%!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: 003_vec.dvi %%Pages: 60 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX12 CMR12 CMR8 CMTI12 CMR7 CMR10 CMTT10 CMMI12 %%+ CMSY10 CMSY8 CMMI8 CMSY6 CMR6 CMMI6 TeX-cmex8 CMEX10 %%DocumentPaperSizes: Letter %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o 003_vec 003_vec %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2010.02.15:2025 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: texps.pro 0 0 %! 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 99 /c put dup 107 /k put readonly def /FontBBox{11 -250 1241 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 53 /five put dup 55 /seven put dup 61 /equal put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 14 /openbullet put dup 49 /infinity put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 58 /period put dup 59 /comma put dup 65 /A put dup 66 /B put dup 67 /C put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 102 /f put dup 105 /i put dup 107 /k put dup 114 /r put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 7 /minusplus put dup 14 /openbullet put dup 49 /infinity put dup 112 /radical put readonly def /FontBBox{-30 -955 1185 779}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 7 /minusplus put dup 20 /lessequal put dup 49 /infinity put dup 106 /bar put dup 112 /radical put dup 120 /section put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 18 /theta put dup 30 /phi put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 65 /A put dup 66 /B put dup 67 /C put dup 97 /a put dup 98 /b put dup 99 /c put dup 105 /i put dup 110 /n put dup 114 /r put dup 117 /u put dup 118 /v put dup 120 /x put dup 121 /y put dup 122 /z put dup 126 /vector put readonly def /FontBBox{-30 -250 1026 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 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cleartomark %%EndFont %%BeginFont: CMTT10 %!PS-AdobeFont-1.1: CMTT10 1.00B %%CreationDate: 1992 Apr 26 10:42:42 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch true def end readonly def /FontName /CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 126 /asciitilde put readonly def /FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 65 /A put dup 66 /B put dup 68 /D put dup 69 /E put dup 73 /I put dup 76 /L put dup 77 /M put dup 79 /O put dup 80 /P put dup 83 /S put dup 84 /T put dup 85 /U put dup 88 /X put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 65 /A put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 121 /y put dup 122 /z put readonly def /FontBBox{-53 -251 1139 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI12 %!PS-AdobeFont-1.1: CMTI12 1.0 %%CreationDate: 