{VERSION 14 0 "Windows 7" "14.0" } {USTYLETAB {PSTYLE "Ordered List 1" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 } {PSTYLE "Ordered List 2" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Ordered List 4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Ordered List 5" -1 204 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier New" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Annotation Title" -1 205 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "C ourier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printe d Output" -1 6 1 {CSTYLE "" -1 -1 "Courier New" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "C ourier New" 1 12 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier New" 1 12 40 120 40 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 " Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "HyperlinkError" -1 206 1 {CSTYLE "" -1 -1 "Courier New" 1 12 255 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier New" 1 12 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 4 " -1 20 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Hyperlink Warning" -1 207 1 {CSTYLE "" -1 -1 "Courier New" 1 12 0 0 255 1 2 2 1 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Left Justified M aple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{CSTYLE "Annotation Text" -1 200 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Maple Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Couri er" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Heading" -1 26 "Ti mes" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic" -1 42 "Ti mes" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Variable" -1 25 " Courier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 38 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined \+ Italic" -1 43 "Times" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Maple Input" -1 0 "Courier New" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 1 0 0 0 1 }{CSTYLE "2D Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "2D Math Small" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Page Number" -1 33 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Output Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Title" -1 27 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 16 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Caption Reference" -1 201 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input Placeholder" -1 202 "Courier \+ New" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "Code" -1 203 "Cour ier New" 1 12 255 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic S mall206" -1 204 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D M ath Italic Small205" -1 205 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 } {CSTYLE "2D Inert Output" -1 206 "Times" 1 12 144 144 144 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 0 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Header and Footer" -1 208 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 209 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Equation Label" -1 210 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Caption Text" -1 211 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fixed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{PSTYLE "" -1 208 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "" -1 209 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 210 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 211 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "" -1 212 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 212 22 "Elliptic-Direct Method" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 213 37 "\251 2011 Sri Harsha Garapat i, Autar Kaw" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 213 28 "University of S outh Florida " }}}{EXCHG {PARA 19 "" 0 "" {TEXT 213 24 "United States \+ of America" }}}{EXCHG {PARA 19 "" 0 "" {TEXT 213 15 "kaw@eng.usf.edu" }}}{EXCHG {PARA 208 "" 0 "" {TEXT 209 