116hw1 test2.nb

$TomMat1[N_] = Table[(1/N) * Exp[-(5 * (i - j)/N)^2], {i, N}, {j, N}]$

$Table[^(-((5 (i - j))/N)^2)/N, {i, N}, {j, N}]$

$General :: spell : Possible spelling error: new symbol name \"part\" is similar to existing symbols {Apart, Part} . More…$

${{1/20, 1/(20 ^(1/16)), 1/(20 ^(1/4)), 1/(20 ^(9/16)), 1/(20 ) ... )), 1/(20 ), 1/(20 ^(9/16)), 1/(20 ^(1/4)), 1/(20 ^(1/16)), 1/20}}$

( 1 1 1 ... #63309; 20  20  20  20  20

( 1 ) ---------------- 81/16 ... 309; 1 --------------- 25/4 20 

$General :: spell1 : Possible spelling error: new symbol name \"line\" is similar to existing symbol \"Line\". More…$

( ... 09; #1 - 25  #1 - 25  #1 - 75  #1 + 125  #1 &, 1]

$Syntax :: tsntxi : \"form . \" is incomplete; more input is needed. More…$

( 0.3317377638726387` ) 0.27174243201597165` 0.19511687292536906` 0.12459441769924659` 0.07680851348677405`

( 0.33012759333047936` ) 0.26666943355347905` 0.18690 ... 0.0035129207299441985` 0.0009287361064987247` 0.00017757741953451395`

( ... 25  3125  3125  3125  3125  3125 

( 1.0000000000000007` 2.220446049250313`*^-16 0.` ... 7787807814457`*^-17 0.` 2.220446049250313`*^-16 1.0000000000000007`

( 0.9391648292451436` ) -2.905598572128823` 7.103417150227679` -2.905598572128823` 0.9391648292451436`

( 0.` ) 1.8041124150158794`*^-16 3.885780586188048`*^-16 1.8041124150158794`*^-16 0.`

( -8.92787710427001`*^-9 ) -9.774467457646097`*^-9 -1. ... -2.878834948205622`*^-10 -5.054126006598381`*^-10 -6.731397661496885`*^-10

( -0.9391648292451436` ) 2.9055985721288224` -7.103417150227679` 2.9055985721288224` -0.9391648292451436`

( -172.55532843602148` ) 477.8036707308623` -751.3964648 ... 245` 311.76946986436906` -158.32895130315356` 49.437929330443154`

$Dipole[x1_, x2_, y1_, y2_, n1_, n2_] = 1/(2 * Pi) * {x1 - y1, x2 - y2} . {n1, n2} * 1/(Norm[({x1 - y1, x2 - y2})] * Norm[{x1 - y1, x2 - y2}] * Norm[{n1, n2}])$

Dipole[{6, 5}, {2, 7}, 1, 8, 1, 0] 

$DipTab[N_] = Table[{i, j}, {i, N}, {j, N}]$

( ) 0 2 ---------- ... ----- 5684785 π 1250 ------------- 125749 π

[Graphics:HTMLFiles/index_93.gif]

${2/(17 π), 4/(15 13^(1/2) π)}$

$XCirclePart[N_] = Array[XCircleMiniPart, {N, 1}, {1, N}]$

$General :: spell1 : Possible spelling error: new symbol name \"YCircleMiniPart\" is similar to existing symbol \"XCircleMiniPart\". More…$

$YCirclePart[N_] = Array[YCircleMiniPart, {N, 1}, {1, N}]$

$General :: spell1 : Possible spelling error: new symbol name \"YCirclePart\" is similar to existing symbol \"XCirclePart\". More…$

( ( 1 ) ( 1 ) ... 2 2 2 ( 0 )

[Graphics:HTMLFiles/index_134.gif]

[Graphics:HTMLFiles/index_138.gif]