1991 Aug 18 21:06:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMTI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 45 /hyphen put dup 48 /zero put dup 49 /one put dup 50 /two put dup 56 /eight put dup 58 /colon put dup 65 /A put dup 67 /C put dup 68 /D put dup 69 /E put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 87 /W put dup 89 /Y put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 121 /y put readonly 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 33 /exclam put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 65 /A put dup 67 /C put dup 70 /F put dup 71 /G put dup 73 /I put dup 76 /L put dup 78 /N put dup 79 /O put dup 80 /P put dup 84 /T put dup 87 /W put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 124 /emdash put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 34 /quotedblright put dup 38 /ampersand put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 124 /emdash put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 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(magnitude)f(and)g(direction)g(in)g(answ)m(ers.)195 5152 y(Wh)m(y)h(do)e(w)m(e)i(need)g(v)m(ector)f(comp)s(onen)m(ts)h(then?)p eop end %%Page: 26 26 TeXDict begin 26 25 bop 1820 90 a Fp({)32 b(26)g({)195 397 y(First)g(for)f(calculations,)i(where)g(v)m(ector)g(comp)s(onen)m (ts)g(are)f(usually)h(the)f(only)g(e\016cien)m(t)i(w)m(a)m(y)f(to)e(do) 0 590 y(the)i(calculations.)195 847 y(But)40 b(second)h(and)e(equally)i (imp)s(ortan)m(tly)f(for)f(conceptual)i(w)m(ork)f(for)f(man)m(y)h(purp) s(oses.)66 b(F)-8 b(or)39 b(ex-)0 1039 y(ample,)45 b(for)d(the)g(pro)s (ofs)g(w)m(e)h(do)e(in)i Fh(x)f Fp(5)g(just)g(b)s(elo)m(w)h(on)f(v)m (ector)h(math.)71 b(In)43 b(tensor)f(math,)j(whic)m(h)e(is)0 1232 y(generalization)33 b(of)g(v)m(ector)g(math,)g(comp)s(onen)m(t)h (formalism)f(is)h(also)e(needed)j(for)d(man)m(y)i(purp)s(oses.)45 b(But)0 1425 y(one)27 b(do)s(es)h(ha)m(v)m(e)g(to)f(sa)m(y)h(that)f (there)g(is)h(a)f(comp)s(onen)m(t-free)h(approac)m(h)f(to)g(tensor)g (math)h(\(see)g(Wikip)s(edia:)0 1617 y(T)-8 b(ensor)34 b(\(in)m(trinsic)g(de\014nition\)\))f(of)f(whic)m(h)i(y)m(ours)g(truly) f(kno)m(ws)h(little.)1416 2089 y Fm(5.)112 b(VECTOR)36 b(MA)-9 b(TH)195 2388 y Fp(W)h(e)33 b(need)h(some)f(v)m(ector)h(math.) 195 2645 y(This)g(v)m(ector)f(math)g(is)g(correct)g(for)f(ph)m (ysically)k(de\014ned)e(v)m(ectors)g(and)e(that)h(is)g(its)g (justi\014cation.)195 2902 y(All)g(our)f(pro)s(ofs)h(and)f (illustrations)i(are)e(for)g(t)m(w)m(o-dimensional)j(v)m(ectors)f(for)e (simplicit)m(y)-8 b(.)195 3159 y(But)31 b(all)g(the)g(pro)s(ofs)f(and)h (illustrations)h(ob)m(viously)g(generalize)g(to)f(m)m(ulti-dimensional) h(v)m(ectors)h(in)0 3352 y(m)m(ulti-dimensional)h(Euclidean)h(space.) 1411 3823 y Fm(5.1.)112 b(V)-9 b(ector)36 b(Addition)195 4123 y Fp(W)-8 b(e)33 b(kno)m(w)h(ho)m(w)f(to)f(add)h(real)g(n)m(um)m (b)s(ers,)h(but)f(ho)m(w)g(do)s(es)g(one)g(add)g(v)m(ectors?)195 4380 y(V)-8 b(ector)33 b(addition)g(has)g(to)f(b)s(e)h(de\014ned)h (actually)-8 b(.)195 4637 y(Y)g(ours)34 b(truly)h(thinks)g(it)f(b)s (est)h(to)e(just)i(de\014ne)g(v)m(ector)g(addition)f(in)g(terms)h(of)e (v)m(ector)i(comp)s(onen)m(ts)0 4830 y(whic)m(h)f(are)f(real)f(n)m(um)m (b)s(ers.)195 5087 y(Sa)m(y)403 5062 y Fi(~)385 5087 y(A)39 b Fp(and)708 5062 y Fi(~)692 5087 y(B)44 b Fp(are)38 b(general)h(v)m(ectors.)63 b(If)38 b(they)h(are)g(actually)g(ph)m (ysical)h(v)m(ectors,)i(they)d(m)m(ust)h(b)s(e)0 5279 y(of)32 b(the)i(same)f(t)m(yp)s(e:)45 b(e.g.,)33 b(displacemen)m(t)j(v) m(ectors)e(or)f(v)m(elo)s(cit)m(y)h(v)m(ectors.)46 b(It)33 b(just)g(turns)h(out)e(in)h(ph)m(ysics)p eop end %%Page: 27 27 TeXDict begin 27 26 bop 1820 90 a Fp({)32 b(27)g({)0 397 y(that)g(the)h(v)m(ectors)h(m)m(ust)g(b)s(e)f(of)f(the)h(same)g(t)m (yp)s(e)h(for)e(the)h(sum)g(to)g(ha)m(v)m(e)h(an)m(y)f(ph)m(ysical)h (meaning.)195 654 y(In)f(comp)s(onen)m(t)h(form)e(one)h(has)1135 917 y Fi(~)1117 942 y(A)28 b Fp(=)f(\()p Fi(A)1432 957 y Ff(x)1476 942 y Fi(;)17 b(A)1593 957 y Ff(y)1634 942 y Fp(\))195 b(and)2235 917 y Fi(~)2220 942 y(B)33 b Fp(=)27 b(\()p Fi(B)2542 957 y Ff(x)2586 942 y Fi(;)17 b(B)2704 957 y Ff(y)2745 942 y Fp(\))944 b(\(42\))195 1294 y(W)-8 b(e)33 b(de\014ne)h(the)f(sum)g(of)f(the)h(v)m(ectors)i(to)d(b)m(y)1324 1556 y Fi(~)1306 1581 y(A)22 b Fp(+)1514 1556 y Fi(~)1499 1581 y(B)33 b Fp(=)27 b(\()p Fi(A)1820 1596 y Ff(x)1886 1581 y Fp(+)22 b Fi(B)2058 1596 y Ff(x)2102 1581 y Fi(;)17 b(A)2219 1596 y Ff(y)2283 1581 y Fp(+)22 b Fi(B)2455 1596 y Ff(y)2496 1581 y Fp(\))33 b Fi(:)1133 b Fp(\(43\))0 1869 y(W)-8 b(e)33 b(add)g(the)g(comp)s(onen)m(ts)h(for)e(eac)m(h)h(co) s(ordinate)g(direction)g(b)m(y)h(real)e(n)m(um)m(b)s(er)i(addition.)195 2126 y(The)g(v)m(ector)f(addition)g(rule)g(has)g(simple)h(geometrical)f (in)m(terpretation.)195 2383 y(One)27 b(tak)m(es)h(v)m(ector)942 2358 y Fi(~)926 2383 y(B)k Fp(and)27 b(men)m(tally)i(transp)s(orts)e (its)g(tail)g(from)f(the)i(origin)e(to)h(the)g(head)g(of)g(v)m(ector)18 2550 y Fi(~)0 2575 y(A)39 b Fp(without)g(c)m(hanging)h(its)f (direction.)63 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y(c)m(ho)s(oses.)42 b(F)-8 b(or)24 b(qualitativ)m(e)j(thinking)f (ab)s(out)e(or)g(illustration)i(of)e(v)m(ector)i(sums)h(this)e(is)h (often)e(v)m(ery)j(useful.)0 4566 y(F)-8 b(or)32 b(quan)m(titativ)m(e)i (calculations)g(it)e(is)h(not)g(usually)h(useful.)792 5038 y Fm(5.2.)112 b(V)-9 b(ector)36 b(Multiplication)j(b)m(y)e(A)g (Real)h(Num)m(b)s(er)195 5338 y Fp(V)-8 b(ector)33 b(m)m(ultiplication) h(b)m(y)f(a)g(real)f(n)m(um)m(b)s(er)i(m)m(ust)g(also)f(b)s(e)f (de\014ned.)p eop end %%Page: 28 28 TeXDict begin 28 27 bop 1820 90 a Fp({)32 b(28)g({)0 961 y(Fig.)51 b(4.|)35 b(A)g(regular)g(hexagon)h(from)f(whic)m(h)i(the) e(sp)s(ecial)h(trig)f(function)h(v)-5 b(alues)36 b(for)f(angles)h(30) 3669 925 y Fg(\016)3743 961 y Fp(and)0 1154 y(60)98 1118 y Fg(\016)170 1154 y Fp(can)c(b)s(e)h(deduced.)0 3609 y(Fig.)43 b(5.|)32 b(V)-8 b(ector)33 b(addition)g(in)f(the)h(geometric) h(in)m(terpretation.)p eop end %%Page: 29 29 TeXDict begin 29 28 bop 1820 90 a Fp({)32 b(29)g({)195 397 y(There)46 b(is)f(no)g(w)m(a)m(y)h(that)e(it)h(can)g(just)g(b)s(e)g (deduced)h(from)f(our)g(de\014nition)g(of)f(v)m(ectors)j(and)e(the)0 590 y(prop)s(erties)33 b(of)g(real)f(n)m(um)m(b)s(ers.)195 847 y(But)h(the)g(de\014nition)g(is)g(the)g(ob)m(vious)h(one.)195 1104 y(Sa)m(y)397 1079 y Fi(~)379 1104 y(A)f Fp(is)g(a)f(general)h(v)m (ector)h(and)f Fi(c)f Fp(is)h(a)g(general)g(real)f(n)m(um)m(b)s(er.)195 1361 y(W)-8 b(e)33 b(de\014ne)1579 1553 y Fi(c)1639 1528 y(~)1621 1553 y(A)28 b Fp(=)f(\()p Fi(cA)1978 1568 y Ff(x)2022 1553 y Fi(;)17 b(cA)2181 1568 y Ff(y)2223 1553 y Fp(\))33 b Fi(;)1406 b Fp(\(44\))0 1796 y(where)34 b Fi(cA)397 1811 y Ff(x)473 1796 y Fp(and)f Fi(cA)778 1811 y Ff(y)852 1796 y Fp(are)g(just)g(ordinary)f(real)h(n)m(um)m(b)s (er)h(m)m(ultiplications.)714 2267 y Fm(5.3.)113 b(The)37 b(In)m(v)m(erse)h(of)g(a)f(V)-9 b(ector)37 b(and)h(the)f(Zero)h(V)-9 b(ector)195 2567 y Fp(The)34 b(de\014nition)f(of)f(an)h(in)m(v)m(erse)i (of)1528 2542 y Fi(~)1510 2567 y(A)d 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3727 y Fp(V)-8 b(ector)33 b(addition)g(has)g(the)g(asso)s(ciativ)m(e)h(prop)s(ert)m(y) -8 b(.)0 4067 y(Fig.)43 b(6.|)32 b(The)h(comm)m(utativ)m(e)i(prop)s (ert)m(y)e(of)f(v)m(ector)i(addition)f(is)g(illustrated.)p eop end %%Page: 32 32 TeXDict begin 32 31 bop 1820 90 a Fp({)32 b(32)g({)195 397 y(Pro)m(v)m(e)i(this.)195 654 y(Y)-8 b(ou)33 b(ha)m(v)m(e)g(1)g (min)m(utes)h(w)m(orking)g(in)e(groups.)195 911 y(Behold:)110 1156 y Fi(~)92 1182 y(A)23 b Fp(+)f(\()340 1156 y Fi(~)324 1182 y(B)27 b Fp(+)537 1156 y Fi(~)523 1182 y(C)7 b Fp(\))83 b(=)g(\()p Fi(A)991 1197 y Ff(x)1034 1182 y Fi(;)17 b(A)1151 1197 y Ff(y)1193 1182 y Fp(\))22 b(+)g(\()p Fi(B)1463 1197 y Ff(x)1529 1182 y Fp(+)g Fi(C)1697 1197 y Ff(x)1741 1182 y Fi(;)17 b(B)1859 1197 y Ff(y)1922 1182 y Fp(+)22 b Fi(C)2090 1197 y Ff(y)2131 1182 y Fp(\))721 1374 y(=)83 b(\()p Fi(A)991 1389 y Ff(x)1057 1374 y Fp(+)22 b([)p Fi(B)1256 1389 y Ff(x)1322 1374 y Fp(+)g Fi(C)1490 1389 y Ff(x)1534 1374 y Fp(])p Fi(;)17 b(A)1678 1389 y Ff(y)1741 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Fp(sin)q(\()p Fi(\022)s Fp(\))2360 3942 y(=)28 b Fh(\000)2660 3875 y Fp(1)p 2551 3919 265 4 v 2551 4011 a(tan\()p Fi(\022)s Fp(\))2854 3942 y(=)g Fh(\000)17 b Fp(cot\()p Fi(\022)s Fp(\))33 b Fi(;)287 b Fp(\(A15\))0 4235 y(whence)1137 4527 y(sin)q(\()p Fi(\022)25 b Fh(\006)e Fp(90)1563 4486 y Fg(\016)1602 4527 y Fp(\))83 b(=)g Fh(\006)17 b Fp(cos\()p Fi(\022)s Fp(\))34 b Fi(;)1362 b Fp(\(A16\))1126 4744 y(cos)q(\()p Fi(\022)25 b Fh(\006)e Fp(90)1563 4703 y Fg(\016)1602 4744 y Fp(\))83 b(=)g Fh(\007)17 b Fp(sin)q(\()p Fi(\022)s Fp(\))33 b Fi(;)1373 b Fp(\(A17\))1116 4962 y(tan\()p Fi(\022)25 b Fh(\006)e Fp(90)1563 4921 y Fg(\016)1602 4962 y Fp(\))83 b(=)g Fh(\000)2077 4894 y Fp(1)p 1969 4939 V 1969 5030 a(tan\()p Fi(\022)s Fp(\))2272 4962 y(=)27 b Fh(\000)17 b Fp(cot)q(\()p Fi(\022)s Fp(\))33 b Fi(;)869 b Fp(\(A18\))p eop end %%Page: 58 58 TeXDict begin 58 57 bop 1820 90 a Fp({)32 b(58)g({)1037 397 y Fm(A.4.)112 b(Iden)m(tities)38 b(for)f(Argumen)m(t)h Fp(90)2654 361 y Fg(\016)2715 397 y Fh(\000)22 b Fi(\022)195 697 y Fp(Behold:)849 936 y(sin\(90)1104 895 y Fg(\016)1165 936 y Fh(\000)h Fi(\022)s Fp(\))83 b(=)g Fh(\000)17 b Fp(sin)q(\()p Fi(\022)25 b Fh(\000)e Fp(90)2113 895 y Fg(\016)2152 936 y Fp(\))k(=)h(cos)q(\()p Fi(\022)s Fp(\))33 b Fi(;)1017 b Fp(\(A19\))838 1154 y(cos\(90)1104 1113 y Fg(\016)1165 1154 y Fh(\000)23 b Fi(\022)s Fp(\))83 b(=)g(cos)q(\()p Fi(\022)25 b Fh(\000)e Fp(90)2030 1113 y Fg(\016)2069 1154 y Fp(\))k(=)h(sin\()p Fi(\022)s Fp(\))34 b Fi(;)1111 b Fp(\(A20\))827 1371 y(tan\(90)1104 1330 y Fg(\016)1165 1371 y Fh(\000)23 b Fi(\022)s Fp(\))83 b(=)g Fh(\000)17 b Fp(tan\()p Fi(\022)25 b Fh(\000)e Fp(90)2134 1330 y Fg(\016)2173 1371 y Fp(\))28 b(=)2460 1304 y(1)p 2352 1348 265 4 v 2352 1440 a(tan\()p Fi(\022)s Fp(\))2655 1371 y(=)f(cot\()p Fi(\022)s Fp(\))33 b Fi(;)581 b Fp(\(A21\))0 1611 y(whence)1223 1850 y(sin)q(\(90)1479 1809 y Fg(\016)1540 1850 y Fh(\000)23 b Fi(\022)s Fp(\))83 b(=)g(cos\()p Fi(\022)s Fp(\))33 b Fi(;)1371 b Fp(\(A22\))1212 2068 y(cos)q(\(90)1479 2026 y Fg(\016)1540 2068 y Fh(\000)23 b Fi(\022)s Fp(\))83 b(=)g(sin\()p Fi(\022)s Fp(\))34 b Fi(;)1381 b Fp(\(A23\))1202 2285 y(tan\(90)1479 2244 y Fg(\016)1540 2285 y Fh(\000)23 b Fi(\022)s Fp(\))83 b(=)2086 2218 y(1)p 1978 2262 V 1978 2353 a(tan)o(\()p Fi(\022)s Fp(\))2280 2285 y(=)28 b(cot\()p Fi(\022)s Fp(\))33 b Fi(:)955 b Fp(\(A24\))711 2797 y Fm(A.5.)112 b(Iden)m(tit)m(y)37 b Fp(cos)q(\()p Fi(a)p Fp(\))17 b(cos\()p Fi(b)p Fp(\))28 b(=)2116 2730 y(1)p 2116 2774 49 4 v 2116 2865 a(2)2174 2797 y([cos)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f(+)g(cos)q(\()p Fi(a)g