0 "" }}}{EXCHG {PARA 209 "" 0 "" {TEXT 209 148 "NOTE: This worksheet demonstrates the use of Maple to \+ illustrate direct method, a technique used in solving elliptic partial differential equations." }}}{EXCHG {PARA 210 "" 0 "" {TEXT 209 0 "" } }}{EXCHG {PARA 211 "" 0 "" {TEXT 209 17 "Problem Statement" }}}{EXCHG {PARA 3 "" 0 "" {TEXT 209 246 "Use the direct method to solve for the \+ temperature distribution of a rectangular plate, rectangular plate wit h a length of 2.4 m and width of 3.0 m. The plate is subjected to diri chlet temperature boundary conditions on the foursides of the plate" } }}{SECT 0 {PARA 3 "" 0 "" {TEXT 214 6 "Inputs" }}{EXCHG {PARA 3 "" 0 " " {TEXT 209 115 "The following simulation approximates the temperature distribution along the length of the rod. The user inputs are" }} {PARA 3 "" 0 "" {TEXT 209 115 " a) Length of the plate \+ b) width of the plate c) Temperature on the left end of the plate" }}{PARA 3 "" 0 "" {TEXT 209 8 " d) " }{TEXT 209 40 "Temper ature on the reft end of the plate" }{TEXT 209 5 " e) " }{TEXT 209 39 "Temperature on the top end of the plate" }{TEXT 209 27 " \+ f) " }{TEXT 209 42 "Temperature on the bottom end of the plate" }}{PARA 212 "" 0 "" {TEXT 209 5 " " }{XPPEDIT 2 0 "Typeset ting:-mrow(Typesetting:-mo(\" \", font_style_name = \"Text\", mathvari ant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em \"), Typesetting:-mi(\"j\", italic = \"false\", font_style_name = \"Te xt\", mathvariant = \"normal\"), Typesetting:-mo(\")\", font_style_nam e = \"Text\", mathvariant = \"normal\", fence = \"true\", separator = \+ \"false\", stretchy = \"true\", symmetric = \"false\", largeop = \"fal se\", movablelimits = \"false\", accent = \"false\", lspace = \"0.1666 667em\", rspace = \"0.1666667em\"), Typesetting:-mi(\"grid\", italic = \"false\", font_style_name = \"Text\", mathvariant = \"normal\"), Typ esetting:-mo(\" \", font_style_name = \"Text\", mathvariant = \"normal \", fence = \"false\", separator = \"false\", stretchy = \"false\", sy mmetric = \"false\", largeop = \"false\", movablelimits = \"false\", a ccent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesettin g:-mi(\"length\", italic = \"false\", font_style_name = \"Text\", math variant = \"normal\"), Typesetting:-mo(\" \", font_style_name = \"Text \", mathvariant = \"normal\", fence = \"false\", separator = \"false\" , stretchy = \"false\", symmetric = \"false\", largeop = \"false\", mo vablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspac e = \"0.0em\"), Typesetting:-mi(\"of\", italic = \"false\", font_style _name = \"Text\", mathvariant = \"normal\"), Typesetting:-mo(\" \", fo nt_style_name = \"Text\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp ace = \"0.0em\", rspace = \"0.0em\"), Typesetting:-mi(\"the\", italic \+ = \"false\", font_style_name = \"Text\", mathvariant = \"normal\"), Ty pesetting:-mo(\" \", font_style_name = \"Text\", mathvariant = \"norma l\", fence = \"false\", separator = \"false\", stretchy = \"false\", s ymmetric = \"false\", largeop = \"false\", movablelimits = \"false\", \+ accent = \"false\", lspace = \"0.0em\", rspace = \"0.0em\"), Typesetti ng:-mi(\"square\", italic = \"false\", font_style_name = \"Text\", mat hvariant = \"normal\"), Typesetting:-mo(\" \", font_style_name = \"Tex t\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rsp ace = \"0.0em\"), Typesetting:-mi(\"mesh\", italic = \"false\", font_s tyle_name = \"Text\", mathvariant = \"normal\"));" "-I%mrowG6#/I+modul enameG6\"I,TypesettingGI(_syslibGF'60-I#moGF$6.Q\"~F'/%0font_style_nam eGQ%TextF'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separatorGF7/% )stretchyGF7/%*symmetricGF7/%(largeopGF7/%.movablelimitsGF7/%'accentGF 7/%'lspaceGQ&0.0emF'/%'rspaceGFF-I#miGF$6&Q\"jF'/%'italicGF7F/F2-F,6.Q \")F'F/F2/F6Q%trueF'F8/F;FSFF@FB/FEQ,0.1666667emF'/FHFV-FJ6&Q%gridF 'FMF/F2F+-FJ6&Q'lengthF'FMF/F2F+-FJ6&Q#ofF'FMF/F2F+-FJ6&Q$theF'FMF/F2F +-FJ6&Q'squareF'FMF/F2F+-FJ6&Q%meshF'FMF/F2" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "Typesetting:-mrow(Typesetting:-mi(\"restart\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesetting: -mo(\";\", bold = \"false\", mathvariant = \"normal\", fence = \"false \", separator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", l space = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mspace(heig ht = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"ne wline\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", d epth = \"0.0ex\", linebreak = \"auto\"), Typesetting:-mi(\"with\", bol d = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesetti ng:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"linalg\", bold = \"fal se\", italic = \"true\", mathvariant = \"italic\")), bold = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\":\", bold = \"false\", m athvariant = \"normal\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspa ce = \"0.2777778em\"), Typesetting:-mo(\" \", bold = \"false\", mathva riant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimit s = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.0e m\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mi(\"with\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesettin g:-mfenced(Typesetting:-mrow(Typesetting:-mi(\"LinearAlgebra\", bold = \"false\", italic = \"true\", mathvariant = \"italic\")), bold = \"fa lse\", mathvariant = \"normal\"), Typesetting:-mo(\":\", bold = \"fals e\", mathvariant = \"normal\", fence = \"false\", separator = \"false \", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", \+ movablelimits = \"false\", accent = \"false\", lspace = \"0.2777778em \", rspace = \"0.2777778em\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Types etting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex \", linebreak = \"newline\"), Typesetting:-mi(\"l\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"&colo neq;\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", l argeop = \"false\", movablelimits = \"false\", accent = \"false\", lsp ace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"2. 4\", bold = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\"; \", bold = \"false\", mathvariant = \"normal\", fence = \"false\", sep arator = \"true\", stretchy = \"false\", symmetric = \"false\", largeo p = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mspace(height = \" 0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\" ), Typesetting:-mi(\"w\", bold = \"false\", italic = \"true\", mathvar iant = \"italic\"), Typesetting:-mo(\"≔\", bold = \"false\", m athvariant = \"normal\", fence = \"false\", separator = \"false\", str etchy = \"false\", symmetric = \"false\", largeop = \"false\", movable limits = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspa ce = \"0.2777778em\"), Typesetting:-mn(\"3.0\", bold = \"false\", math variant = \"normal\"), Typesetting:-mo(\";\", bold = \"false\", mathva riant = \"normal\", fence = \"false\", separator = \"true\", stretchy \+ = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.277 7778em\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", \+ depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mi(\"TL\", b old = \"false\", italic = \"true\", mathvariant = \"italic\"), Typeset ting:-mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fe nce = \"false\", separator = \"false\", stretchy = \"false\", symmetri c = \"false\", largeop = \"false\", movablelimits = \"false\", accent \+ = \"false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Type setting:-mn(\"75.0\", bold = \"false\", mathvariant = \"normal\"), Typ esetting:-mo(\";\", bold = \"false\", mathvariant = \"normal\", fence \+ = \"false\", separator = \"true\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-m space(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebr eak = \"newline\"), Typesetting:-mi(\"TR\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesetting:-mo(\"≔\", b old = \"false\", mathvariant = \"normal\", fence = \"false\", separato r = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \+ \"false\", movablelimits = \"false\", accent = \"false\", lspace = \"0 .2777778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"100.0\", bo ld = \"false\", mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"true\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.0em \", rspace = \"0.2777778em\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Types etting:-mi(\"TU\", bold = \"false\", italic = \"true\", mathvariant = \+ \"italic\"), Typesetting:-mo(\"≔\", bold = \"false\", mathvari ant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\", movablelimits \+ = \"false\", accent = \"false\", lspace = \"0.2777778em\", rspace = \" 0.2777778em\"), Typesetting:-mn(\"300.0\", bold = \"false\", mathvaria nt = \"normal\"), Typesetting:-mo(\";\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"true\", stretchy = \"f alse\", symmetric = \"false\", largeop = \"false\", movablelimits = \" false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0.2777778e m\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mi(\"TB\", bold = \"false\", italic = \"true\", mathvariant = \"italic\"), Typesetting: -mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \"false\", stretchy = \"false\", symmetric = \+ \"false\", largeop = \"false\", movablelimits = \"false\", accent = \" false\", lspace = \"0.2777778em\", rspace = \"0.2777778em\"), Typesett ing:-mn(\"50.0\", bold = \"false\", mathvariant = \"normal\"), Typeset ting:-mo(\";\", bold = \"false\", mathvariant = \"normal\", fence = \" false\", separator = \"true\", stretchy = \"false\", symmetric = \"fal se\", largeop = \"false\", movablelimits = \"false\", accent = \"false \", lspace = \"0.0em\", rspace = \"0.2777778em\"), Typesetting:-mspace (height = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mi(\"dx\", bold = \"false\", italic = \"tr ue\", mathvariant = \"italic\"), Typesetting:-mo(\"≔\", bold = \"false\", mathvariant = \"normal\", fence = \"false\", separator = \+ \"false\", stretchy = \"false\", symmetric = \"false\", largeop = \"fa lse\", movablelimits = \"false\", accent = \"false\", lspace = \"0.277 7778em\", rspace = \"0.2777778em\"), Typesetting:-mn(\"0.6\", bold = \+ \"false\", mathvariant = \"normal\"), Typesetting:-mo(\";\", bold = \" false\", mathvariant = \"normal\", fence = \"false\", separator = \"tr ue\", stretchy = \"false\", symmetric = \"false\", largeop = \"false\" , movablelimits = \"false\", accent = \"false\", lspace = \"0.0em\", r space = \"0.2777778em\"), Typesetting:-mo(\" \", bold = \"false\", mat hvariant = \"normal\", fence = \"false\", separator = \"false\", stret chy = \"false\", symmetric = \"false\", largeop = \"false\", movableli mits = \"false\", accent = \"false\", lspace = \"0.0em\", rspace = \"0 .0em\"), Typesetting:-mspace(height = \"0.0ex\", width = \"0.0em\", de pth = \"0.0ex\", linebreak = \"newline\"), Typesetting:-mspace(height \+ = \"0.0ex\", width = \"0.0em\", depth = \"0.0ex\", linebreak = \"auto \"), Typesetting:-mi(\"\"));" "-I%mrowG6#/I+modulenameG6\"I,Typesettin gGI(_syslibGF'6V-I#miGF$6&Q(restartF'/%%boldGQ&falseF'/%'italicGQ%true F'/%,mathvariantGQ'italicF'-I#moGF$6.Q\";F'F//F6Q'normalF'/%&fenceGF1/ %*separatorGF4/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimi tsGF1/%'accentGF1/%'lspaceGQ&0.0emF'/%'rspaceGQ,0.2777778emF'-I'mspace GF$6&/%'heightGQ&0.0exF'/%&widthGFN/%&depthGFW/%*linebreakGQ(newlineF' -FS6&FUFXFZ/FgnQ%autoF'-F,6&Q%withF'F/F2F5-I(mfencedGF$6%-F#6#-F,6&Q'l inalgF'F/F2F5F/F<-F96.Q\":F'F/F/FAF1FBFDFFFHFJ/FMFQFO-F96.Q\"~F'F/F F[pFBFDFFFHFJFL/FPFNFRF]o-Fao6%-F#6#-F,6&Q.LinearAlgebraF'F/F2F5F/F F[pFBFDFFFHFJF\\pFO-I #mnGF$6%Q$2.4F'F/F " 0 "" {XPPEDIT 0 1 "`assign`(dy, dx);" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_sys libGF'64-I#miGF$6&Q#dyF'/%%boldGQ&falseF'/%'italicGQ%trueF'/%,mathvari antGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normalF'/%&fenceGF1/%*sepa ratorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.movablelimitsGF1/ %'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-F,6&Q#dxF'F/F2F5-F96. Q\";F'F/F/FAF4FBFDFFFHFJ/FMQ&0.0emF'FO-I'mspaceGF$6&/%'heightGQ&0.0 exF'/%&widthGFY/%&depthGFin/%*linebreakGQ(newlineF'-F96.Q\"~F'F/FF@ FBFDFFFHFJFX/FPFY-F,6&Q\"mF'F/F2F5F8-F,6&Q&roundF'F//F3F1F<-I(mfencedG F$6%-F#6#-I&mfracGF$6(-F,6&Q\"lF'F/F2F5-F#6#FQ/%.linethicknessGQ\"1F'/ %+denomalignGQ'centerF'/%)numalignGF^q/%)bevelledGF1F/F " 0 "" {XPPEDIT 0 1 "` assign`(A, matrix(`*`(`+`(m, `-`(1)), `*`(`+`(n, `-`(1)))), `*`(`+`(m, `-`(1)), `*`(`+`(n, `-`(1)))))):" "-I%mrowG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6*-I#miGF$6&Q\"AF'/%%boldGQ&falseF'/%'italicGQ%true F'/%,mathvariantGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normalF'/%&fe nceGF1/%*separatorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/%.mova blelimitsGF1/%'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-F,6&Q'ma trixF'F/F2F5-I(mfencedGF$6%-F#6)-FU6%-F#6%-F,6&Q\"mF'F/F2F5-F96.Q(&min us;F'F/FF@FBFDFFFHFJ/FMQ,0.2222222emF'/FPF^o-I#mnGF$6%Q\"1F'F/FF@FBFDFFFHFJ/FMQ&0.0emF'/FPFho-FU6%-F#6%-F,6&Q\" nF'F/F2F5FjnF`oF/F<-F96.Q\",F'F/F/FAF4FBFDFFFHFJFgo/FPQ,0.3333333em F'FYFdoFjoF/F<-F96.Q\":F'F/FF@FBFDFFFHFJFLFO-F96.Q\"~F'F/FF@FBFD FFFHFJFgoFioFjpFjp" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 209 28 "Creating a constant matrix " }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`assign `(B, matrix(`*`(`+`(m, `-`(1)), `*`(`+`(n, `-`(1)))), 1)):" "-I%mrowG6 #/I+modulenameG6\"I,TypesettingGI(_syslibGF'6*-I#miGF$6(Q\"BF'/%'famil yGQ,Courier~NewF'/%'italicGQ%trueF'/%+foregroundGQ*[255,0,0]F'/%0font_ style_nameGQ,Maple~InputF'/%,mathvariantGQ'italicF'-I#moGF$60Q*&colone q;F'F/F5F8/F " 0 "" {XPPEDIT 19 1 "for i to `*`(`+`(m, `-`(1)), `*`(`+`(n, `-`(1))) ) do for j to `*`(`+`(m, `-`(1)), `*`(`+`(n, `-`(1)))) do `assign`(A[i , j], 0) end do; `assign`(B[i, 1], 0) end do:" "-I%mrowG6#/I+modulenam eG6\"I,TypesettingGI(_syslibGF'6^p-I#moGF$62Q$forF'/%'familyGQ,Courier ~NewF'/%%boldGQ%trueF'/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ, Maple~InputF'/%,mathvariantGQ%boldF'/%+fontweightGF=/%&fenceGQ&falseF' /%*separatorGFB/%)stretchyGFB/%*symmetricGFB/%(largeopGFB/%.movablelim itsGFB/%'accentGFB/%'lspaceGQ&0.0emF'/%'rspaceGFQ-F,60Q\"~F'F/F5F8/FF@FCFEFGFIFKFMFOFRFT-I#mnGF$6'Q\"1F'F/F 5F8FWFT-F,62Q#byF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTF^oFT-F,62Q#toF'F/F2 F5F8F;F>F@FCFEFGFIFKFMFOFRFT-I(mfencedGF$6'-F#6%-FZ6(Q\"mF'F/FgnF5F8Fi n-F,60Q(−F'F/F5F8FWF@FCFEFGFIFKFM/FPQ,0.2222222emF'/FSFdpF^oF/F5 F8FW-F,60Q'⋅F'F/F5F8FWF@FCFEFGFIFKFMFOFR-Fio6'-F#6%-FZ6(Q\"nF'F/F gnF5F8FinF`pF^oF/F5F8FWFT-F,62Q#doF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFR-I'm spaceGF$6&/%'heightGQ&0.0exF'/%&widthGFQ/%&depthGFhq/%*linebreakGQ(new lineF'FTFTFTFTF+FT-FZ6(Q\"jF'F/FgnF5F8FinFTF[oFTF^oFTFboFTF^oFTFeoFTFh oFfpFipFTF`qFTFTFcqFTFTFTFTFTFTFT-FZ6(Q\"AF'F/FgnF5F8Fin-Fio6+-F#6%FY- F,60Q\",F'F/F5F8FWF@/FDF4FEFGFIFKFMFO/FSQ,0.3333333emF'F`rF/F2F5F8F;F> /%%openGQ\"[F'/%&closeGQ\"]F'-F,60Q*≔F'F/F5F8FWF@FCFEFGFIFKFM/ FPQ,0.2777778emF'/FSFjs-F_o6'Q\"0F'F/F5F8FW-F,60Q\";F'F/F5F8FWF@F]sFEF GFIFKFMFOF[tFcqFTFTFTFT-F,62Q$endF'F/F2F5F8F;F>F@FCFEFGFIFKFMFOFRFTF`q -F,60Q\":F'F/F5F8FWF@FCFEFGFIFKFMFisF[tFcqFTFTFTFT-FZ6(Q\"BF'F/FgnF5F8 Fin-Fio6)-F#6%FYFjrF^oF/F5F8FWF`sFcsFfsF\\tF_tFcqFbtFTF`qFet" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 209 63 "The following loop assigns the va lues to the coefficeint matrix" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`assign`(count, 0):" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI (_syslibGF'6by-I#miGF$6(Q&countF'/%'familyGQ,Courier~NewF'/%'italicGQ% trueF'/%+foregroundGQ*[255,0,0]F'/%0font_style_nameGQ,Maple~InputF'/%, mathvariantGQ'italicF'-I#moGF$60Q*≔F'F/F5F8/FFep-F?60Q\";F'F/F5F8FBFD/FHF4FIFKFMFOFQF joFVFinFgoFgoFgoF+F>F+-F?60Q\"+F'F/F5F8FBFDFGFIFKFMFOFQF_rFarF[qFfnFin FgoFgoFgo-F,6(Q\"AF'F/F2F5F8F;-Feq6)-F#6%Fep-F?60Q\",F'F/F5F8FBFDF]tFI FKFMFOFQFjo/FWQ,0.3333333emF'FgsF/F5F8FB/%%openGQ\"[F'/%&closeGQ\"]F'F >-F?60Q*&uminus0;F'F/F5F8FBFDFGFIFKFMFOFQF_rFar-FY6'Q\"4F'F/F5F8FBFjsF inFgoFgoFgoFinFgoFgoFgo-F?62Q#ifF'F/F_pF5F8FapFcpFDFGFIFKFMFOFQFjoF[pF go-Feq6'-F#6%F+-F?60Q+≠F'F/F5F8FBFDFGFIFKFMFOFQFSFVF[qF/F5F8F BFgo-F?62Q%thenF'F/F_pF5F8FapFcpFDFGFIFKFMFOFQFjoF[pFinFgoFgoFgoFgoFgo Fat-Feq6)-F#6'FepFhtFgsF\\rF[qF/F5F8FBF]uF`uF>F[qFjsFinFgoFgoFgo-F?62Q $endF'F/F_pF5F8FapFcpFDFGFIFKFMFOFQFjoF[pFgoFiuFfnFgoFinFgoFgoFgoFgoFi nFgoFgoFgoFiuFgo-Feq6'-F#6'F+F`vFirF\\rF[qF/F5F8FBFgoFcvFinFgoFgoFgoFg oFgoFat-Feq6)-F#6'FepFhtFgsF^tF[qF/F5F8FBF]uF`uF>F[qFjsFinFgoFgoFgoFjv FgoFiuFfnFinFgoFinFgoFgoFgoFiuFgo-Feq6'-F#6+FgsF^tFirF\\rF[q-F?60Q&&le q;F'F/F5F8FBFDFGFIFKFMFOFQFSFVFdqFbr-Feq6'-F#6%FirF\\rF[qF/F5F8FBF/F5F 8FBFgoFcvFinFgoFgoFgoFgoFgoFgoFat-Feq6)-F#6)FepFhtFgsF^tFirF\\rF[qF/F5 F8FBF]uF`uF>F[qFjsFinFgoFgoFgoFjvFgoFiuFfnFgoFgoFgoFgoFgoFinFgoFinFgoF goFgoFiuFgo-Feq6'-F#6)FgsF\\rFirF^tF[q-F?60Q\">F'F/F5F8FBFDFGFIFKFMFOF QFSFVFXF/F5F8FBFgoFcvFinFgoFgoFgoFgoFgoFgoFgoFat-Feq6)-F#6)FepFhtFgsF \\rFirF^tF[qF/F5F8FBF]uF`uF>F[qFjsFinFgoFgoFgoFjvFgoFiuFfnFinFgoFgoFin FgoFgoFgoFiuFgo-Feq6'-F#6'F+-F?60Q\"=F'F/F5F8FBFDFGFIFKFMFOFQFSFVFirF \\rF[qF/F5F8FBFgoFcvFinFgoFgoFgoFgoFgoFgoFgoF+F>FXFjsFinFgoFgoFgoFjvFg oFiuFfnFin-Fjn6&F\\oF_oFbo/FeoQ%autoF'FinFinFgoFjvFgoFdsFfnFfyF_s" }}} {EXCHG {PARA 0 "" 0 "" {TEXT 209 53 "This loop creates the right hand \+ side constant matrix" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "count = 0:" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF'6e[l-I#mo GF$60Q\"~F'/%'familyGQ,Courier~NewF'/%+foregroundGQ*[255,0,0]F'/%0font _style_nameGQ,Maple~InputF'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF' /%*separatorGF=/%)stretchyGF=/%*symmetricGF=/%(largeopGF=/%.movablelim itsGF=/%'accentGF=/%'lspaceGQ&0.0emF'/%'rspaceGFL-I#miGF$6(Q&countF'F/ /%'italicGQ%trueF'F2F5/F9Q'italicF'-F,60Q\"=F'F/F2F5F8F;F>F@FBFDFFFH/F KQ,0.2777778emF'/FNFfn-I#mnGF$6'Q\"0F'F/F2F5F8-F,60Q\":F'F/F2F5F8F;F>F @FBFDFFFHFenFgn-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFL/%&depthGFd o/%*linebreakGQ(newlineF'F+-F,62Q$forF'F//%%boldGFUF2F5/F9Q%boldF'/%+f ontweightGFbpF;F>F@FBFDFFFHFJFMF+-FP6(Q\"iF'F/FSF2F5FVF+-F,62Q%fromF'F /F_pF2F5FapFcpF;F>F@FBFDFFFHFJFMF+-Fin6'Q\"1F'F/F2F5F8F+-F,62Q#byF'F/F _pF2F5FapFcpF;F>F@FBFDFFFHFJFMF+F[qF+-F,62Q#toF'F/F_pF2F5FapFcpF;F>F@F BFDFFFHFJFMF+-FP6(Q\"mF'F/FSF2F5FV-F,60Q(−F'F/F2F5F8F;F>F@FBFDFF FH/FKQ,0.2222222emF'/FNF[rF[qF+-F,62Q#doF'F/F_pF2F5FapFcpF;F>F@FBFDFFF HFJFMF_oF+F+F+F\\pF+-FP6(Q\"jF'F/FSF2F5FVF+FhpF+F[qF+F^qF+F[qF+FaqF+-F P6(Q\"nF'F/FSF2F5FVFgqF[qF+F]rF_oF+F+F+F+F+F+FO-F,60Q*≔F'F/F2F 5F8F;F>F@FBFDFFFHFenFgnFO-F,60Q\"+F'F/F2F5F8F;F>F@FBFDFFFHFjqF\\rF[qF \\oF_oF+F+F+F+F+F+-FP6(Q&temp1F'F/FSF2F5FVFfrFhnF\\oF_oF+F+F+F+F+F+-FP 6(Q&temp2F'F/FSF2F5FVFfrFhnF\\oF_o-F`o6&FboFeoFgo/FjoQ%autoF'F_oF+F+F+ F+F+F+-F,62Q#ifF'F/F_pF2F5FapFcpF;F>F@FBFDFFFHFJFMF+-I(mfencedGF$6'-F# 6'FepFgqF[qFXFhnF/F2F5F8F+-F,62Q%thenF'F/F_pF2F5FapFcpF;F>F@FBFDFFFHFJ FMF_oF+F+F+F+F+F+F+F+F\\sFfr-FP6(Q#TLF'F/FSF2F5FVF\\oF_oF+F+F+F+F+F+-F ,62Q$endF'F/F_pF2F5FapFcpF;F>F@FBFDFFFHFJFMF+FfsF\\oF_oF+F_oF+F+F+F+F+ F+FfsF+-Fjs6'-F#6'FepFirF[qFXFdqF/F2F5F8F+F^tF_oF+F+F+F+F+F+F+F+F+F\\s Ffr-FP6(Q#TRF'F/FSF2F5FVF\\oF_oF+F+F+F+F+F+FdtF+FfsF\\oF_oF+F_oF+F+F+F +F+F+FfsF+-Fjs6'-F#6'F`rFgqF[qFXFhnF/F2F5F8F+F^tF_oF+F+F+F+F+F+F+F+F+F _sFfr-FP6(Q#TUF'F/FSF2F5FVF\\oF+F_oF+F+F+F+F+F+FdtF+FfsF\\oF_oF+F_oF+F +F+F+F+FfsF+-Fjs6'-F#6'F`rFirF[qFXFcrF/F2F5F8F+F^tF_oF+F+F+F+F+F+F+F+F _sFfr-FP6(Q#TBF'F/FSF2F5FVF\\oF_oF+F+F+F+F+FdtF+FfsF\\oF_oF+F_oF+F+F+F +F+-FP6(Q\"BF'F/FSF2F5FV-Fjs6)-F#6%FO-F,60Q\",F'F/F2F5F8F;/F?FUF@FBFDF FFHFJ/FNQ,0.3333333emF'F[qF/F2F5F8/%%openGQ\"[F'/%&closeGQ\"]F'Ffr-F,6 0Q*&uminus0;F'F/F2F5F8F;F>F@FBFDFFFHFjqF\\r-Fjs6'-F#6%F\\sFirF_sF/F2F5 F8F\\oF_oF+F+F+FdtF+F]rF\\oF_oF+FdtF+F]rF\\o" }}}{EXCHG {PARA 0 "" 0 " " {TEXT 209 24 "Solving for temperatures" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 0 1 "`assign`(sol, linsolve(A, B));" "-I%mrowG6#/I+modulename G6\"I,TypesettingGI(_syslibGF'6'-I#miGF$6&Q$solF'/%%boldGQ&falseF'/%'i talicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'n ormalF'/%&fenceGF1/%*separatorGF1/%)stretchyGF1/%*symmetricGF1/%(large opGF1/%.movablelimitsGF1/%'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspace GFN-F,6&Q)linsolveF'F/F2F5-I(mfencedGF$6%-F#6%-F,6&Q\"AF'F/F2F5-F96.Q \",F'F/F/FAF4FBFDFFFHFJ/FMQ&0.0emF'/FPQ,0.3333333emF'-F,6&Q\"BF'F/F 2F5F/F<-F96.Q\";F'F/FFinFBFDFFFHFJFjnFO" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"#7;F&F&E\\[l-6$\"\"*F&$\"+9lXC=!