .62946 .60221 L .63383 .60108 L .6385 .59946 L .64405 .59696 L .64929 .59405 L .6591 .58723 L .67912 .56817 L .69757 .54548 L .73697 .48712 L .77486 .43037 L .79594 .40383 L .8152 .38502 L .82473 .37804 L .82976 .37503 L .83511 .37236 L .84026 .37033 L .84493 .36894 L Mistroke .84718 .36843 L .84961 .368 L .85073 .36784 L .85191 .36769 L .85301 .36759 L .85402 .36751 L .85525 .36745 L .85589 .36743 L .85658 .36742 L .85773 .36742 L .859 .36745 L .86012 .36751 L .86133 .36759 L .86248 .36771 L .86353 .36783 L .8659 .3682 L .86849 .36873 L .8737 .37022 L .8783 .37198 L .88321 .37432 L .89205 .3797 L .90232 .38775 L .91343 .39848 L .9336 .42251 L .97457 .48284 L .97619 .48537 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{345, 213.125}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`03o`000?oooooooooo05_o oooo00?o0000ooooooooool0Z_ooool004oooooo00?o0000ooooooooool0F_ooool00ol0003ooooo ooooo`2Zooooo`00D?ooool00ol0003oooooooooo`1Iooooo`03o`000?oooooooooo0:[ooooo001@ ooooo`03o`000?oooooooooo05Wooooo00?o0000ooooooooool0Z_ooool0057ooooo00?o0000oooo ooooool0F?ooool00ol0003oooooooooo`2Zooooo`00D_ooool00ol0003oooooooooo`1Gooooo`03 o`000?oooooooooo0:[ooooo001Booooo`03o`000?oooooooooo05Oooooo0_l0002[ooooo`00Dooo ool00ol0003oooooooooo`1Fooooo`03o`000?oooooooooo0:[ooooo001Dooooo`03o`000?oooooo oooo05Gooooo00?o0000ooooooooool0Z_ooool005Cooooo00?o0000ooooooooool0EOooool00ol0 003oooooooooo`2Zooooo`00EOooool00ol0003oooooooooo`1Dooooo`03o`000?oooooooooo0:[o oooo001Fooooo`03o`000?oooooooooo05?ooooo00?o0000ooooooooool0Z_ooool005Kooooo00?o 0000ooooooooool0Doooool00ol0003oooooooooo`2Zooooo`00Eoooool00ol0003oooooooooo`1B ooooo`03o`000?oooooooooo0:[ooooo001Hooooo`03o`000?oooooooooo057ooooo0_l0002[oooo o`00F?ooool00ol0003oooooooooo`1Aooooo`03o`000?oooooooooo0:[ooooo001Iooooo`03o`00 0?oooooooooo053ooooo00?o0000ooooooooool0Z_ooool005[ooooo00?o0000ooooooooool0Cooo ool00ol0003oooooooooo`2Zooooo`00F_ooool00ol0003oooooooooo`1?ooooo`03o`000?oooooo oooo0:[ooooo001Kooooo`03o`000?oooooooooo04kooooo00?o0000ooooooooool0Z_ooool005co oooo00?o0000ooooooooool0@oooool3o`0000Oooooo00?o0000ooooooooool0Z_ooool005cooooo 00?o0000ooooooooool0@_ooool01Ol0003ooooooooooooooooo000000Kooooo00?o0000oooooooo ool0Z_ooool005gooooo00?o0000ooooooooool0>oooool5o`0000Gooooo00?o0000ooooooooool0 1?ooool00ol0003oooooooooo`2Zooooo`00G_ooool00ol0003oooooooooo`12ooooo`;o00001ooo ool3o`000:[ooooo001Nooooo`03o`000?oooooooooo04Cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`2Zooooo`00Goooool00ol0003oooooooooo`0oooooo`05o`000?oooooooooo ooooool000001_ooool00ol0003oooooooooo`2Zooooo`00Goooool00ol0003oooooooooo`10oooo o`?o00001oooool00ol0003oooooooooo`2Zooooo`00H?ooool00ol0003oooooooooo`19ooooo`03 o`000?oooooooooo0:[ooooo001Qooooo`03o`000?oooooooooo04Sooooo00?o0000ooooooooool0 Z_ooool0067ooooo00?o0000ooooooooool0B?ooool00ol0003oooooooooo`2Zooooo`00H_ooool0 0ol0003oooooooooo`17ooooo`03o`000?oooooooooo0:[ooooo001Sooooo`03o`000?oooooooooo 04Kooooo0_l0002[ooooo`00Hoooool00ol0003oooooooooo`16ooooo`03o`000?oooooooooo0:[o oooo001Tooooo`03o`000?oooooooooo04Gooooo00?o0000ooooooooool0Z_ooool006Gooooo00?o 0000ooooooooool0A?ooool00ol0003oooooooooo`2Zooooo`00IOooool00ol0003oooooooooo`14 ooooo`03o`000?oooooooooo0:[ooooo001Vooooo`03o`000?oooooooooo04?ooooo00?o0000oooo ooooool0Z_ooool006Kooooo00?o0000ooooooooool0@oooool00ol0003oooooooooo`2Zooooo`00 Ioooool00ol0003oooooooooo`12ooooo`03o`000?oooooooooo0:[ooooo001Xooooo`03o`000?oo oooooooo047ooooo0_l0002[ooooo`00J?ooool00ol0003oooooooooo`11ooooo`03o`000?oooooo oooo0:[ooooo001Yooooo`03o`000?oooooooooo043ooooo00?o0000ooooooooool0Z_ooool006[o oooo00?o0000ooooooooool0?oooool00ol0003oooooooooo`2Zooooo`00J_ooool00ol0003ooooo ooooo`0oooooo`03o`000?oooooooooo0:[ooooo001[ooooo`03o`000?oooooooooo03kooooo00?o 0000ooooooooool0Z_ooool006cooooo00?o0000ooooooooool0?Oooool00ol0003oooooooooo`2Z ooooo`00K?ooool00ol0003oooooooooo`0mooooo`03o`000?oooooooooo0:[ooooo001]ooooo`03 o`000?oooooooooo03cooooo0_l0002[ooooo`00K_ooool00ol0003oooooooooo`0kooooo`03o`00 0?oooooooooo0:[ooooo001^ooooo`03o`000?oooooooooo03_ooooo00?o0000ooooooooool0Z_oo ool006oooooo00?o0000ooooooooool0>_ooool00ol0003oooooooooo`2Zooooo`00L?ooool00ol0 003oooooooooo`0iooooo`03o`000?oooooooooo0:[ooooo001`ooooo`03o`000?oooooooooo03Wo oooo00?o0000ooooooooool0Z_ooool0077ooooo00?o0000ooooooooool0>?ooool00ol0003ooooo ooooo`2Zooooo`00L_ooool00ol0003oooooooooo`0gooooo`03o`000?oooooooooo0:[ooooo001b ooooo`03o`000?oooooooooo03Oooooo0_l0002[ooooo`00Loooool00ol0003oooooooooo`0foooo o`03o`000?oooooooooo0:[ooooo001dooooo`03o`000?oooooooooo03Gooooo00?o0000oooooooo ool0Z_ooool007Cooooo00?o0000ooooooooool0=Oooool00ol0003oooooooooo`2Zooooo`00MOoo ool00ol0003oooooooooo`0dooooo`03o`000?oooooooooo0:[ooooo001fooooo`03o`000?oooooo oooo02Sooooo1Ol00006ooooo`03o`000?oooooooooo0:[ooooo001fooooo`03o`000?oooooooooo 02Wooooo00Co0000oooooooooooo00001_ooool00ol0003oooooooooo`2Zooooo`00Moooool00ol0 003oooooooooo`0Qooooo`Go00000oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo 0:[ooooo001hooooo`03o`000?oooooooooo02Wooooo00?o0000ooooooooool01Oooool3o`000:[o oooo001hooooo`03o`000?oooooooooo02Kooooo00Go0000ooooooooooooooooo`000006ooooo`03 o`000?oooooooooo0:[ooooo001iooooo`03o`000?oooooooooo02Gooooo00Go0000oooooooooooo ooooo`000006ooooo`03o`000?oooooooooo0:[ooooo001iooooo`03o`000?oooooooooo02Kooooo 0ol00007ooooo`03o`000?oooooooooo0:[ooooo001jooooo`03o`000?oooooooooo02oooooo00?o 0000ooooooooool0Z_ooool007_ooooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`2Z ooooo`00Noooool00ol0003oooooooooo`0^ooooo`03o`000?oooooooooo0:[ooooo001looooo`03 o`000?oooooooooo02gooooo00?o0000ooooooooool0Z_ooool007gooooo00?o0000ooooooooool0 ;?ooool2o`000:_ooooo001mooooo`03o`000?oooooooooo02cooooo00?o0000ooooooooool0Z_oo ool007kooooo00?o0000ooooooooool0:oooool00ol0003oooooooooo`2Zooooo`00O_ooool00ol0 003oooooooooo`0[ooooo`03o`000?oooooooooo0:[ooooo001oooooo`03o`000?oooooooooo02[o oooo00?o0000ooooooooool0Z_ooool0083ooooo00?o0000ooooooooool0:Oooool00ol0003ooooo ooooo`2Zooooo`00P?ooool00ol0003oooooooooo`0Yooooo`03o`000?oooooooooo0:[ooooo0021 ooooo`03o`000?oooooooooo02Sooooo00?o0000ooooooooool0Z_ooool0087ooooo00?o0000oooo ooooool0:?ooool2o`000:_ooooo0022ooooo`03o`000?oooooooooo02Oooooo00?o0000oooooooo ool0Z_ooool008?ooooo00?o0000ooooooooool09_ooool00ol0003oooooooooo`2Zooooo`00Pooo ool00ol0003oooooooooo`0Vooooo`03o`000?oooooooooo0:[ooooo0024ooooo`03o`000?oooooo oooo02Gooooo00?o0000ooooooooool0Z_ooool008Gooooo00?o0000ooooooooool09?ooool00ol0 003oooooooooo`2Zooooo`00QOooool00ol0003oooooooooo`0Tooooo`03o`000?oooooooooo0:[o oooo0026ooooo`03o`000?oooooooooo02?ooooo00?o0000ooooooooool0Z_ooool008Oooooo00?o 0000ooooooooool08_ooool2o`000:_ooooo0027ooooo`03o`000?oooooooooo02;ooooo00?o0000 ooooooooool0Z_ooool008Sooooo00?o0000ooooooooool08Oooool00ol0003oooooooooo`2Zoooo o`00ROooool00ol0003oooooooooo`0Pooooo`03o`000?oooooooooo0:[ooooo0029ooooo`03o`00 0?oooooooooo023ooooo00?o0000ooooooooool0Z_ooool008[ooooo00?o0000ooooooooool07ooo ool00ol0003oooooooooo`2Zooooo`00Roooool00ol0003oooooooooo`0Nooooo`03o`000?oooooo oooo0:[ooooo002;ooooo`03o`000?oooooooooo01kooooo00?o0000ooooooooool0Z_ooool008co oooo00?o0000ooooooooool07Oooool2o`000:_ooooo002=ooooo`03o`000?oooooooooo01cooooo 00?o0000ooooooooool0Z_ooool008gooooo00?o0000ooooooooool07?ooool00ol0003ooooooooo o`2Zooooo`00S_ooool00ol0003oooooooooo`0Kooooo`03o`000?oooooooooo0:[ooooo002?oooo o`03o`000?oooooooooo01[ooooo00?o0000ooooooooool0Z_ooool008oooooo00?o0000oooooooo ool06_ooool00ol0003oooooooooo`2Zooooo`00T?ooool00ol0003oooooooooo`0?ooooo`?o0000 1oooool00ol0003oooooooooo`2Zooooo`00TOooool00ol0003oooooooooo`0?ooooo`03o`000?oo oooooooo00Kooooo00?o0000ooooooooool0Z_ooool0097ooooo00?o0000ooooooooool01oooool5 o`0000?ooooo00?o0000ooooooooool01_ooool3o`0007Kooooo0ol0000aooooo`00T_ooool00ol0 003oooooooooo`0>ooooo`03o`000?oooooooooo00Kooooo00?o0000ooooooooool0LOooool6o`00 0003ooooool0003o000000Co0000;?ooool009;ooooo00?o0000ooooooooool03_ooool00ol0003o ooooooooo`06ooooo`03o`000?oooooooooo06oooooo0_l0000=ooooo`;o0000:_ooool009?ooooo 00?o0000ooooooooool03?ooool2o`0000Sooooo00?o0000ooooooooool0KOooool2o`00017ooooo 0_l0000Xooooo`00U?ooool00ol0003oooooooooo`0ooooo`00[?ooool2o`0004kooooo00?o0000ooooooooool0 F_ooool00:cooooo0_l0001=ooooo`03o`000?oooooooooo05_ooooo002/ooooo`03o`000?oooooo 000004cooooo00?o0000ooooooooool0Foooool00:cooooo00Co0000oooooooooooo0000B_ooool0 0ol0003oooooooooo`1Looooo`00[?ooool01Ol0003ooooooooooooooooo000004Sooooo00?o0000 ooooooooool0GOooool00:cooooo0_l00002ooooo`03o`000?oooooooooo04Gooooo00?o0000oooo ooooool0G_ooool00:cooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`14ooooo`03 o`000?oooooooooo05kooooo002/ooooo`03o`000?oooooooooo00?ooooo00?o0000ooooooooool0 @_ooool00ol0003oooooooooo`1Oooooo`00[?ooool00ol0003oooooooooo`03ooooo`03o`000?oo oooooooo047ooooo00?o0000ooooooooool0H?ooool00:cooooo00?o0000ooooooooool01?ooool0 0ol0003oooooooooo`10ooooo`03o`000?oooooooooo063ooooo002/ooooo`03o`000?oooooooooo 00Gooooo00?o0000ooooooooool0?_ooool00ol0003oooooooooo`1Qooooo`00[?ooool00ol0003o ooooooooo`05ooooo`03o`000?oooooooooo03gooooo00?o0000ooooooooool0H_ooool00:cooooo 00?o0000ooooooooool01_ooool00ol0003oooooooooo`0looooo`03o`000?oooooooooo06;ooooo 002/ooooo`;o00002?ooool00ol0003oooooooooo`0jooooo`03o`000?oooooooooo06?ooooo002/ ooooo`03o`000?oooooooooo00Sooooo00?o0000ooooooooool0>?ooool00ol0003oooooooooo`1T ooooo`00[?ooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo03Oooooo00?o0000oooo ooooool0IOooool00:cooooo00?o0000ooooooooool02Oooool00ol0003oooooooooo`0fooooo`03 o`000?oooooooooo06Gooooo002/ooooo`03o`000?oooooooooo00[ooooo00?o0000ooooooooool0 =?ooool00ol0003oooooooooo`1Vooooo`00[?ooool00ol0003oooooooooo`0:ooooo`03o`000?oo oooooooo03?ooooo00?o0000ooooooooool0Ioooool00:cooooo00?o0000ooooooooool02oooool0 0ol0003oooooooooo`0booooo`03o`000?oooooooooo06Oooooo002/ooooo`03o`000?oooooooooo 00cooooo00?o0000ooooooooool0ooooo`03o`000?oooooooooo02cooooo00?o0000ooooooooool0J_ooool00:cooooo00?o 0000ooooooooool03oooool00ol0003oooooooooo`0Zooooo`03o`000?oooooooooo06_ooooo002/ ooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0:?ooool00ol0003oooooooooo`1/ ooooo`00[?ooool00ol0003oooooooooo`0Aooooo`03o`000?oooooooooo02Kooooo00?o0000oooo ooooool0KOooool00:cooooo00?o0000ooooooooool04Oooool00ol0003oooooooooo`0Uooooo`03 o`000?oooooooooo06kooooo002/ooooo`03o`000?oooooooooo01;ooooo00?o0000ooooooooool0 8oooool00ol0003oooooooooo`1_ooooo`00[?ooool00ol0003oooooooooo`0Cooooo`03o`000?oo oooooooo027ooooo00?o0000ooooooooool0L?ooool00:cooooo0_l0000Eooooo`03o`000?oooooo oooo01oooooo00?o0000ooooooooool0LOooool00:cooooo00?o0000ooooooooool05Oooool00ol0 003oooooooooo`0Mooooo`03o`000?oooooooooo07;ooooo002/ooooo`03o`000?oooooooooo01Ko oooo00?o0000ooooooooool06oooool00ol0003oooooooooo`1cooooo`00[?ooool00ol0003ooooo ooooo`0Gooooo`;o00006Oooool2o`0007Kooooo002/ooooo`03o`000?oooooooooo01Wooooo0_l0 000Fooooo`03o`000?oooooooooo07Kooooo002/ooooo`03o`000?oooooooooo01_ooooo0_l0000B ooooo`;o0000NOooool00:;ooooo0ol00007ooooo`03o`000?oooooooooo01gooooo0_l0000>oooo o`;o0000Noooool00:?ooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`0Oooooo`03 o`000?oooooooooo00Wooooo0_l0001mooooo`00Xoooool00ol0003oooooooooo`06ooooo`?o0000 8?ooool;o`0007oooooo002Sooooo`03o`000?oooooooooo00Kooooo00?o0000ooooooooool0Z_oo ool00:?ooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`2Zooooo`00X_ooool2o`00 00Sooooo00?o0000ooooooooool0Z_ooool00:?ooooo00?o0000ooooooooool01_ooool00ol0003o ooooooooo`2Zooooo`00[?ooool00ol0003oooooooooo`2Zooooo`00\ \>"], ImageRangeCache->{{{0, 344}, {212.125, 0}} -> {-6.61225, -4.11494, \ 0.0384433, 0.0247009}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Which[\ 7 > 8, a, x < y, b, 6 < 9, c]\)\(\ \)\( (*if\ part\ of\ the\ Which\ is\ neither\ true\ nor\ false, \ \ then\ the\ remaining\ which\ list\ is\ returned*) \)\)\)], "Input"], Cell[BoxData[ \(Which[x < y, b, 6 < 9, c]\)], "Output"] }, Open ]], Cell[BoxData[ \(\(\( (*\ Example\ of\ using\ the\ Switch\ form*) \)\(\[IndentingNewLine]\)\(r[ x_] := Switch[Mod[x, 3], 0, a, 1, b, 2, c]\)\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(r[4]\)\(\[IndentingNewLine]\) \)\)], "Input"], Cell[BoxData[ \(b\)], "Output"] }, Open ]], Cell[BoxData[ \(Clear[r]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Slide 04: Do, while loops", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Example\ of\ using\ nested\ do\ loop*) \)\(\[IndentingNewLine]\)\(Do[ Plot[Sin[n\ *\ x], {x, 0, 2 \[Pi]}], {n, 1, 3, 2}];\)\)\)], "Input"], Cell[CellGroupData[{ Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.309016 