Abs[((-1 + p1) Cos[thet] + p2 Sin[thet])/(2 π (Abs[-1 + p1]^2 + Abs[p2]^2) (Abs[Cos[thet] ... + p1]^2 + Abs[1/2 (1/2 (5 + 5^(1/2)))^(1/2) + p2]^2) (Abs[Cos[thet]]^2 + Abs[Sin[thet]]^2)^(1/2))]

$IntAprox[q1_, q2_] = Sum[ProbAprox[q1, q2, 2 * Pi * i/10] * 2 * Pi/10, {i, 1, 10}]$

1/5 π Abs[(1 - q1)/(2 π (Abs[-1 + q1]^2 + Abs[q2]^2)) + (-1 - q1)/(2 π (Abs[1 + ... 1/2)))^(1/2) π (Abs[1/4 (-1 + 5^(1/2)) + q1]^2 + Abs[1/2 (1/2 (5 + 5^(1/2)))^(1/2) + q2]^2))]

SO it apears with my system I get numbers greater than 1 outside and numbers less than 1 insid ... ting about the desired results . Plot3D[N[IntAprox[x, y]], {x, -5, 5}, {y, -5, 5}]

$General :: spell1 : Possible spelling error: new symbol name \"with\" is similar to existing symbol \"With\". More…$

$General :: spell1 : Possible spelling error: new symbol name \"get\" is similar to existing symbol \"Get\". More…$

$General :: spell1 : Possible spelling error: new symbol name \"greater\" is similar to existing symbol \"Greater\". More…$

[Graphics:HTMLFiles/index_180.gif]

$XCirclePart[N_] = Array[XCircleMiniPart, {N, 1}, {1, N}] XCircleMiniPart[i_, N_] = Cos[2 * Pi * i/N]$

$RadialXpart[N_] = Array[RadialXmini, {N, 1}, {1, N}]$

$RadialYpart[N_] = Array[RadialYmini, {N, 1}, {1, N}]$

$DsAprox[i_, N_] = NIntegrate[1 + (2 * Pi/(3 * N) * .03 * Sin[2 * Pi/3 * x/N])^2, {x, 2 * Pi/3 * (i - 1)/N, 2 * Pi/3 * (i)/N}, AccuracyGoal1/10^3]$

$RowBox[{NIntegrate, [, RowBox[{RowBox[{1, +, RowBox[{RowBox[{(, RowBox[{RowBox[{(, RowBox[{2, ... 2}]}], ,, {x, (2 π (i - 1))/(3 N), (2 π i)/(3 N)}, ,, AccuracyGoal1/10^3}], ]}]$

$RowBox[{NIntegrate, [, RowBox[{RowBox[{1, +, RowBox[{RowBox[{(, RowBox[{RowBox[{(, RowBox[{2, ... }], )}], /, (3 10)}], )}], ^, 2}]}], ,, {x, (2 π (j - 1))/(3 10), (2 π j)/(3 10)}}], ]}]$

$RowBox[{Abs, [, RowBox[{RowBox[{RowBox[{(, RowBox[{(p1 - π/15) thet, +, RowBox[{RowBox[{( ... Box[{1, +, RowBox[{0.03, , Cos[(i π)/15]}]}], ]}], ^, 2}]}], )}], ^, (1/2)}]}], )}]}]}], ]}]$

$RadialInt[q1_, q2_] = Sum[RadialAprox[q1, q2, 2 * Pi * i/10] * DsAprox2[i], {i, 1, 10}]$

$RowBox[{RowBox[{0.209441, , RowBox[{Abs, [, RowBox[{RowBox[{RowBox[{(, RowBox[{0.0250247, , ... 2, +, RowBox[{RowBox[{Abs, [, RowBox[{RowBox[{-, 0.985}], +, q2}], ]}], ^, 2}]}], )}]}]}], ]}]}]}]$

[Graphics:HTMLFiles/index_223.gif]

Created by Mathematica (January 19, 2006)