\"(6$\"\"# F&$\"+%Hp!*>\"F.6$\"#6F&$\"+`%))Q/\"F.6$\"\"%F&$\"+uwB*Q(!\")6$\"\"&F& $\"++/7&)>F.6$\"\"'F&$\"+iwZ#Q\"F.6$\"\"(F&$\"+'H:I.\"F.6$F'F&$\"+$eG$ )H)F;6$\"#5F&$\"+dcq78F.6$F&F&$\"+BuaL " 0 "" {XPPEDIT 0 1 "`assign`(count, 0):" "-I%mrowG6#/I+modulenameG6\"I,Type settingGI(_syslibGF'6gq-I#miGF$6&Q&countF'/%%boldGQ&falseF'/%'italicGQ %trueF'/%,mathvariantGQ'italicF'-I#moGF$6.Q*≔F'F//F6Q'normalF' /%&fenceGF1/%*separatorGF1/%)stretchyGF1/%*symmetricGF1/%(largeopGF1/% .movablelimitsGF1/%'accentGF1/%'lspaceGQ,0.2777778emF'/%'rspaceGFN-I#m nGF$6%Q\"0F'F/F<-F96.Q\":F'F/FF@FBFDFFFHFJFLFO-I'mspaceGF$6&/%'heig htGQ&0.0exF'/%&widthGQ&0.0emF'/%&depthGFgn/%*linebreakGQ(newlineF'-F96 .Q\"~F'F/FF@FBFDFFFHFJ/FMFjn/FPFjn-F,6&Q*TinternalF'F/F2F5F8-F,6&Q' matrixF'F/F2F5-I(mfencedGF$6%-F#6)-F,6&Q\"mF'F/F2F5-F96.Q(−F'F/F F@FBFDFFFHFJ/FMQ,0.2222222emF'/FPFgp-FR6%Q\"1F'F/F<-F96.Q\",F'F/F/FAF4FBFDFFFHFJFco/FPQ,0.3333333emF'-F,6&Q\"nF'F/F2F5FcpFip/F6Q%boldF '/%+fontweightGFfqFUF`oF`oF`oFXF`o-F96.Q$forF'FeqFgqF>F@FBFDFFFHFJFcoF doF`o-F,6&Q\"iF'F/F2F5F`o-F96.Q%fromF'FeqFgqF>F@FBFDFFFHFJFcoFdoF`oFip F`o-F96.Q#byF'FeqFgqF>F@FBFDFFFHFJFcoFdoF`oFipF`o-F96.Q#toF'FeqFgqF>F@ FBFDFFFHFJFcoFdoF`oF`pFcpFipF`o-F96.Q#doF'FeqFgqF>F@FBFDFFFHFJFcoFdoFX F`oF`oF`oFiqF`o-F,6&Q\"jF'F/F2F5F`oF_rF`oFipF`oFbrF`oFipF`oFerF`oFbqFc pFipF`oFhrFXF`oF`oF`oF`oF`oF`oF+F8F+-F96.Q\"+F'F/FF@FBFDFFFHFJFfpFh pFipFUFXF`oF`oF`oF`oF`oF`oFeo-F\\p6'-F#6%F\\rF\\qF[sF/FF@FBFDFFFHFJFcoFdoF`oFhrFUFXF`oFbtF`oFhrF UFX-FY6&FenFhnF[o/F^oQ%autoF'FXF`oFeoF8-F,6&Q*transposeF'F/F2F5-F\\p6% -F#6#FeoF/F " 0 "" {XPPEDIT 0 1 "`assign`(T, matrix(`+`(n, 1), `+`(m, 1))):" "-I%mrowG6# /I+modulenameG6\"I,TypesettingGI(_syslibGF'6f]l-I#miGF$6&Q\"TF'/%%bold GQ&falseF'/%'italicGQ%trueF'/%,mathvariantGQ'italicF'-I#moGF$6.Q*&colo neq;F'F//F6Q'normalF'/%&fenceGF1/%*separatorGF1/%)stretchyGF1/%*symmet ricGF1/%(largeopGF1/%.movablelimitsGF1/%'accentGF1/%'lspaceGQ,0.277777 8emF'/%'rspaceGFN-F,6&Q'matrixF'F/F2F5-I(mfencedGF$6%-F#6)-F,6&Q\"nF'F /F2F5-F96.Q\"+F'F/FF@FBFDFFFHFJ/FMQ,0.2222222emF'/FPFjn-I#mnGF$6%Q \"1F'F/F<-F96.Q\",F'F/F/FAF4FBFDFFFHFJ/FMQ&0.0emF'/FPQ,0.3333333emF '-F,6&Q\"mF'F/F2F5FfnF\\oF/F<-F96.Q\":F'F/FF@FBFDFFFHFJFLFO-I'mspac eGF$6&/%'heightGQ&0.0exF'/%&widthGFeo/%&depthGFcp/%*linebreakGQ(newlin eF'-F_p6&FapFdpFfp/FipQ%autoF'-F96.Q$forF'/F6Q%boldF'/%+fontweightGFcq F>F@FBFDFFFHFJFdo/FPFeo-F96.Q\"~F'F/FF@FBFDFFFHFJFdoFfq-F,6&Q\"iF'F /F2F5Fgq-F96.Q%fromF'FbqFdqF>F@FBFDFFFHFJFdoFfqFgqF\\oFgq-F96.Q#byF'Fb qFdqF>F@FBFDFFFHFJFdoFfqFgqF\\oFgq-F96.Q#toF'FbqFdqF>F@FBFDFFFHFJFdoFf qFgqFYFfnF\\oFgq-F96.Q#doF'FbqFdqF>F@FBFDFFFHFJFdoFfqF^pFgqFgqFgqFgqF_ qFgq-F,6&Q\"jF'F/F2F5FgqF]rFgqF\\oFgqF`rFgqF\\oFgqFcrFgqFhoFfnF\\oFgqF frF^pFgqFgqFgqFgqFgqFgqFgqFgqFgqFgqFgqF^pFgqFgqFgqFgqFgqFgqFgqFgq-F96. Q#ifF'FbqFdqF>F@FBFDFFFHFJFdoFfqFgq-FU6%-F#6%Fjq-F96.Q\"=F'F/FF@FBF DFFFHFJFLFOF\\oF/FF@FBFDFFFHFJFdoFfqF^pFgqFgq FgqFgqFgqFgqFgqFgqFgqFgqF+-FU6'-F#6%FjqF`oFirF/FF@FBFDFFFHFJFdoFfqFgq-FU6%-F#6'FjqFcsFYFfnF\\oF/FF@FBFDFFFHFJFdoFfqFgqF\\sF[pF^pFgqFgqFgqFgqFgqF^vFgqFfr F[pF^pFgqF^vFgqFfrF[pF^pFgqFgqFgqFgqFgqF^pF_qFgqFjqFgqF]rFgqF\\oFgqF`r FgqF\\oFgqFcrFgqFY-F96.Q(−F'F/FF@FBFDFFFHFJFinF[oF\\oFgqFfrF^ pFgqFgqFgqFgqF_qFgqFirFgqF]rFgqF\\oFgqF`rFgqF\\oFgqFcrFgqFhoFavF\\oFgq FfrF^pFgqFgqFgqFgqFgqFgqFgqF+-FU6'-F#6)FjqFfnF\\oF`oFirFfnF\\oF/F " 0 "" {XPPEDIT 0 1 "sprintf(\"\\n \\n \\t \\t \+ \\t \\t \\t \\t \\t %g \", TU);" "-I%mrowG6#/I+modulenameG6\"I,Types ettingGI(_syslibGF'6en-I#miGF$6&Q(sprintfF'/%%boldGQ&falseF'/%'italicG Q%trueF'/%,mathvariantGQ'italicF'-I(mfencedGF$6%-F#6&-F,6#Q!F'-I#msGF$ 6#QA\\n~\\n~\\t~\\t~\\t~\\t~\\t~\\t~\\t~~%g~~F'-I#moGF$6.Q\",F'F//F6Q' normalF'/%&fenceGF1/%*separatorGF4/%)stretchyGF1/%*symmetricGF1/%(larg eopGF1/%.movablelimitsGF1/%'accentGF1/%'lspaceGQ&0.0emF'/%'rspaceGQ,0. 3333333emF'-F,6&Q#TUF'F/F2F5/F6Q%boldF'/%+fontweightGF\\o-FE6.Q\";F'F/ FHFJFLFNFPFRFTFVFX/FfnQ,0.2777778emF'-I'mspaceGF$6&/%'heightGQ&0.0exF' /%&widthGFZ/%&depthGFio/%*linebreakGQ(newlineF'-Feo6&FgoFjoF\\p/F_pQ%a utoF'F+-F96%-F#6%F=-FA6#Qju~~~~~~~~~~~~~~−−−−& minus;−−−−−−−−−& minus;−−−−−−−~~~~~~~F'F=F[oF ]oF_oFdoFdoF+-F96%-F#6%F=-FA6#QT~~~~~~~~~~~~~~~|gr~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~|gr~~~~~~F'F=F[oF]oF_oFdoF+F\\qF_oFdoF+F\\qF_oFdoF+-F96%-F#6(F =-FA6#QY~~~~~~~~~~~~~~~%g~~|gr~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~|gr%gF' FD-F,6&Q#TLF'F/F2F5FD-F,6&Q#TRF'F/F2F5F[oF]oF_oFdoFdoF+F\\qF_oFdoF+F \\qF_oFdoF+F\\qF_oFdoFapF+-F96%-F#6%F=-FA6#Qju~~~~~~~~~~~~~~−&mi nus;−−−−−−−−−&mi nus;−−−−−−−−−&mi nus;~~~~~~~F'F=F[oF]oF_oFdoFdoF+-F96%-F#6&F=-FA6#QC~\\t~\\t~\\t~\\t~ \\t~\\t~\\t~~%g~\\n~\\n~\\nF'FD-F,6&Q#TBF'F/F2F5F[oF]oF_oFdoF+-F96%-F# 6%F=-FA6#Q`wTo~give~a~better~idea~the~nodal~locations~are~also~given~a s~the~cordinates~of~x&y~and~the~origin~is~choosen~at~the~intersection~ of~cordinates~of~x&y~and~the~origin~is~choosen~at~the~intersection~ofF 'F=F[oF]oF_oFdoF+-F96%-F#6%F=-FA6#Q:bottom~edge~and~left~edgeF'F=F[oF] oF_o-FE6.Q\"~F'F/FHFJ/FMF1FNFPFRFTFVFX/FfnFZ" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q9|+~|+~|*~|*~|*~|*~|*~|*~|*~~300~~6\"" }}{PARA 11 "" 1 " " {XPPMATH 20 "QL~~~~~~~~~~~~~~----------------------~~~~~~~6\"" }} {PARA 11 "" 1 "" {XPPMATH 20 "QT~~~~~~~~~~~~~~~|gr~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~|gr~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QT~~~~~~~~~~~~~~ ~|gr~~~~~~~~~~~~~~~~~~~~~~~~~~~~|gr~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QT~~~~~~~~~~~~~~~|gr~~~~~~~~~~~~~~~~~~~~~~~~~~~~|gr~~~~~~ 6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QZ~~~~~~~~~~~~~~~75~~|gr~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~|gr1006\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QT~ ~~~~~~~~~~~~~~|gr~~~~~~~~~~~~~~~~~~~~~~~~~~~~|gr~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QT~~~~~~~~~~~~~~~|gr~~~~~~~~~~~~~~~~~~~~~~~~~~~~| gr~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "QT~~~~~~~~~~~~~~~|gr~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~|gr~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q L~~~~~~~~~~~~~~----------------------~~~~~~~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q9~|*~|*~|*~|*~|*~|*~|*~~50~|+~|+~|+6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q`wTo~give~a~better~idea~the~nodal~locations~are~also~ given~as~the~cordinates~of~x&y~and~the~origin~is~choosen~at~the~inters ection~of~cordinates~of~x&y~and~the~origin~is~choosen~at~the~intersect ion~of6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "Q:bottom~edge~and~left~edge 6\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 209 18 "Output Temperature" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "`*`(printf(\"Temperature=\"), \+ `*`(print(T)));" "-I%mrowG6#/I+modulenameG6\"I,TypesettingGI(_syslibGF '6)-I#moGF$6-Q\"~F'/%,mathvariantGQ'normalF'/%&fenceGQ&falseF'/%*separ atorGF4/%)stretchyGF4/%*symmetricGF4/%(largeopGF4/%.movablelimitsGF4/% 'accentGF4/%'lspaceGQ&0.0emF'/%'rspaceGFC-I#miGF$6(Q'printfF'/%'family GQ,Courier~NewF'/%'italicGQ%trueF'/%+foregroundGQ*[255,0,0]F'/%0font_s tyle_nameGQ,Maple~InputF'/F0Q'italicF'-I(mfencedGF$6)-F#6%-FG6#Q!F'-I# msGF$6#Q-Temperature=F'FgnFJ/%%boldGFOFPFS/F0Q%boldF'/%+fontweightGFao Fgn-I'mspaceGF$6&/%'heightGQ&0.0exF'/%&widthGFC/%&depthGFio/%*linebrea kGQ(newlineF'-FG6(Q&printF'FJFMFPFSFV-FY6)-F#6#-FG6(Q\"TF'FJFMFPFSFVFJ F^oFPFSF`oFbo" }}{PARA 6 "" 1 "" {TEXT 215 12 "Temperature=" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"TG6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "*$6 \"\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}}} {MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }