{"text_format":"1","workbook":"xlsx","n_sheets":6,"sheets":["Cover","Kubische Splines","Ausflusszeit","Konstante Zugspannung","Lineare Approximation","Newton"],"not_rendered":{"charts":5,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Cover","index":0,"n_rows":21,"n_cols":3,"rows_kept":21,"cut":false,"hidden":false,"merged":[]}
[]
[null,"Algorithmen"]
[null,"für"]
[null,"Ingenieure"]
[]
[null,"Kapitel",4]
[null,"Thema","Funktionen"]
[]
[null,"Inhalt","Interpolation von Funktionen durch Polynome"]
[null,null,"Approximation von Funktionen durch Polynome"]
[null,null,"Numerische Integration"]
[]
[]
[]
[null,"Autor","Harald Nahrstedt"]
[null,"Datum","2014-03-01"]
[null,"Version","1.0"]
[]
[null,"Springer "]
[null,"Vieweg"]
[null,"Verlag"]

{"sheet":"Kubische Splines","index":1,"n_rows":52,"n_cols":9,"rows_kept":52,"cut":false,"hidden":false,"merged":[]}
["x","y=a","b","c","d",null,null,"x","y"]
[0,30,-1.3156458797327395,0,1.156458797327394E-3,null,null,0,30]
[10,18,-0.9687082405345212,3.4693763919821818E-2,-2.8229398663697061E-4,null,null,1,28.685510579064591]
[20,11.5,-0.35952115812917601,2.6224944320712699E-2,-5.2728285077951022E-4,null,null,2,27.377959910913138]
[30,10,6.7928730512249597E-3,1.0406458797327394E-2,1.6469933184855234E-3,null,null,3,26.084286748329621]
[35,10.5,0.23438195991091315,3.5111358574610244E-2,-3.9755011135857442E-4,null,null,4,24.811429844097994]
[40,12.5,0.5556792873051225,2.9148106904231627E-2,-9.7160356347438751E-4,null,null,5,23.566327951002226]
[50,20,null,null,null,null,null,6,22.35591982182628]
[null,null,null,null,null,null,null,7,21.18714420935412]
["Gl.Matrix",null,null,null,null,null,null,8,20.066939866369708]
[40,10,0,0,0,1.65,null,9,19.002245545657015]
[10,40,10,0,0,1.5,null,10,18]
[0,10,30,5,0,0.75,null,11,17.065703229398665]
[0,0,5,20,5,0.9,null,12,16.199100222717146]
[0,0,0,5,30,1.05,null,13,15.398497216035633]
[null,null,null,null,null,null,null,14,14.662200445434298]
[null,null,null,null,null,null,null,15,13.988516146993318]
[null,null,null,null,null,null,null,16,13.375750556792873]
[null,null,null,null,null,null,null,17,12.822209910913141]
[null,null,null,null,null,null,null,18,12.326200445434299]
[null,null,null,null,null,null,null,19,11.886028396436526]
[null,null,null,null,null,null,null,20,11.5]
[null,null,null,null,null,null,null,21,11.166176503340758]
[null,null,null,null,null,null,null,22,10.881639198218263]
[null,null,null,null,null,null,null,23,10.643224387527839]
[null,null,null,null,null,null,null,24,10.447768374164809]
[null,null,null,null,null,null,null,25,10.292107461024498]
[null,null,null,null,null,null,null,26,10.173077951002227]
[null,null,null,null,null,null,null,27,10.08751614699332]
[null,null,null,null,null,null,null,28,10.032258351893097]
[null,null,null,null,null,null,null,29,10.004140868596881]
[null,null,null,null,null,null,null,30,10]
[null,null,null,null,null,null,null,31,10.018846325167038]
[null,null,null,null,null,null,null,32,10.068387527839644]
[null,null,null,null,null,null,null,33,10.15850556792873]
[null,null,null,null,null,null,null,34,10.299082405345212]
[null,null,null,null,null,null,null,35,10.5]
[null,null,null,null,null,null,null,36,10.769095768374164]
[null,null,null,null,null,null,null,37,11.106028953229398]
[null,null,null,null,null,null,null,38,11.508414253897548]
[null,null,null,null,null,null,null,39,11.973866369710468]
[null,null,null,null,null,null,null,40,12.5]
[null,null,null,null,null,null,null,41,13.083855790645881]
[null,null,null,null,null,null,null,42,13.720178173719376]
[null,null,null,null,null,null,null,43,14.403137527839645]
[null,null,null,null,null,null,null,44,15.126904231625835]
[null,null,null,null,null,null,null,45,15.885648663697104]
[null,null,null,null,null,null,null,46,16.673541202672606]
[null,null,null,null,null,null,null,47,17.484752227171491]
[null,null,null,null,null,null,null,48,18.313452115812918]