0.294303 [ [.17539 .29652 -3 -9 ] [.17539 .29652 3 0 ] [.32696 .29652 -3 -9 ] [.32696 .29652 3 0 ] [.47854 .29652 -3 -9 ] [.47854 .29652 3 0 ] [.63011 .29652 -3 -9 ] [.63011 .29652 3 0 ] [.78169 .29652 -3 -9 ] [.78169 .29652 3 0 ] [.93327 .29652 -3 -9 ] [.93327 .29652 3 0 ] [.01131 .01471 -12 -4.5 ] [.01131 .01471 0 4.5 ] [.01131 .16187 -24 -4.5 ] [.01131 .16187 0 4.5 ] [.01131 .45617 -18 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .30902 m .17539 .31527 L s [(1)] .17539 .29652 0 1 Mshowa .32696 .30902 m .32696 .31527 L s [(2)] .32696 .29652 0 1 Mshowa .47854 .30902 m .47854 .31527 L s [(3)] .47854 .29652 0 1 Mshowa .63011 .30902 m .63011 .31527 L s [(4)] .63011 .29652 0 1 Mshowa .78169 .30902 m .78169 .31527 L s [(5)] .78169 .29652 0 1 Mshowa .93327 .30902 m .93327 .31527 L s [(6)] .93327 .29652 0 1 Mshowa .125 Mabswid .05412 .30902 m .05412 .31277 L s .08444 .30902 m .08444 .31277 L s .11476 .30902 m .11476 .31277 L s .14507 .30902 m .14507 .31277 L s .2057 .30902 m .2057 .31277 L s .23602 .30902 m .23602 .31277 L s .26633 .30902 m .26633 .31277 L s .29665 .30902 m .29665 .31277 L s .35728 .30902 m .35728 .31277 L s .38759 .30902 m .38759 .31277 L s .41791 .30902 m .41791 .31277 L s .44822 .30902 m .44822 .31277 L s .50885 .30902 m .50885 .31277 L s .53917 .30902 m .53917 .31277 L s .56948 .30902 m .56948 .31277 L s .5998 .30902 m .5998 .31277 L s .66043 .30902 m .66043 .31277 L s .69074 .30902 m .69074 .31277 L s .72106 .30902 m .72106 .31277 L s .75138 .30902 m .75138 .31277 L s .81201 .30902 m .81201 .31277 L s .84232 .30902 m .84232 .31277 L s .87264 .30902 m .87264 .31277 L s .90295 .30902 m .90295 .31277 L s .96358 .30902 m .96358 .31277 L s .9939 .30902 m .9939 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .01471 m .03006 .01471 L s [(-1)] .01131 .01471 1 0 Mshowa .02381 .16187 m .03006 .16187 L s [(-0.5)] .01131 .16187 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(0.5)] .01131 .45617 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04414 m .02756 .04414 L s .02381 .07357 m .02756 .07357 L s .02381 .103 m .02756 .103 L s .02381 .13243 m .02756 .13243 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .25016 m .02756 .25016 L s .02381 .27959 m .02756 .27959 L s .02381 .33845 m .02756 .33845 L s .02381 .36788 m .02756 .36788 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .4856 m .02756 .4856 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .06244 .38322 L .10458 .45852 L .14415 .51889 L .18221 .56357 L .20178 .58047 L .21267 .58793 L .22272 .59354 L .23293 .59796 L .23832 .59976 L .24402 .60127 L .24641 .60178 L .24897 .60225 L .25119 .60258 L .25361 .60288 L .25507 .60302 L .25643 .60313 L .25773 .60321 L .2584 .60324 L .25912 .60327 L .25983 .60329 L .26048 .60331 L .26176 .60332 L .26293 .60331 L .26416 .60329 L .26538 .60324 L .26607 .60321 L .26671 .60317 L .26912 .60299 L .27131 .60275 L .27364 .60244 L .27847 .60156 L .2838 .60025 L .29326 .59705 L .30213 .59301 L .32232 .58025 L .34082 .56432 L .38045 .51781 L .41855 .45965 L .45912 .38744 L .49816 .31259 L .53966 .23289 L .57964 .1614 L .61811 .10221 L .63759 .07707 L .65902 .05386 L .67938 .03652 L .69843 .02473 L .70884 .02018 L .71396 .01844 L Mistroke .71872 .01712 L .72301 .01617 L .72758 .01542 L .7302 .01511 L .73148 .01499 L .73266 .0149 L .73371 .01484 L .73487 .01478 L .73603 .01474 L .73725 .01472 L .73856 .01472 L .73977 .01473 L .7404 .01475 L .7411 .01477 L .74251 .01484 L .74375 .01492 L .74508 .01503 L .74748 .01528 L .74985 .0156 L .75235 .01601 L .7568 .01695 L .76198 .01836 L .7668 .01998 L .77773 .02472 L .78828 .0307 L .79823 .03757 L .81683 .05353 L .85534 .09846 L .89632 .16101 L .93577 .23146 L .97371 .3042 L .97619 .30902 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOooool00ol0003oooooooooo`0Vooooo`006oooool00ol0003o ooooooooo`2Looooo`03o`000?oooooooooo03_ooooo00?o0000ooooooooool09Oooool001_ooooo 0_l0002Looooo`03o`000?oooooooooo03cooooo00?o0000ooooooooool09Oooool001_ooooo00?o 0000ooooooooool0Voooool00ol0003oooooooooo`0mooooo`03o`000?oooooooooo02Cooooo000K ooooo`03o`000?oooooooooo09[ooooo00?o0000ooooooooool0?oooool00ol0003oooooooooo`0S ooooo`006oooool00ol0003oooooooooo`2Iooooo`03o`000?oooooooooo043ooooo00?o0000oooo ooooool08oooool001_ooooo00?o0000ooooooooool0VOooool00ol0003oooooooooo`11ooooo`03 o`000?oooooooooo02;ooooo000Kooooo`03o`000?oooooooooo09Sooooo00?o0000ooooooooool0 @oooool00ol0003oooooooooo`0Qooooo`006oooool00ol0003oooooooooo`2Hooooo`03o`000?oo oooooooo04?ooooo00?o0000ooooooooool08Oooool001_ooooo00?o0000ooooooooool0Uoooool0 0ol0003oooooooooo`15ooooo`03o`000?oooooooooo023ooooo000Kooooo`;o0000Uoooool00ol0 003oooooooooo`17ooooo`03o`000?oooooooooo01oooooo000Kooooo`03o`000?oooooooooo09Ko oooo00?o0000ooooooooool0Aoooool00ol0003oooooooooo`0Oooooo`006oooool00ol0003ooooo ooooo`2Eooooo`03o`000?oooooooooo04Wooooo00?o0000ooooooooool07_ooool001_ooooo00?o 0000ooooooooool0U?ooool00ol0003oooooooooo`1:ooooo`03o`000?oooooooooo01kooooo000K ooooo`03o`000?oooooooooo09Cooooo00?o0000ooooooooool0Boooool00ol0003oooooooooo`0M ooooo`002?ooool2o`0000Cooooo00?o0000ooooooooool00_ooool3o`0000Gooooo00?o0000oooo ooooool0Toooool00ol0003oooooooooo`1=ooooo`03o`000?oooooooooo01cooooo0007ooooo`04 o`000?ooooooooooo`0000Oooooo00Go0000ooooooooooooooooo`000004ooooo`03o`000?oooooo oooo09?ooooo00?o0000ooooooooool0COooool00ol0003oooooooooo`0Looooo`001Ol00002oooo o`04o`000?ooooooooooo`0000_ooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`2B ooooo`03o`000?oooooooooo04oooooo00?o0000ooooooooool06oooool000Oooooo00Co0000oooo oooooooo00002oooool00ol0003oooooooooo`02ooooo`;o0000T_ooool00ol0003oooooooooo`1A ooooo`03o`000?oooooooooo01[ooooo0007ooooo`04o`000?ooooooooooo`0000Oooooo1?l00005 ooooo`03o`000?oooooooooo097ooooo00?o0000ooooooooool0DOooool00ol0003oooooooooo`0J ooooo`001oooool01?l0003oooooooooool00007ooooo`03o`000?oooooooooo00Kooooo00?o0000 ooooooooool0T?ooool00ol0003oooooooooo`1Cooooo`03o`000?oooooooooo01Wooooo0008oooo o`;o00002?ooool5o`0000Cooooo00?o0000ooooooooool0T?ooool00ol0003oooooooooo`1Coooo o`03o`000?oooooooooo01Wooooo000Kooooo`03o`000?oooooooooo08oooooo00?o0000oooooooo ool0EOooool00ol0003oooooooooo`0Hooooo`006oooool00ol0003oooooooooo`2>ooooo`03o`00 0?oooooooooo05Oooooo00?o0000ooooooooool05oooool001_ooooo00?o0000ooooooooool0S_oo ool00ol0003oooooooooo`1Gooooo`03o`000?oooooooooo01Oooooo000Kooooo`03o`000?oooooo oooo08gooooo00?o0000ooooooooool0FOooool00ol0003oooooooooo`0Fooooo`006oooool2o`00 08kooooo00?o0000ooooooooool0FOooool00ol0003oooooooooo`0Fooooo`006oooool00ol0003o ooooooooo`2 ooooo`006oooool00ol0003oooooooooo`08ooooo`03o`000?oooooooooo06Kooooo00?o0000oooo ooooool0S_ooool001_ooooo00?o0000ooooooooool02?ooool00ol0003oooooooooo`1Uooooo`03 o`000?oooooooooo08oooooo000Kooooo`;o00002_ooool00ol0003oooooooooo`1Tooooo`03o`00 0?oooooooooo08oooooo000Kooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0Hooo ool00ol0003oooooooooo`2@ooooo`006oooool00ol0003oooooooooo`0:ooooo`03o`000?oooooo oooo067ooooo00?o0000ooooooooool0TOooool001_ooooo00?o0000ooooooooool02oooool00ol0 003oooooooooo`1Pooooo`03o`000?oooooooooo097ooooo000Kooooo`03o`000?oooooooooo00_o oooo00?o0000ooooooooool0Goooool00ol0003oooooooooo`2Booooo`006oooool00ol0003ooooo ooooo`0ooooo`03o`000?oooooooooo05Wooooo00?o0000oooooooo ool0UOooool001_ooooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`1Iooooo`03o`00 0?oooooooooo09Gooooo000Kooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool0Eooo ool00ol0003oooooooooo`2Fooooo`006oooool00ol0003oooooooooo`0@ooooo`03o`000?oooooo oooo05Kooooo00?o0000ooooooooool0U_ooool000Sooooo0_l00004ooooo`03o`000?oooooooooo 00;ooooo0ol00005ooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0EOooool00ol0 003oooooooooo`2Gooooo`001oooool01?l0003oooooooooool00007ooooo`05o`000?oooooooooo ooooool000001?ooool00ol0003oooooooooo`0Aooooo`03o`000?oooooooooo05?ooooo00?o0000 ooooooooool0V?ooool000Oooooo00Co0000oooooooooooo00002oooool00ol0003oooooooooo`02 ooooo`;o00004_ooool00ol0003oooooooooo`1Cooooo`03o`000?oooooooooo09Sooooo0007oooo o`04o`000?ooooooooooo`0000_ooooo00?o0000ooooooooool00_ooool00ol0003oooooooooo`0B ooooo`03o`000?oooooooooo057ooooo00?o0000ooooooooool0VOooool000Oooooo00Co0000oooo oooooooo00001oooool4o`0000Gooooo00?o0000ooooooooool04_ooool00ol0003oooooooooo`1A ooooo`03o`000?oooooooooo09Wooooo0007ooooo`04o`000?ooooooooooo`0000Oooooo00?o0000 ooooooooool01_ooool00ol0003oooooooooo`0Cooooo`03o`000?oooooooooo04oooooo00?o0000 ooooooooool0V_ooool000Sooooo0_l00008ooooo`Go00001?ooool00ol0003oooooooooo`0Doooo o`03o`000?oooooooooo04gooooo00?o0000ooooooooool0Voooool001_ooooo00?o0000oooooooo ool05?ooool00ol0003oooooooooo`1=ooooo`03o`000?oooooooooo09_ooooo000Kooooo`03o`00 0?oooooooooo01Gooooo00?o0000ooooooooool0Boooool00ol0003oooooooooo`2Looooo`006ooo ool00ol0003oooooooooo`0Fooooo`03o`000?oooooooooo04[ooooo00?o0000ooooooooool0W?oo ool001_ooooo0_l0000Gooooo`03o`000?oooooooooo04Wooooo00?o0000ooooooooool0WOooool0 01_ooooo00?o0000ooooooooool05oooool00ol0003oooooooooo`17ooooo`03o`000?oooooooooo 09kooooo000Kooooo`03o`000?oooooooooo01Sooooo00?o0000ooooooooool0A_ooool00ol0003o ooooooooo`2Nooooo`006oooool00ol0003oooooooooo`0Iooooo`03o`000?oooooooooo04Cooooo 00?o0000ooooooooool0Woooool001_ooooo00?o0000ooooooooool06Oooool00ol0003ooooooooo o`13ooooo`03o`000?oooooooooo0:3ooooo000Kooooo`03o`000?oooooooooo01[ooooo00?o0000 ooooooooool0@_ooool00ol0003oooooooooo`2Pooooo`006oooool00ol0003oooooooooo`0Koooo o`03o`000?oooooooooo043ooooo00?o0000ooooooooool0XOooool001_ooooo00?o0000oooooooo ool06oooool00ol0003oooooooooo`10ooooo`03o`000?oooooooooo0:7ooooo000Kooooo`;o0000 7Oooool00ol0003oooooooooo`0nooooo`03o`000?oooooooooo0:;ooooo000Kooooo`03o`000?oo oooooooo01gooooo00?o0000ooooooooool0??ooool00ol0003oooooooooo`2Sooooo`006oooool0 0ol0003oooooooooo`0Mooooo`03o`000?oooooooooo03cooooo00?o0000ooooooooool0Xoooool0 01_ooooo00?o0000ooooooooool07_ooool00ol0003oooooooooo`0jooooo`03o`000?oooooooooo 0:Cooooo000Kooooo`03o`000?oooooooooo01oooooo00?o0000ooooooooool0>?ooool00ol0003o ooooooooo`2Uooooo`006oooool00ol0003oooooooooo`0Pooooo`03o`000?oooooooooo03Kooooo 00?o0000ooooooooool0Y_ooool001_ooooo00?o0000ooooooooool08Oooool00ol0003ooooooooo o`0dooooo`03o`000?oooooooooo0:Oooooo000Kooooo`03o`000?oooooooooo02;ooooo00?o0000 ooooooooool0<_ooool00ol0003oooooooooo`2Xooooo`006oooool2o`0002?ooooo00?o0000oooo ooooool0"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.677733, -1.13007, \ 0.0248015, 0.0127736}}], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.151576 0.309016 0.294303 [ [.17539 .29652 -3 -9 ] [.17539 .29652 3 0 ] [.32696 .29652 -3 -9 ] [.32696 .29652 3 0 ] [.47854 .29652 -3 -9 ] [.47854 .29652 3 0 ] [.63011 .29652 -3 -9 ] [.63011 .29652 3 0 ] [.78169 .29652 -3 -9 ] [.78169 .29652 3 0 ] [.93327 .29652 -3 -9 ] [.93327 .29652 3 0 ] [.01131 .01471 -12 -4.5 ] [.01131 .01471 0 4.5 ] [.01131 .16186 -24 -4.5 ] [.01131 .16186 0 4.5 ] [.01131 .45617 -18 -4.5 ] [.01131 .45617 0 4.5 ] [.01131 .60332 -6 -4.5 ] [.01131 .60332 0 4.5 ] [ 0 0 0 0 ] [ 1 .61803 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 g .25 Mabswid [ ] 0 setdash .17539 .30902 m .17539 .31527 L s [(1)] .17539 .29652 0 1 Mshowa .32696 .30902 m .32696 .31527 L s [(2)] .32696 .29652 0 1 Mshowa .47854 .30902 m .47854 .31527 L s [(3)] .47854 .29652 0 1 Mshowa .63011 .30902 m .63011 .31527 L s [(4)] .63011 .29652 0 1 Mshowa .78169 .30902 m .78169 .31527 L s [(5)] .78169 .29652 0 1 Mshowa .93327 .30902 m .93327 .31527 L s [(6)] .93327 .29652 0 1 Mshowa .125 Mabswid .05412 .30902 m .05412 .31277 L s .08444 .30902 m .08444 .31277 L s .11476 .30902 m .11476 .31277 L s .14507 .30902 m .14507 .31277 L s .2057 .30902 m .2057 .31277 L s .23602 .30902 m .23602 .31277 L s .26633 .30902 m .26633 .31277 L s .29665 .30902 m .29665 .31277 L s .35728 .30902 m .35728 .31277 L s .38759 .30902 m .38759 .31277 L s .41791 .30902 m .41791 .31277 L s .44822 .30902 m .44822 .31277 L s .50885 .30902 m .50885 .31277 L s .53917 .30902 m .53917 .31277 L s .56948 .30902 m .56948 .31277 L s .5998 .30902 m .5998 .31277 L s .66043 .30902 m .66043 .31277 L s .69074 .30902 m .69074 .31277 L s .72106 .30902 m .72106 .31277 L s .75138 .30902 m .75138 .31277 L s .81201 .30902 m .81201 .31277 L s .84232 .30902 m .84232 .31277 L s .87264 .30902 m .87264 .31277 L s .90295 .30902 m .90295 .31277 L s .96358 .30902 m .96358 .31277 L s .9939 .30902 m .9939 .31277 L s .25 Mabswid 0 .30902 m 1 .30902 L s .02381 .01471 m .03006 .01471 L s [(-1)] .01131 .01471 1 0 Mshowa .02381 .16186 m .03006 .16186 L s [(-0.5)] .01131 .16186 1 0 Mshowa .02381 .45617 m .03006 .45617 L s [(0.5)] .01131 .45617 1 0 Mshowa .02381 .60332 m .03006 .60332 L s [(1)] .01131 .60332 1 0 Mshowa .125 Mabswid .02381 .04414 m .02756 .04414 L s .02381 .07357 m .02756 .07357 L s .02381 .103 m .02756 .103 L s .02381 .13243 m .02756 .13243 L s .02381 .1913 m .02756 .1913 L s .02381 .22073 m .02756 .22073 L s .02381 .25016 m .02756 .25016 L s .02381 .27959 m .02756 .27959 L s .02381 .33845 m .02756 .33845 L s .02381 .36788 m .02756 .36788 L s .02381 .39731 m .02756 .39731 L s .02381 .42674 m .02756 .42674 L s .02381 .4856 m .02756 .4856 L s .02381 .51503 m .02756 .51503 L s .02381 .54446 m .02756 .54446 L s .02381 .57389 m .02756 .57389 L s .25 Mabswid .02381 0 m .02381 .61803 L s 0 0 m 1 0 L 1 .61803 L 0 .61803 L closepath clip newpath .5 Mabswid .02381 .30902 m .04262 .41606 L .06244 .51276 L .07286 .5519 L .08255 .57915 L .08813 .59036 L .09076 .59448 L .0932 .5976 L .096 .60036 L .09748 .60145 L .09824 .60191 L .09905 .60234 L .09976 .60265 L .10041 .60288 L .10168 .60319 L .10239 .60328 L .10317 .60332 L .1039 .60329 L .10458 .60321 L .10587 .6029 L .10651 .60268 L .10722 .60237 L .10848 .6017 L .10966 .6009 L .11231 .59853 L .11515 .59509 L .12035 .58647 L .1251 .57604 L .13466 .54801 L .14371 .51358 L .18204 .31193 L .20142 .20156 L .21172 .14833 L .22282 .09846 L .23339 .06036 L .23801 .04701 L .24307 .03492 L .24787 .02599 L .25234 .01998 L .25481 .01761 L .25705 .01607 L .25829 .01546 L .259 .0152 L .25964 .01501 L .26083 .01478 L .26209 .01472 L .2633 .01483 L .26462 .01514 L .26586 .01562 L .26702 .01622 L Mistroke .2692 .01778 L .27152 .02003 L .27427 .02348 L .27684 .02749 L .28166 .03693 L .29046 .06049 L .29997 .09438 L .31995 .1885 L .34103 .30762 L .36093 .42068 L .37905 .50916 L .3891 .54783 L .3986 .57578 L .40382 .58716 L .40863 .59506 L .41115 .59815 L .41392 .60072 L .41532 .60169 L .41605 .60211 L .41682 .60248 L .41749 .60275 L .41823 .60299 L .41953 .60325 L .42017 .60331 L .42086 .60332 L .42208 .6032 L .42339 .60288 L .42414 .60261 L .42483 .6023 L .42724 .6008 L .4286 .59967 L .42983 .59846 L .43463 .5921 L .43918 .58372 L .44922 .55747 L .46014 .51783 L .47989 .42306 L .50089 .30381 L .52056 .19252 L .53861 .10537 L .54802 .06955 L .55794 .04079 L .56309 .02985 L .56789 .02227 L .57065 .01909 L .57315 .01693 L .57454 .01605 L .57527 .01568 L .57605 .01535 L .57672 .01512 L Mistroke .57747 .01492 L .57878 .01473 L .58007 .01474 L .58127 .01492 L .58259 .01531 L .58332 .01561 L .58399 .01594 L .58653 .01767 L .58893 .01997 L .59339 .02597 L .59821 .03494 L .6035 .04765 L .60909 .06418 L .61909 .10109 L .65708 .29942 L .67824 .41987 L .69753 .51344 L .70711 .54968 L .71216 .56538 L .71752 .57926 L .7222 .58887 L .72468 .59301 L .72736 .5967 L .72981 .59937 L .73088 .60032 L .73205 .60122 L .73309 .60188 L .7342 .60244 L .73537 .60289 L .73645 .60316 L .73769 .60331 L .73839 .60331 L .73905 .60327 L .73974 .60316 L .74037 .60302 L .7411 .6028 L .74179 .60253 L .74301 .60193 L .74414 .60121 L .74671 .59905 L .74953 .59581 L .75209 .5921 L .75782 .58118 L .76281 .5688 L .7682 .55259 L .77797 .51632 L .81905 .29977 L .83953 .18454 L .84952 .13458 L .85861 .09497 L Mistroke .86742 .06317 L .87699 .03711 L .88224 .02689 L .88455 .02336 L .88709 .02016 L .88949 .01781 L .89173 .01621 L .89297 .01557 L .8941 .01514 L .89541 .01483 L .89665 .01472 L .89789 .01478 L .89859 .01489 L .89924 .01505 L .90042 .01546 L .90168 .01607 L .90385 .01755 L .90623 .0198 L .90878 .02291 L .91151 .02706 L .91645 .03663 L .92606 .06263 L .93483 .09413 L .95391 .18339 L .97467 .30013 L .97619 .30902 L Mfstroke % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 177.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgooooo`03o`000?oooooooooo00;ooooo00?o0000 ooooooooool0C?ooool2o`0000Cooooo00?o0000ooooooooool05oooool001?ooooo0_l00006oooo o`03o`000?oooooooooo03Wooooo00?o0000ooooooooool00oooool00ol0003oooooooooo`1?ooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo04[ooooo00?o0000oooooooo ool01?ooool00ol0003oooooooooo`1:ooooo`03o`000?oooooooooo00Gooooo00?o0000oooooooo ool05_ooool001_ooooo00?o0000ooooooooool0>?ooool00ol0003oooooooooo`05ooooo`03o`00 0?oooooooooo04Wooooo00?o0000ooooooooool01_ooool00ol0003oooooooooo`19ooooo`03o`00 0?oooooooooo00Gooooo00?o0000ooooooooool05_ooool001_ooooo00?o0000ooooooooool0=ooo ool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo04Sooooo00?o0000ooooooooool01ooo ool00ol0003oooooooooo`17ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool05Ooo ool001_ooooo00?o0000ooooooooool0=oooool00ol0003oooooooooo`07ooooo`03o`000?oooooo oooo04Oooooo00?o0000ooooooooool02?ooool00ol0003oooooooooo`17ooooo`03o`000?oooooo oooo00Oooooo00?o0000ooooooooool05Oooool001_ooooo00?o0000ooooooooool0=_ooool00ol0 003oooooooooo`08ooooo`03o`000?oooooooooo04Oooooo00?o0000ooooooooool02?ooool00ol0 003oooooooooo`17ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool05Oooool001_o oooo0_l0000gooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool0A_ooool00ol0003o ooooooooo`09ooooo`03o`000?oooooooooo04Gooooo00?o0000ooooooooool02Oooool00ol0003o ooooooooo`0Dooooo`006oooool00ol0003oooooooooo`0fooooo`03o`000?oooooooooo00Wooooo 00?o0000ooooooooool0AOooool00ol0003oooooooooo`0:ooooo`03o`000?oooooooooo04Gooooo 00?o0000ooooooooool02Oooool00ol0003oooooooooo`0Dooooo`006oooool00ol0003ooooooooo o`0fooooo`03o`000?oooooooooo00[ooooo00?o0000ooooooooool0A?ooool00ol0003ooooooooo o`0:ooooo`03o`000?oooooooooo04Cooooo00?o0000ooooooooool02oooool00ol0003ooooooooo o`0Cooooo`006oooool00ol0003oooooooooo`0eooooo`03o`000?oooooooooo00_ooooo00?o0000 ooooooooool0@oooool00ol0003oooooooooo`0ooooo`03o`00 0?oooooooooo047ooooo00?o0000ooooooooool03Oooool00ol0003oooooooooo`0Booooo`006ooo ool2o`0003Gooooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`10ooooo`03o`000?oo oooooooo00kooooo00?o0000ooooooooool0@Oooool00ol0003oooooooooo`0>ooooo`03o`000?oo oooooooo017ooooo000Kooooo`03o`000?oooooooooo03Cooooo00?o0000ooooooooool03_ooool0 0ol0003oooooooooo`10ooooo`03o`000?oooooooooo00oooooo00?o0000ooooooooool0?oooool0 0ol0003oooooooooo`0?ooooo`03o`000?oooooooooo017ooooo000Kooooo`03o`000?oooooooooo 03Cooooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`0oooooo`03o`000?oooooooooo 013ooooo00?o0000ooooooooool0?oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo 017ooooo000Kooooo`03o`000?oooooooooo03?ooooo00?o0000ooooooooool03oooool00ol0003o ooooooooo`0oooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0?oooool00ol0003o ooooooooo`0?ooooo`03o`000?oooooooooo017ooooo000Kooooo`03o`000?oooooooooo03?ooooo 00?o0000ooooooooool03oooool00ol0003oooooooooo`0oooooo`03o`000?oooooooooo013ooooo 00?o0000ooooooooool0?oooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo017ooooo 000Kooooo`03o`000?oooooooooo03?ooooo00?o0000ooooooooool04?ooool00ol0003ooooooooo o`0nooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0?_ooool00ol0003ooooooooo o`0Aooooo`03o`000?oooooooooo013ooooo000Kooooo`03o`000?oooooooooo03;ooooo00?o0000 ooooooooool04Oooool00ol0003oooooooooo`0nooooo`03o`000?oooooooooo017ooooo00?o0000 ooooooooool0?Oooool00ol0003oooooooooo`0Aooooo`03o`000?oooooooooo013ooooo000Koooo o`03o`000?oooooooooo03;ooooo00?o0000ooooooooool04Oooool00ol0003oooooooooo`0moooo o`03o`000?oooooooooo01;ooooo00?o0000ooooooooool0?Oooool00ol0003oooooooooo`0Aoooo o`03o`000?oooooooooo013ooooo000Kooooo`;o0000_ooool00ol0003oooooooooo`0D ooooo`03o`000?oooooooooo03Wooooo00?o0000ooooooooool05_ooool00ol0003oooooooooo`0> ooooo`006oooool00ol0003oooooooooo`0`ooooo`03o`000?oooooooooo01Kooooo00?o0000oooo ooooool0>?ooool00ol0003oooooooooo`0Fooooo`03o`000?oooooooooo03Sooooo00?o0000oooo ooooool05_ooool00ol0003oooooooooo`0>ooooo`006oooool00ol0003oooooooooo`0`ooooo`03 o`000?oooooooooo01Kooooo00?o0000ooooooooool0>?ooool00ol0003oooooooooo`0Fooooo`03 o`000?oooooooooo03Sooooo00?o0000ooooooooool05_ooool00ol0003oooooooooo`0>ooooo`00 6oooool00ol0003oooooooooo`0_ooooo`03o`000?oooooooooo01Oooooo00?o0000ooooooooool0 >?ooool00ol0003oooooooooo`0Fooooo`03o`000?oooooooooo03Sooooo00?o0000ooooooooool0 5oooool00ol0003oooooooooo`0=ooooo`006oooool00ol0003oooooooooo`0_ooooo`03o`000?oo oooooooo01Oooooo00?o0000ooooooooool0>?ooool00ol0003oooooooooo`0Fooooo`03o`000?oo oooooooo03Sooooo00?o0000ooooooooool05oooool00ol0003oooooooooo`0=ooooo`002?ooool2 o`0000Cooooo00?o0000ooooooooool00_ooool3o`0000Gooooo00?o0000ooooooooool0;oooool0 0ol0003oooooooooo`0Gooooo`03o`000?oooooooooo03Oooooo00?o0000ooooooooool05oooool0 0ol0003oooooooooo`0gooooo`03o`000?oooooooooo01Sooooo00?o0000ooooooooool03Oooool0 00Oooooo00Co0000oooooooooooo00001oooool01Ol0003ooooooooooooooooo000000Cooooo00?o 0000ooooooooool0;oooool00ol0003oooooooooo`0Hooooo`03o`000?oooooooooo03Kooooo00?o 0000ooooooooool06?ooool00ol0003oooooooooo`0fooooo`03o`000?oooooooooo01Sooooo00?o 0000ooooooooool03Oooool000Go00000_ooool01?l0003oooooooooool0000;ooooo`03o`000?oo oooooooo00;ooooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`0Iooooo`03o`000?oo oooooooo03Kooooo00?o0000ooooooooool06?ooool00ol0003oooooooooo`0fooooo`03o`000?oo oooooooo01Sooooo00?o0000ooooooooool03Oooool000Oooooo00Co0000oooooooooooo00002ooo ool00ol0003oooooooooo`02ooooo`;o0000;oooool00ol0003oooooooooo`0Iooooo`03o`000?oo oooooooo03Kooooo00?o0000ooooooooool06?ooool00ol0003oooooooooo`0fooooo`03o`000?oo oooooooo01Wooooo00?o0000ooooooooool03?ooool000Oooooo00Co0000oooooooooooo00001ooo ool4o`0000Gooooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`0Iooooo`03o`000?oo oooooooo03Kooooo00?o0000ooooooooool06?ooool00ol0003oooooooooo`0fooooo`03o`000?oo oooooooo01Wooooo00?o0000ooooooooool03?ooool000Oooooo00Co0000oooooooooooo00001ooo ool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo02kooooo00?o0000ooooooooool06_oo ool00ol0003oooooooooo`0dooooo`03o`000?oooooooooo01Wooooo00?o0000ooooooooool0=_oo ool00ol0003oooooooooo`0Iooooo`03o`000?oooooooooo00cooooo0008ooooo`;o00002?ooool5 o`0000Cooooo00?o0000ooooooooool0;_ooool00ol0003oooooooooo`0Jooooo`03o`000?oooooo oooo03Cooooo00?o0000ooooooooool06_ooool00ol0003oooooooooo`0eooooo`03o`000?oooooo oooo01Wooooo00?o0000ooooooooool03?ooool001_ooooo00?o0000ooooooooool0;Oooool00ol0 003oooooooooo`0Kooooo`03o`000?oooooooooo03Cooooo00?o0000ooooooooool06_ooool00ol0 003oooooooooo`0dooooo`03o`000?oooooooooo01[ooooo00?o0000ooooooooool03?ooool001_o oooo00?o0000ooooooooool0;Oooool00ol0003oooooooooo`0Kooooo`03o`000?oooooooooo03Co oooo00?o0000ooooooooool06_ooool00ol0003oooooooooo`0dooooo`03o`000?oooooooooo01_o oooo00?o0000ooooooooool02oooool001_ooooo00?o0000ooooooooool0;Oooool00ol0003ooooo ooooo`0Looooo`03o`000?oooooooooo03?ooooo00?o0000ooooooooool06_ooool00ol0003ooooo ooooo`0dooooo`03o`000?oooooooooo01_ooooo00?o0000ooooooooool02oooool001_ooooo00?o 0000ooooooooool0;Oooool00ol0003oooooooooo`0Looooo`03o`000?oooooooooo03;ooooo00?o 0000ooooooooool06oooool00ol0003oooooooooo`0dooooo`03o`000?oooooooooo01_ooooo00?o 0000ooooooooool02oooool001_ooooo0_l0000^ooooo`03o`000?oooooooooo01cooooo00?o0000 ooooooooool0<_ooool00ol0003oooooooooo`0Looooo`03o`000?oooooooooo03?ooooo00?o0000 ooooooooool06oooool00ol0003oooooooooo`0;ooooo`006oooool00ol0003oooooooooo`0/oooo o`03o`000?oooooooooo01gooooo00?o0000ooooooooool0<_ooool00ol0003oooooooooo`0Loooo o`03o`000?oooooooooo03?ooooo00?o0000ooooooooool06oooool00ol0003oooooooooo`0;oooo o`006oooool00ol0003oooooooooo`0/ooooo`03o`000?oooooooooo01gooooo00?o0000oooooooo ool0<_ooool00ol0003oooooooooo`0Looooo`03o`000?oooooooooo03;ooooo00?o0000oooooooo ool07Oooool00ol0003oooooooooo`0:ooooo`006oooool00ol0003oooooooooo`0/ooooo`03o`00 0?oooooooooo01kooooo00?o0000ooooooooool0?ooool001_ooooo 00?o0000ooooooooool01Oooool00ol0003oooooooooo`0Gooooo`03o`000?oooooooooo03Oooooo 00?o0000ooooooooool05oooool00ol0003oooooooooo`0hooooo`03o`000?oooooooooo01Kooooo 00?o0000ooooooooool0>?ooool001_ooooo00?o0000ooooooooool01Oooool00ol0003ooooooooo o`0Gooooo`03o`000?oooooooooo03Sooooo00?o0000ooooooooool05_ooool00ol0003ooooooooo o`0hooooo`03o`000?oooooooooo01Kooooo00?o0000ooooooooool0>?ooool001_ooooo00?o0000 ooooooooool01Oooool00ol0003oooooooooo`0Gooooo`03o`000?oooooooooo03Sooooo00?o0000 ooooooooool05_ooool00ol0003oooooooooo`0hooooo`03o`000?oooooooooo01Kooooo00?o0000 ooooooooool0>?ooool001_ooooo0_l00007ooooo`03o`000?oooooooooo01Gooooo00?o0000oooo ooooool0>Oooool00ol0003oooooooooo`0Fooooo`03o`000?oooooooooo03Sooooo00?o0000oooo ooooool05_ooool00ol0003oooooooooo`0hooooo`006oooool00ol0003oooooooooo`06ooooo`03 o`000?oooooooooo01Gooooo00?o0000ooooooooool0>Oooool00ol0003oooooooooo`0Fooooo`03 o`000?oooooooooo03Wooooo00?o0000ooooooooool05?ooool00ol0003oooooooooo`0iooooo`00 6oooool00ol0003oooooooooo`06ooooo`03o`000?oooooooooo01Gooooo00?o0000ooooooooool0 >Oooool00ol0003oooooooooo`0Eooooo`03o`000?oooooooooo03[ooooo00?o0000ooooooooool0 5?ooool00ol0003oooooooooo`0iooooo`006oooool00ol0003oooooooooo`06ooooo`03o`000?oo oooooooo01Gooooo00?o0000ooooooooool0>Oooool00ol0003oooooooooo`0Eooooo`03o`000?oo oooooooo03[ooooo00?o0000ooooooooool05?ooool00ol0003oooooooooo`0iooooo`006oooool0 0ol0003oooooooooo`06ooooo`03o`000?oooooooooo01Gooooo00?o0000ooooooooool0>_ooool0 0ol0003oooooooooo`0Dooooo`03o`000?oooooooooo03[ooooo00?o0000ooooooooool05?ooool0 0ol0003oooooooooo`0iooooo`006oooool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo 01?ooooo00?o0000ooooooooool0>oooool00ol0003oooooooooo`0Dooooo`03o`000?oooooooooo 03[ooooo00?o0000ooooooooool05?ooool00ol0003oooooooooo`0iooooo`006oooool00ol0003o ooooooooo`07ooooo`03o`000?oooooooooo01?ooooo00?o0000ooooooooool0>oooool00ol0003o ooooooooo`0Dooooo`03o`000?oooooooooo03_ooooo00?o0000ooooooooool04_ooool00ol0003o ooooooooo`0jooooo`006oooool00ol0003oooooooooo`07ooooo`03o`000?oooooooooo01?ooooo 00?o0000ooooooooool0>oooool00ol0003oooooooooo`0Cooooo`03o`000?oooooooooo03cooooo 00?o0000ooooooooool04_ooool00ol0003oooooooooo`0jooooo`006oooool2o`0000Sooooo00?o 0000ooooooooool04oooool00ol0003oooooooooo`0kooooo`03o`000?oooooooooo01?ooooo00?o 0000ooooooooool0??ooool00ol0003oooooooooo`0Booooo`03o`000?oooooooooo03[ooooo000K ooooo`03o`000?oooooooooo00Oooooo00?o0000ooooooooool04oooool00ol0003oooooooooo`0l ooooo`03o`000?oooooooooo01;ooooo00?o0000ooooooooool0??ooool00ol0003oooooooooo`0B ooooo`03o`000?oooooooooo03[ooooo000Kooooo`03o`000?oooooooooo00Sooooo00?o0000oooo ooooool04Oooool00ol0003oooooooooo`0mooooo`03o`000?oooooooooo01;ooooo00?o0000oooo ooooool0?Oooool00ol0003oooooooooo`0Aooooo`03o`000?oooooooooo03[ooooo000Kooooo`03 o`000?oooooooooo00Sooooo00?o0000ooooooooool04Oooool00ol0003oooooooooo`0mooooo`03 o`000?oooooooooo01;ooooo00?o0000ooooooooool0?Oooool00ol0003oooooooooo`0@ooooo`03 o`000?oooooooooo03_ooooo000Kooooo`03o`000?oooooooooo00Sooooo00?o0000ooooooooool0 4Oooool00ol0003oooooooooo`0nooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0 ?_ooool00ol0003oooooooooo`0@ooooo`03o`000?oooooooooo03_ooooo000Kooooo`03o`000?oo oooooooo00Wooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`0oooooo`03o`000?oo oooooooo013ooooo00?o0000ooooooooool0?oooool00ol0003oooooooooo`0?ooooo`03o`000?oo oooooooo03_ooooo000Kooooo`03o`000?oooooooooo00Wooooo00?o0000ooooooooool03oooool0 0ol0003oooooooooo`0oooooo`03o`000?oooooooooo013ooooo00?o0000ooooooooool0?oooool0 0ol0003oooooooooo`0?ooooo`03o`000?oooooooooo03_ooooo000Kooooo`03o`000?oooooooooo 00Wooooo00?o0000ooooooooool03oooool00ol0003oooooooooo`0oooooo`03o`000?oooooooooo 00oooooo00?o0000ooooooooool0@?ooool00ol0003oooooooooo`0?ooooo`03o`000?oooooooooo 03_ooooo000Kooooo`;o00002_ooool00ol0003oooooooooo`0>ooooo`03o`000?oooooooooo047o oooo00?o0000ooooooooool03_ooool00ol0003oooooooooo`11ooooo`03o`000?oooooooooo00go oooo00?o0000ooooooooool0??ooool001_ooooo00?o0000ooooooooool02_ooool00ol0003ooooo ooooo`0=ooooo`03o`000?oooooooooo047ooooo00?o0000ooooooooool03_ooool00ol0003ooooo ooooo`11ooooo`03o`000?oooooooooo00gooooo00?o0000ooooooooool0??ooool001_ooooo00?o 0000ooooooooool02_ooool00ol0003oooooooooo`0=ooooo`03o`000?oooooooooo047ooooo00?o 0000ooooooooool03Oooool00ol0003oooooooooo`12ooooo`03o`000?oooooooooo00gooooo00?o 0000ooooooooool0??ooool001_ooooo00?o0000ooooooooool02_ooool00ol0003oooooooooo`0= ooooo`03o`000?oooooooooo04;ooooo00?o0000ooooooooool03?ooool00ol0003oooooooooo`12 ooooo`03o`000?oooooooooo00gooooo00?o0000ooooooooool0??ooool001_ooooo00?o0000oooo ooooool02_ooool00ol0003oooooooooo`0ooooo`03o`000?oooooooooo00Gooooo00?o 0000ooooooooool0BOooool00ol0003oooooooooo`05ooooo`03o`000?oooooooooo04[ooooo00?o 0000ooooooooool01Oooool00ol0003oooooooooo`10ooooo`004oooool3o`0000Gooooo00?o0000 ooooooooool03oooool00ol0003oooooooooo`03ooooo`03o`000?oooooooooo04_ooooo00?o0000 ooooooooool01?ooool00ol0003oooooooooo`1:ooooo`03o`000?oooooooooo00Cooooo00?o0000 ooooooooool0@Oooool001Cooooo00?o0000ooooooooool01?ooool00ol0003oooooooooo`0?oooo o`03o`000?oooooooooo00;ooooo00?o0000ooooooooool0COooool00ol0003oooooooooo`02oooo o`03o`000?oooooooooo04cooooo0_l00003ooooo`03o`000?oooooooooo04;ooooo000Dooooo`03 o`000?oooooooooo00Cooooo0_l0000Aooooo`Go0000D?ooool4o`00053ooooo1?l00015ooooo`00 5?ooool00ol0003oooooooooo`04ooooo`03o`000?oooooooooo0?oooooo0oooool001Cooooo00?o 0000ooooooooool01?ooool00ol0003oooooooooo`3oooooo`?ooooo000Cooooo`;o00001_ooool0 0ol0003oooooooooo`3oooooo`?ooooo000Dooooo`03o`000?oooooooooo00Cooooo00?o0000oooo ooooool0ooooool3ooooo`00oooooolQooooo`00oooooolQooooo`00oooooolQooooo`00oooooolQ ooooo`00oooooolQooooo`00oooooolQooooo`00\ \>"], ImageRangeCache->{{{0, 287}, {176.938, 0}} -> {-0.677733, -1.13007, \ 0.0248015, 0.0127736}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Example\ of\ While\ loop\ *) \)\(\[IndentingNewLine]\)\(nn = 10; While[\((nn = nn - 1)\) > 5, Print[nn]]; \ Clear[nn];\)\)\)], "Input"], Cell[BoxData[ \(9\)], "Print"], Cell[BoxData[ \(8\)], "Print"], Cell[BoxData[ \(7\)], "Print"], Cell[BoxData[ \(6\)], "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(nn\ = \ 10; \ While[\ nn > 5, \ Print[nn]; \ nn = nn - 1]\)], "Input"], Cell[BoxData[ \(10\)], "Print"], Cell[BoxData[ \(9\)], "Print"], Cell[BoxData[ \(8\)], "Print"], Cell[BoxData[ \(7\)], "Print"], Cell[BoxData[ \(6\)], "Print"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*\ Example\ of\ For\ loop . \ \ The\ \(i++\)\ form\ is\ i = i + 1*) \)\(\[IndentingNewLine]\)\(For[i = 1; t = x, i\^2 < 10, \(i++\), t = t + i; Print[t]]; \ Clear[i, t]\)\)\)], "Input"], Cell[BoxData[ \(1 + x\)], "Print"], Cell[BoxData[ \(3 + x\)], "Print"], Cell[BoxData[ \(6 + x\)], "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Slide 05: Function forms in more detail", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(\((#\ + \ 1)\) &\)[ x]\)\(\ \ \)\( (*Form\ using\ slot\ number\ for\ parameter*) \)\)\)], \ "Input"], Cell[BoxData[ \(1 + x\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(\((#1/#2)\) &\)[x, y]\)\(\ \)\( (*Form\ with\ two\ arguments*) \)\)\)], "Input"], Cell[BoxData[ \(x\/y\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\(Function[z, z\^2]\)[{1, 2, 3}]\)\(\ \)\( (*\ Form\ using\ variable\ names\ are\ arguments*) \)\)\)], "Input"], Cell[BoxData[ \({1, 4, 9}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(z\)\(\ \ \)\( (*z\ has\ not\ been\ set\ in\ Global`\ context*) \)\)\ \)], "Input"], Cell[BoxData[ \(z\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*Example\ of\ using\ the\ Map\ feature . \ \ Reverse\ is\ a\ \ built\ in\ function\ to\ reverse\ lists*) \)\(\[IndentingNewLine]\)\(Reverse /@ \ {{a, b, x\ }, {c, d}, {e, f}}\)\)\)], "Input"], Cell[BoxData[ \({{x, b, a}, {d, c}, {f, e}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*Example\ using\ function\ f*) \)\(\[IndentingNewLine]\)\(Clear[ x]\[IndentingNewLine] \ Sin /@ \((1 + 2\ x + x\^2)\)\ \[IndentingNewLine] \)\)\)], "Input"], Cell[BoxData[ \(Sin[1] + Sin[2\ x] + Sin[x\^2]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*Use\ of\ Apply\ in\ shorthand\ \ form*) \)\(\[IndentingNewLine]\)\(New @@ Old[a, b, c]\)\)\)], "Input"], Cell[BoxData[ \(New[a, b, c]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\( (*Here\ I\ can\ multiply\ all\ the\ elements\ in\ a\ list\ \ together*) \)\(\[IndentingNewLine]\)\(Times\ @@ \ {a, b, c}\[IndentingNewLine] mylist\ = \ {\ 1, \ 2, \ 3, \ 4, \ 5}; \ Plus\ @@ \ mylist\[IndentingNewLine] Clear[mylist]\)\)\)], "Input"], Cell[BoxData[ \(a\ b\ c\)], "Output"], Cell[BoxData[ \(15\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Slide 08: Directories and files", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(Directory[]\)\(\ \ \)\( (*\ lists\ the\ current\ direcory*) \)\)\)], "Input"], Cell[BoxData[ \("/Users/tah"\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(SetDirectory["\"]\)\(\ \)\( (*This\ will\ change\ \ to\ a\ new\ direcory*) \)\)\)], "Input"], Cell[BoxData[ \("/Users/tah/TAH_docs/12.010"\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(FileNames["\<*.nb\>"]\)\(\ \ \)\(//\)\(\ \)\(TableForm\)\( (*\ This\ will\ list\ all\ the\ . nb\ files\ in\ the\ directory*) \)\)\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {"\<\"12.010.Lec08.nb\"\>"}, {"\<\"12.010.Lec09.nb\"\>"}, {"\<\"12.010_Lec13.nb\"\>"}, {"\<\"12.010.Lec14.nb\"\>"}, {"\<\"12.010.Lec15.nb\"\>"}, {"\<\"Essential_Mathematica_1.3.nb\"\>"}, {"\<\"Minimal_Mathematica_1.2.nb\"\>"}, {"\<\"PS6_Solutions_1.2.nb\"\>"} }, RowSpacings->1, ColumnSpacings->3, RowAlignments->Baseline, ColumnAlignments->{Left}], TableForm[ {"12.010.Lec08.nb", "12.010.Lec09.nb", "12.010_Lec13.nb", "12.010.Lec14.nb", "12.010.Lec15.nb", "Essential_Mathematica_1.3.nb", "Minimal_Mathematica_1.2.nb", "PS6_Solutions_1.2.nb"}]]], "Output"] }, Open ]] }, Closed]] }, FrontEndVersion->"5.0 for Macintosh", ScreenRectangle->{{0, 1280}, {0, 794}}, WindowSize->{657, 653}, WindowMargins->{{59, Automatic}, {Automatic, 22}}, StyleDefinitions -> "Classroom.nb" ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1754, 51, 55, 3, 108, "Title"], Cell[CellGroupData[{ Cell[1834, 58, 58, 0, 59, "Section"], Cell[CellGroupData[{ Cell[1917, 62, 113, 2, 27, "Input"], Cell[2033, 66, 35, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2105, 72, 155, 3, 59, "Input"], Cell[2263, 77, 56, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2356, 83, 165, 3, 59, "Input"], Cell[2524, 88, 35, 1, 27, "Output"] }, Open ]], Cell[2574, 92, 155, 3, 50, "Text"], Cell[CellGroupData[{ Cell[2754, 99, 137, 3, 27, "Input"], Cell[2894, 104, 23094, 549, 222, 4409, 314, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[26025, 658, 209, 3, 75, "Input"], Cell[26237, 663, 59, 1, 27, "Output"] }, Open ]], Cell[26311, 667, 173, 3, 43, "Input"], Cell[CellGroupData[{ Cell[26509, 674, 73, 2, 43, "Input"], Cell[26585, 678, 35, 1, 27, "Output"] }, Open ]], Cell[26635, 682, 41, 1, 27, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[26713, 688, 44, 0, 39, "Section"], Cell[CellGroupData[{ Cell[26782, 692, 183, 3, 43, "Input"], Cell[CellGroupData[{ Cell[26990, 699, 21865, 538, 186, 4588, 320, "GraphicsData", "PostScript", \ "Graphics"], Cell[48858, 1239, 39500, 833, 186, 6088, 416, "GraphicsData", "PostScript", \ "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[88407, 2078, 176, 3, 59, "Input"], Cell[88586, 2083, 34, 1, 23, "Print"], Cell[88623, 2086, 34, 1, 23, "Print"], Cell[88660, 2089, 34, 1, 23, "Print"], Cell[88697, 2092, 34, 1, 23, "Print"] }, Open ]], Cell[CellGroupData[{ Cell[88768, 2098, 91, 1, 27, "Input"], Cell[88862, 2101, 35, 1, 23, "Print"], Cell[88900, 2104, 34, 1, 23, "Print"], Cell[88937, 2107, 34, 1, 23, "Print"], Cell[88974, 2110, 34, 1, 23, "Print"], Cell[89011, 2113, 34, 1, 23, "Print"] }, Closed]], Cell[CellGroupData[{ Cell[89082, 2119, 234, 4, 77, "Input"], Cell[89319, 2125, 38, 1, 23, "Print"], Cell[89360, 2128, 38, 1, 23, "Print"], Cell[89401, 2131, 38, 1, 23, "Print"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[89488, 2138, 58, 0, 39, "Section"], Cell[CellGroupData[{ Cell[89571, 2142, 133, 3, 43, "Input"], Cell[89707, 2147, 39, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89783, 2153, 113, 2, 27, "Input"], Cell[89899, 2157, 38, 1, 42, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[89974, 2163, 142, 2, 48, "Input"], Cell[90119, 2167, 43, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90199, 2173, 106, 2, 27, "Input"], Cell[90308, 2177, 35, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90380, 2183, 217, 3, 59, "Input"], Cell[90600, 2188, 61, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90698, 2194, 196, 4, 80, "Input"], Cell[90897, 2200, 64, 1, 29, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[90998, 2206, 130, 2, 43, "Input"], Cell[91131, 2210, 46, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91214, 2216, 298, 6, 91, "Input"], Cell[91515, 2224, 41, 1, 27, "Output"], Cell[91559, 2227, 36, 1, 27, "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[91644, 2234, 50, 0, 39, "Section"], Cell[CellGroupData[{ Cell[91719, 2238, 108, 2, 27, "Input"], Cell[91830, 2242, 46, 1, 27, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[91913, 2248, 134, 2, 43, "Input"], Cell[92050, 2252, 62, 1, 27, "Output"] }, Closed]], Cell[CellGroupData[{ Cell[92149, 2258, 189, 3, 56, "Input"], Cell[92341, 2263, 748, 17, 149, "Output"] }, Open ]] }, Closed]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)