Fp(+)g Fi(b)p Fp(\)])195 3097 y(Add)33 b(the)g(expansions)i(for)d(cos\()p Fi(a)23 b Fh(\000)f Fi(b)p Fp(\))33 b(and)g(cos\()p Fi(a)23 b Fp(+)f Fi(b)p Fp(\))33 b(to)f(get)1110 3336 y(cos)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f(+)g(cos)q(\()p Fi(a)g Fp(+)g Fi(b)p Fp(\))28 b(=)g(2)17 b(cos\()p Fi(a)p Fp(\))g(cos\()p Fi(b)p Fp(\))864 b(\(A25\))0 3576 y(whic)m(h)34 b(yields)g(immediately) 1051 3815 y(cos)q(\()p Fi(a)p Fp(\))17 b(cos\()p Fi(b)p Fp(\))28 b(=)1715 3748 y(1)p 1715 3792 V 1715 3883 a(2)1774 3815 y([cos\()p Fi(a)23 b Fh(\000)f Fi(b)p Fp(\))h(+)f(cos\()p Fi(a)h Fp(+)f Fi(b)p Fp(\)])33 b Fi(:)805 b Fp(\(A26\))195 4119 y(If)33 b Fi(a)27 b Fp(=)h Fi(b)p Fp(,)33 b(w)m(e)h(get)1407 4311 y(cos)1537 4270 y Fo(2)1577 4311 y Fp(\()p Fi(a)p Fp(\))27 b(=)1845 4244 y(1)p 1845 4288 V 1845 4380 a(2)1904 4311 y([1)22 b(+)g(cos\(2)p Fi(a)p Fp(\)])33 b Fi(:)1160 b Fp(\(A27\))721 4798 y Fm(A.6.)112 b(Iden)m(tit)m(y)37 b Fp(sin)q(\()p Fi(a)p Fp(\))17 b(sin\()p Fi(b)p Fp(\))28 b(=)2104 4731 y(1)p 2104 4775 V 2104 4867 a(2)2163 4798 y([cos\()p Fi(a)23 b Fh(\000)f Fi(b)p Fp(\))h Fh(\000)f Fp(cos)q(\()p Fi(a)g Fp(+)g Fi(b)p Fp(\)])195 5098 y(Subtract)33 b(form)f(the)h(expansions)i(for)d(cos)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))32 b(the)h(expansion)i(from)d(cos\()p Fi(a)23 b Fp(+)f Fi(b)p Fp(\))33 b(to)f(get)1120 5338 y(cos)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f Fh(\000)h Fp(cos)q(\()p Fi(a)f Fp(+)g Fi(b)p Fp(\))28 b(=)g(2)17 b(sin\()p Fi(a)p Fp(\))g(sin\()p Fi(b)p Fp(\))874 b(\(A28\))p eop end %%Page: 59 59 TeXDict begin 59 58 bop 1820 90 a Fp({)32 b(59)g({)0 397 y(whic)m(h)i(yields)g(immediately)1062 689 y(sin\()p Fi(a)p Fp(\))17 b(sin)q(\()p Fi(b)p Fp(\))28 b(=)1703 622 y(1)p 1703 667 49 4 v 1703 758 a(2)1762 689 y([cos)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f Fh(\000)h Fp(cos\()p Fi(a)g Fp(+)f Fi(b)p Fp(\)])33 b Fi(:)815 b Fp(\(A29\))195 1046 y(If)33 b Fi(a)27 b Fp(=)h Fi(b)p Fp(,)33 b(w)m(e)h(get)1411 1239 y(sin)1531 1197 y Fo(2)1570 1239 y Fp(\()p Fi(a)p Fp(\))28 b(=)1839 1171 y(1)p 1839 1216 V 1839 1307 a(2)1897 1239 y([1)22 b Fh(\000)h Fp(cos)q(\(2)p Fi(a)p Fp(\)])33 b Fi(:)1164 b Fp(\(A30\))727 1726 y Fm(A.7.)112 b(Iden)m(tit)m(y)37 b Fp(sin)q(\()p Fi(a)p Fp(\))17 b(cos\()p Fi(b)p Fp(\))28 b(=)2121 1658 y(1)p 2121 1703 V 2121 1794 a(2)2180 1726 y([sin)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f(+)g(sin)q(\()p Fi(a)g Fp(+)g Fi(b)p Fp(\)])195 2026 y(Add)33 b(the)g(expansions)i(for) d(sin\()p Fi(a)23 b Fp(+)f Fi(b)p Fp(\))33 b(and)f(sin)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))33 b(to)f(get)1127 2318 y(sin\()p Fi(a)23 b Fp(+)f Fi(b)p Fp(\))g(+)g(sin)q(\()p Fi(a)g