[null,null,null,null,null,null,null,49,19.153811247216037]
[null,null,null,null,null,null,null,50,20]

{"sheet":"Ausflusszeit","index":2,"n_rows":51,"n_cols":10,"rows_kept":51,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["Ausflusszeit bei abnehmendem Flüssigkeitsstand"]
["A [mm² ]",10,null,"x [mm]","y1","y2","t1 [s]","t2 [s]","tm [s]","dtm [s]"]
["h [mm]",400,null,400,6283.1853071795867,6222.2258605001143,34.988471430637716,34.649013376434688,34.819156044596369,34.819156044596369]
["u [mm]",10,null,392.2,6222.2258605001143,6161.881903624595,69.637484807072411,68.961996107913194,69.300563055269862,34.481407010673486]
["n",50,null,384.4,6161.881903624595,6102.17284047879,103.95046753855092,102.942483656154,103.44770176927065,34.147138714000782]
[null,null,null,376.6,6102.17284047879,6043.1195118947289,137.93095508679173,136.59412753688645,137.26416489608485,33.816463126814192]
["t (TR) [s]",1480.4257738736528,null,368.8,6043.1195118947289,5984.7443392749165,171.58259896752418,169.92070412139688,170.75366550837532,33.489500612290477]
[null,null,null,361,5984.7443392749165,5927.0714861136639,204.90917555203461,202.92612433752038,203.92004628103521,33.166380772659892]
[null,null,null,353.2,5927.0714861136639,5870.1270400409212,237.91459576815811,235.61444438435984,236.76728968492947,32.847243403894247]
[null,null,null,345.4,5870.1270400409212,5813.9392185213774,270.60291581499757,267.98987759245847,269.29952925798642,32.532239573056934]
[null,null,null,337.6,5813.9392185213774,5758.5386019036068,302.9783490230962,300.05680758172707,301.52106209524004,32.221532837253591]
[null,null,null,329.8,5758.5386019036068,5703.9583981927572,335.04527901236474,331.81980289378134,333.43636272180055,31.915300626560494]
[null,null,null,322,5703.9583981927572,5650.2347447431539,366.80827432441902,363.28363330428112,365.05009853926788,31.61373581746733]
[null,null,null,314.2,5650.2347447431539,5597.4070530694971,398.2721047349188,394.45328805538117,396.36714706769385,31.31704852842595]
[null,null,null,306.39999999999998,5597.4070530694971,5545.5184042015908,429.44175948601884,425.33399628974951,427.39261524296109,31.025468175267225]
[null,null,null,298.60000000000002,5545.5184042015908,5494.6160035151725,460.32246772038718,455.9312500173516,458.13186107477713,30.739245831816046]
[null,null,null,290.8,5494.6160035151725,5444.7517058342455,490.91972144798928,486.25083000631287,488.59051802513829,30.458656950361171]
[null,null,null,283,5444.7517058342455,5395.9826239144249,521.23930143695054,516.29883506217448,518.77452253333047,30.184004508192135]
[null,null,null,275.2,5395.9826239144249,5348.3718363075586,551.28730649281215,546.08171524895579,548.69014519413929,29.915622660808868]
[null,null,null,267.39999999999998,5348.3718363075586,5301.9892142402141,581.07018667959346,575.60630971476257,578.34402619458206,29.653881000442816]
[null,null,null,259.60000000000002,5301.9892142402141,5256.91239173139,610.59478114540025,604.87988991958116,607.74321573583859,29.399189541256515]
[null,null,null,251.8,5256.91239173139,5213.227909019939,639.86836135021883,633.91020923034887,636.89522031725846,29.152004581419906]
[null,null,null,244,5213.227909019939,5171.0325668632986,668.89868066098654,662.70556005755668,665.80805594633875,28.912835629080327]
[null,null,null,236.2,5171.0325668632986,5130.4350389404672,697.69403148819436,691.27483997065997,694.49030957294042,28.6822536266017]
[null,null,null,228.4,5130.4350389404672,5091.5578021763204,726.26331140129764,719.62762856267,722.95121034176566,28.460900768825191]
[null,null,null,220.6,5091.5578021763204,5054.5394613154949,754.61609999330767,747.77427725934092,751.20071263306056,28.249502291294931]
[null,null,null,212.8,5054.5394613154949,5019.5375659305782,782.76274868997859,775.72601481511424,779.24959334312712,28.048880710066612]
[null,null,null,205,5019.5375659305782,4986.7320472573165,810.71448624575191,803.49507194738408,807.10956647838384,27.859973135256741]
[null,null,null,197.2,4986.7320472573165,4956.3294416799399,838.48354337802175,831.09482948961227,834.79341894762297,27.683852469239078]
[null,null,null,189.4,4956.3294416799399,4928.5681215035911,866.08330092024994,858.53999567246149,862.31517250419438,27.521753556571447]
[null,null,null,181.6,4928.5681215035911,4903.7248279621981,893.52846710309916,885.84681978455831,889.69027820857332,27.375105704378914]
[null,null,null,173.8,4903.7248279621981,4882.1229053346879,920.83529121519598,913.033351685659,916.93585168910158,27.245573480528261]
[null,null,null,166,4882.1229053346879,4864.1427823898803,948.02182311629667,940.11975968666479,944.07096007395808,27.135108384856498]
[null,null,null,158.19999999999999,4864.1427823898803,4850.2354594340641,975.10823111730247,967.12872353345142,971.11697504518793,27.046014971229813]
[null,null,null,150.4,4850.2354594340641,4840.9400694178266,1002.1171949640891,994.08592518127068,998.09801146866585,26.981036423477878]
[null,null,null,142.6,4840.9400694178266,4836.9070434422583,1029.0743966119082,1021.020668568315,1025.041478159965,26.943466691299236]
[null,null,null,134.80000000000001,4836.9070434422583,4838.9291124100509,1056.0091399989526,1047.9666720247114,1051.9787776139008,26.937299453935761]
[null,null,null,127,4838.9291124100509,4847.9834650738794,1082.9551434553489,1074.9630954423239,1078.9462066456224,26.967429031721583]
[null,null,null,119.2,4847.9834650738794,4865.2901132560446,1109.9515668729614,1102.0558924564289,1105.9861326304251,27.039925984802682]
[null,null,null,111.4,4865.2901132560446,4892.3943415713593,1137.0443638870663,1129.2996217559426,1133.148555041779,27.16242241135382]
[null,null,null,103.6,4892.3943415713593,4931.2858785701765,1164.28809318658,1156.7599220086672,1160.4932173437176,27.344662301938591]
[null,null,null,95.799999999999628,4931.2858785701765,4984.5757231754196,1191.7483934393047,1184.5169714601436,1188.092524486073,27.599307142355475]
[null,null,null,87.999999999999631,4984.5757231754196,5055.7666099154922,1219.5054428907811,1212.6704536420029,1216.0356733440062,27.943148857933252]
[null,null,null,80.199999999999633,5055.7666099154922,5149.681682685321,1247.6589250726404,1241.3469101879573,1244.4346703322483,28.398996988242089]
[null,null,null,72.399999999999636,5149.681682685321,5273.1732702388026,1276.3353816185947,1270.7110405286192,1273.4334010991397,28.998730766891388]
[null,null,null,64.599999999999639,5273.1732702388026,5436.3562988505064,1305.6995119592566,1300.9838699534894,1303.2218707054235,29.788469606283712]
[null,null,null,56.799999999999642,5436.3562988505064,5654.8948263960474,1335.9723413841268,1332.4736504395967,1334.0597141485791,30.837843443155709]
[null,null,null,48.999999999999645,5654.8948263960474,5954.595838344705,1367.4621218702341,1365.6323424382001,1366.3175516678141,32.257837519235046]
[null,null,null,41.199999999999648,5954.595838344705,6381.6718778071445,1400.6208138688376,1401.1692450218657,1400.5559997414559,34.238448073641955]
[null,null,null,33.39999999999965,6381.6718778071445,7029.3172733467245,1436.1577164525031,1440.3126180995857,1437.6946509125758,37.13865117111979]
[null,null,null,25.59999999999965,7029.3172733467245,8123.7539318714153,1475.3010895302232,1485.5504582170854,1479.4382095818339,41.743558669258128]

{"sheet":"Konstante Zugspannung","index":3,"n_rows":52,"n_cols":5,"rows_kept":52,"cut":false,"hidden":false,"merged":[[0,0,0,4]]}
["Träger mit konstanter Zugspannung"]
["Ao [m² ]",0.2,null,"x [m]","A [m²]"]
["l [m]",0.5,null,0.01,0.2154017]
["ρ [kg/m³ ]",7.8499999999999993E-3,null,0.02,0.23198946181444999]
["σ [N/m² ]",0.01,null,0.03,0.24985462228458805]
["n",50,null,0.04,0.26909555196479074]
[null,null,null,0.05,0.28981819677827131]
[null,null,null,0.06,0.31213666138487084]
[null,null,null,7.0000000000000007E-2,0.33617383747312768]
[null,null,null,0.08,0.36206208043617705]
[null,null,null,0.09,0.38994393815744638]
[null,null,null,0.1,0.41997293591904405]
[null,null,null,0.11,0.45231442175476577]
[null,null,null,0.12,0.48714647690246765]
[null,null,null,0.13,0.52466089636901136]
[null,null,null,0.14000000000000001,0.56506424500704433]
[null,null,null,0.15,0.60857899491866929]
[null,null,null,0.16,0.65544475044886363]
[null,null,null,0.17,0.70591956751380491]
[null,null,null,0.18,0.76028137452869171]
[null,null,null,0.19,0.8188295027590845]
[null,null,null,0.2,0.88188633452230747]
[null,null,null,0.21,0.94979907831436861]
[null,null,null,0.22,1.0229416806367406]
[null,null,null,0.23,1.1017168850500552]
[null,null,null,0.24,1.1865584497924324]
[null,null,null,0.25,1.2779335361732729]
[null,null,null,0.26,1.3763452808936723]
[null,null,null,0.27,1.4823355664573725]
[null,null,null,0.28000000000000003,1.596488004926905]
[null,null,null,0.28999999999999998,1.7194311514543186]
[null,null,null,0.3,1.8518419652810885]
[null,null,null,0.31,1.9944495372644371]
[null,null,null,0.32,2.1480391044548655]
[null,null,null,0.33,2.3134563738302778]
[null,null,null,0.34,2.4916121789943868]
[null,null,null,0.35,2.6834874954804762]
[null,null,null,0.36,2.8901388422761842]
[null,null,null,0.37,3.1127040993116095]
[null,null,null,0.38,3.3524087729434475]
[null,null,null,0.39,3.6105727439346631]
[null,null,null,0.4,3.8886175350859555]
[null,null,null,0.41,4.1880741385366225]
[null,null,null,0.42,4.5105914458341196]
[null,null,null,0.43,4.8579453271906363]
[null,null,null,0.44,5.2320484099195967]
[null,null,null,0.45,5.6349606098948897]
[null,null,null,0.46,6.0689004740219801]
[null,null,null,0.47,6.536257396175702]
[null,null,null,0.48,7.0396047738690983]
[null,null,null,0.49,7.581714178097597]
[null,null,null,0.5,8.1655706143816253]

{"sheet":"Lineare Approximation","index":4,"n_rows":9,"n_cols":10,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[20,20,20,43.315498154981547,null,null,"y =",0.88749999999999996,"x +",2.25]
[30,55,28.875,50.662361623616235]
[40,70,37.75,58.009225092250922,null,null,"y =",0.73468634686346868,"x +",28.621771217712176]
[50,75,46.625,65.35608856088561]
[65,82,59.9375,76.376383763837637]
[70,86,64.375,80.049815498154985]
[80,89,73.25,87.396678966789665]
[90,90,82.125,94.743542435424359]
[100,91,91,102.09040590405905]

{"sheet":"Newton","index":5,"n_rows":60,"n_cols":8,"rows_kept":60,"cut":false,"hidden":false,"merged":[]}
[0,30,-1.2,2.75E-2,-8.333333333333329E-5,-7.1428571428571461E-6,1.0119047619047621E-6,-5.3571428571428578E-8]
[10,18,-0.65,2.5000000000000001E-2,-3.3333333333333338E-4,3.3333333333333335E-5,-1.6666666666666667E-6]
[20,11.5,-0.15,1.6666666666666666E-2,6.6666666666666664E-4,-3.3333333333333335E-5]
[30,10,0.1,0.03,-3.3333333333333338E-4]
[35,10.5,0.4,2.3333333333333331E-2]
[40,12.5,0.75]
[50,20]
[]
[]
[0,30]
[1,29.096550750000002]
[2,28.004607999999998]
[3,26.785108000000001]
[4,25.489403428571428]
[5,24.16015625]
[6,22.832192000000003]
[7,21.5333155]
[8,20.285087999999998]
[9,19.103565750000001]
[10,18]
[11,16.981498428571431]
[12,16.051648]
[13,15.21109925]
[14,14.458112]
[15,13.7890625]
[16,13.198912000000002]
[17,12.681636750000003]
[18,12.23061942857143]
[19,11.839002000000001]
[20,11.5]
[21,11.207178249999998]
[22,10.954688000000001]
[23,10.737465500000003]
[24,10.551392000000003]
[25,10.393415178571429]
[26,10.261631999999999]
[27,10.155333000000002]
[28,10.075007999999999]
[29,10.022313250000003]
[30,10]
[31,10.011804500000004]
[32,10.06229942857143]
[33,10.156706749999996]
[34,10.300672000000006]
[35,10.5]
[36,10.760352000000001]
[37,11.086904250000007]
[38,11.483967999999997]
[39,11.95457092857143]
[40,12.5]
[41,13.119305750000004]
[42,13.808768000000002]
[43,14.561323000000003]
[44,15.365952000000002]
[45,16.20703125]
[46,17.063643428571432]
[47,17.9088505]
[48,18.708928000000007]
[49,19.422560750000002]
[50,20]