%PDF-1.5 % 4 0 obj << /S /GoTo /D (section*.2) >> endobj 7 0 obj (Introduction) endobj 8 0 obj << /S /GoTo /D (section.1) >> endobj 11 0 obj (1. Exterior algebra) endobj 12 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 15 0 obj (1.1. Vectors and dual vectors) endobj 16 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 19 0 obj (1.2. The wedge of two vectors) endobj 20 0 obj << /S /GoTo /D (subsection.1.3) >> endobj 23 0 obj (1.3. Defining the exterior algebra) endobj 24 0 obj << /S /GoTo /D (subsection.1.4) >> endobj 27 0 obj (1.4. The wedge of two dual vectors) endobj 28 0 obj << /S /GoTo /D (subsection.1.5) >> endobj 31 0 obj (1.5. R3 has no mixed wedges) endobj 32 0 obj << /S /GoTo /D (subsection.1.6) >> endobj 35 0 obj (1.6. Interior multiplication) endobj 36 0 obj << /S /GoTo /D (section.2) >> endobj 39 0 obj (2. Integration) endobj 40 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 43 0 obj (2.1. Differential forms) endobj 44 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 47 0 obj (2.2. Visualizing differential forms) endobj 48 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 51 0 obj (2.3. Integrating differential forms over manifolds) endobj 52 0 obj << /S /GoTo /D (section.3) >> endobj 55 0 obj (3. Differentiation) endobj 56 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 59 0 obj (3.1. Exterior Derivative) endobj 60 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 63 0 obj (3.2. Visualizing the exterior derivative) endobj 64 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 67 0 obj (3.3. Closed and exact forms) endobj 68 0 obj << /S /GoTo /D (subsection.3.4) >> endobj 71 0 obj (3.4. Future work: Lie derivative) endobj 72 0 obj << /S /GoTo /D (section*.3) >> endobj 75 0 obj (Acknowledgments) endobj 76 0 obj << /S /GoTo /D (section*.4) >> endobj 79 0 obj (References) endobj 80 0 obj << /S /GoTo /D [81 0 R /Fit] >> endobj 102 0 obj << /Length 1673 /Filter /FlateDecode >> stream xڭXYs6~ϯ`DqD_2cxG9ڦI)C~}X@d} .h%'?\>y~)H*ei\GT("I-n/gsrrayq9?:{x~D*KHy4g*ſx 6s)Ňq/ӄǹ (YQMobY@!cbtW#)YjltmQ_g"-!#fVf43Jָ, ͌'TENhm˭A):A 뀠1E.=a7]Qxe*!*ULa#ZR֎DjwWWN@7Vӻ{9{F;mjTl.KL%Buxwi9qY~]~6VDmx8wxׅ֮f[xs=\w|UKo(Ө9c\8 U=opGs*x8S1X=91YNJ!b9_P+)Bh$#sU 6ͺg~798]`9תhXdrJ,b63A`7~ƊtZ<8#i;^iHJT;)Ӛ<)`H7ʀ%9PUC=F,J~bdz9!8S|D-|lroenIIYPH4uP ͪe$r ;S)ɧ$[*;4QDM/{RU SRES:YOvESۺW3qj~'ޡ2N#`i`3줠^=%^o2J/V@*-lh#*>b2g+Kt۸~!vV=tZm W.1d;n>ǒy䡗Nmh#=({OuEv݈W kWOo69{ƀܡٞئ8wZ$#]Kk;TqT"fByBu^V'%W88:C- Tᐳ|LdRn$=/wEW<7蘇D=m^ߕwOWVގf"!g.Q]8m^]5#Vu(3&&Lf݄*N)_1jBl^C 0F:TUo`c7FWqy Ͼ#Ӹ#2L<,'gIԸ .ǩ ʝyQ0^;O?h~S--]9'Se$fȂSQf-Ra4}a j߆QcpЪ@" YdLv&V U<@.`KUcfG7 ʃRjۨlU-9ՍL*]Up{ vQ\4c(= "}u$5J4 Ḻ=m7< hTh.?`X>HY endstream endobj 81 0 obj << /Type /Page /Contents 102 0 R /Resources 101 0 R /MediaBox [0 0 612 792] /Parent 115 0 R /Annots [ 82 0 R 83 0 R 84 0 R 85 0 R 86 0 R 87 0 R 88 0 R 89 0 R 90 0 R 91 0 R 92 0 R 93 0 R 94 0 R 95 0 R 96 0 R 97 0 R 98 0 R 99 0 R 100 0 R ] >> endobj 82 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 475.44 194.169 484.351] /A << /S /GoTo /D (section*.2) >> >> endobj 83 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 461.547 228.126 472.396] /A << /S /GoTo /D (section.1) >> >> endobj 84 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 451.529 272.625 460.44] /A << /S /GoTo /D (subsection.1.1) >> >> endobj 85 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 437.637 275.863 448.485] /A << /S /GoTo /D (subsection.1.2) >> >> endobj 86 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 425.682 290.392 436.53] /A << /S /GoTo /D (subsection.1.3) >> >> endobj 87 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 413.727 298.002 424.575] /A << /S /GoTo /D (subsection.1.4) >> >> endobj 88 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 401.772 271.505 413.811] /A << /S /GoTo /D (subsection.1.5) >> >> endobj 89 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 389.816 261.722 400.665] /A << /S /GoTo /D (subsection.1.6) >> >> endobj 90 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 377.861 205.516 388.599] /A << /S /GoTo /D (section.2) >> >> endobj 91 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 367.843 241.16 376.754] /A << /S /GoTo /D (subsection.2.1) >> >> endobj 92 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 353.951 290.337 364.799] /A << /S /GoTo /D (subsection.2.2) >> >> endobj 93 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 341.996 357.087 352.844] /A << /S /GoTo /D (subsection.2.3) >> >> endobj 94 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 331.978 220.321 340.889] /A << /S /GoTo /D (section.3) >> >> endobj 95 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 320.023 248.743 328.823] /A << /S /GoTo /D (subsection.3.1) >> >> endobj 96 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 306.13 312.725 316.978] /A << /S /GoTo /D (subsection.3.2) >> >> endobj 97 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 296.112 267.063 305.023] /A << /S /GoTo /D (subsection.3.3) >> >> endobj 98 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 284.157 284.719 293.068] /A << /S /GoTo /D (subsection.3.4) >> >> endobj 99 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 270.265 217.443 281.113] /A << /S /GoTo /D (section*.3) >> >> endobj 100 0 obj << /Type /Annot /Subtype /Link /Border[0 0 1]/H/I/C[1 0 0] /Rect [137.631 260.247 185.507 269.158] /A << /S /GoTo /D (section*.4) >> >> endobj 103 0 obj << /D [81 0 R /XYZ 125.672 698.868 null] >> endobj 104 0 obj << /D [81 0 R /XYZ 126.672 675.95 null] >> endobj 108 0 obj << /D [81 0 R /XYZ 281.86 506.324 null] >> endobj 5 0 obj << /D [81 0 R /XYZ 272.144 225.119 null] >> endobj 101 0 obj << /ColorSpace 3 0 R /Pattern 2 0 R /ExtGState 1 0 R /Font << /F50 105 0 R /F24 106 0 R /F49 107 0 R /F8 109 0 R /F45 110 0 R /F7 111 0 R /F11 112 0 R /F14 113 0 R /F52 114 0 R >> /ProcSet [ /PDF /Text ] >> endobj 122 0 obj << /Length 2961 /Filter /FlateDecode >> stream xڽk۸ #_"kF|Hr8H) MAksmueɑur3e3^Q,p8:^lիo"efqs"edd0Yg&2?+iջO7=o"cY*R,I+!Y ۻj)L5rq]T[&evqK]Oϫ.7vlyY~!.kzji#tyQElS<#)ՂiXqbMD~n;] ~F%4O'ЌgB'LN@-WJK##O TengEQ7k6@1 Ů/=ƶN@Nɯ܅j "㎋I8T"Ě>MQ9de1ŝ"-I}jB!ӷ*h26x"zvR9WnWξ6jcCjQ-ۑCx?_Ιvւ64#;p8 -P$$8B>@>}PѳPr\>;0 ݝ={cysQ]bu BEH9fIVz>m0qC)>~[8MHH3ܺsHa=`DBp,·Ö́ApIaHi%sOȹwz-%;qb7z'911FO#.88$Lg:4 ]9XI:5OG[[5(q&4:t T|IbY,(4'N'&NvCc[KN