Fh(\000)h Fi(b)p Fp(\))28 b(=)g(2)17 b(sin\()p Fi(a)p Fp(\))g(cos\()p Fi(b)p Fp(\))880 b(\(A31\))0 2610 y(whic)m(h)34 b(yields)g(immediately)1068 2902 y(sin\()p Fi(a)p Fp(\))17 b(cos)q(\()p Fi(b)p Fp(\))28 b(=)1720 2835 y(1)p 1720 2879 V 1720 2971 a(2)1779 2902 y([sin)q(\()p Fi(a)22 b Fh(\000)h Fi(b)p Fp(\))f(+)g(sin)q(\()p Fi(a)g Fp(+)g Fi(b)p Fp(\)])34 b Fi(:)821 b Fp(\(A32\))195 3259 y(If)33 b Fi(a)27 b Fp(=)h Fi(b)p Fp(,)33 b(w)m(e)h(get)1390 3451 y(sin\()p Fi(a)p Fp(\))17 b(cos)q(\()p Fi(a)p Fp(\))27 b(=)2052 3384 y(1)p 2052 3429 V 2052 3520 a(2)2127 3451 y(sin)q(\(2)p Fi(a)p Fp(\)])33 b Fi(:)1143 b Fp(\(A33\))1569 3923 y Fm(REFERENCES)0 4200 y Fp(Arfk)m(en,)34 b(G.)e(1970,)g (Mathematical)h(Metho)s(ds)h(for)e(Ph)m(ysicists)k(\(New)d(Y)-8 b(ork:)44 b(Academic)34 b(Press\))0 4476 y(Barger,)42 b(V.)e(D.,)i(&)e(Olson,)j(M.)d(G.)g(1987,)h Fn(Classic)-5 b(al)41 b(Ele)-5 b(ctricity)42 b(and)g(Magnetism)d Fp(\(Boston:)59 b(Allyn)293 4668 y(and)32 b(Bacon,)h(Inc.\))0 4944 y(Enge,)25 b(H.)e(A.)g(1966,)h(In)m(tro)s(duction)f(to)f(Nuclear)i(Ph)m(ysics)h (\(Reading,)g(Massac)m(h)m(usetts:)42 b(Addison-W)-8 b(esley)293 5136 y(Publishing)34 b(Compan)m(y\))p eop end %%Page: 60 60 TeXDict begin 60 59 bop 1820 90 a Fp({)32 b(60)g({)0 397 y(Gri\016ths,)49 b(D.)c(J.)h(1999,)i Fn(Intr)-5 b(o)g(duction)46 b(to)h(Ele)-5 b(ctr)g(o)g(dynamics)44 b Fp(\(Upp)s(er)i(Saddle)g(Riv)m (er,)k(New)c(Jersey:)293 590 y(Pren)m(tice)34 b(Hall\))0 865 y(Ohanian,)f(H.)f(C.)i(1988,)d Fn(Classic)-5 b(al)34 b(Ele)-5 b(ctr)g(o)g(dynamics)31 b Fp(\(Boston:)44 b(Allyn)33 b(and)g(Bacon,)g(Inc.\))0 1141 y(Serw)m(a)m(y)-8 b(,)38 b(R.)e(A.)g(&)g(Jew)m(ett,)i(J.)e(W.,)h(Jr.)f(2008,)g(Ph)m(ysics)j(for) c(Scien)m(tists)j(and)e(Engineers,)j(7th)c(Edition)293 1334 y(\(Belmon)m(t,)e(California:)44 b(Thomson\))0 1609 y(Tipler,)h(P)-8 b(.)42 b(A.,)h(&)f(Mosca,)i(G.)d(2008,)i(Ph)m(ysics)h (for)d(Scien)m(tists)j(and)d(Engineers,)46 b(6th)41 b(Edition)h(\(New) 293 1802 y(Y)-8 b(ork:)43 b(W.H.)33 b(F)-8 b(reeman)33 b(and)g(Compan)m(y\))0 2078 y(W)-8 b(eb)s(er,)35 b(H.)g(J.,)g(&)f(Arfk) m(en,)i(G.)e(B.)g(2004,)g(Essen)m(tial)i(Mathematical)f(Metho)s(ds)g (for)f(Ph)m(ysicists)k(\(Ams-)293 2270 y(terdam:)44 b(Elsevier)34 b(Academic)g(Press\))0 2546 y(W)-8 b(olfson,)46 b(R.)d(&)f(P)m(asac)m (ho\013,)47 b(J.)c(M.)h(1990,)g(Ph)m(ysics:)67 b(Extended)45 b(with)f(Mo)s(dern)f(Ph)m(ysics)j(\(London:)293 2738 y(Scott,)32 b(F)-8 b(oresman/Little,)34 b(Bro)m(wn)f(Higher)g (Education\))p 0 5187 1560 4 v 149 5337 a Fk(This)28 b(preprin)n(t)f(w)n(as)g(prepared)f(with)i(the)g(AAS)g(L)1723 5322 y Fl(A)1760 5337 y Fk(T)1806 5355 y(E)1852 5337 y(X)g(macros)e(v5.2.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF