CoCalc Shared FilesLab4-turnin.sagews
Author: Brian Clark
Views : 23
# Lab 4

# Name: Brian Clark
# I worked on this code with: Christy Seguritan and Ana Leon

# Please do all of your work for this week's lab in this worksheet. If
# you wish to create other worksheets for scratch work, you can, but
# this is the one that will be graded. You do not need to do anything
# to turn in your lab. It will be collected by your TA at the beginning
# of (or right before) next week’s lab.

# Be sure to clearly label which question you are answering as you go and to


#1
# Step 2: Plug in the initial N value into the differential equation
# Step 3: Compute the new N by adding the initial N + stepsize*N'
# Step 4: Save the new N and add it a storage
# Step 5: Treat the new N as the intial N and repeat from step 2

#2.a
N_prime(n) = 0.2*n*(1-(n/100))
NewN(n) = Nprime(n)*0.1 + n
NewN(10)

10.1800000000000
#2.b
N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
N_init = [10]
iterations = srange(0,1000)
for i in iterations:
n_new = N_init[i]+delta_t*N_prime(N_init[i])
N_init.append(n_new)

N_init

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99.9999980964426, 99.9999981345138, 99.9999981718235, 99.9999982083870, 99.9999982442193, 99.9999982793349, 99.9999983137482, 99.9999983474732, 99.9999983805238, 99.9999984129133]
#3
N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
N_init = [101]
iterations = srange(0,1000)
for i in iterations:
n_new = N_init[i]+delta_t*N_prime(N_init[i])
N_init.append(n_new)

N_init

[101, 100.979800000000, 100.960011998392, 100.940627433817, 100.921637929147, 100.903035287269, 100.884811486978, 100.866958678965, 100.849469181915, 100.832335478699, 100.815550212655, 100.799106183972, 100.782996346154, 100.767213802575, 100.751751803120, 100.736603740903, 100.721763149070, 100.707223697680, 100.692979190655, 100.679023562810, 100.665350876954, 100.651955321057, 100.638831205488, 100.625972960316, 100.613375132681, 100.601032384216, 100.588939488547, 100.577091328832, 100.565482895375, 100.554109283286, 100.542965690201, 100.532047414049, 100.521349850877, 100.510868492726, 100.500598925549, 100.490536827181, 100.480677965361, 100.471018195793, 100.461553460249, 100.452279784725, 100.443193277629, 100.434290128020, 100.425566603877, 100.417019050413, 100.408643888427, 100.400437612693, 100.392396790382, 100.384518059527, 100.376798127508, 100.369233769592, 100.361821827485, 100.354559207929, 100.347442881324, 100.340469880386, 100.333637298830, 100.326942290084, 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100.000000056018, 100.000000054898, 100.000000053800, 100.000000052724, 100.000000051669, 100.000000050636, 100.000000049623, 100.000000048631, 100.000000047658, 100.000000046705, 100.000000045771, 100.000000044855, 100.000000043958, 100.000000043079, 100.000000042218, 100.000000041373, 100.000000040546, 100.000000039735, 100.000000038940, 100.000000038161, 100.000000037398, 100.000000036650, 100.000000035917, 100.000000035199, 100.000000034495, 100.000000033805, 100.000000033129, 100.000000032466, 100.000000031817, 100.000000031181, 100.000000030557, 100.000000029946, 100.000000029347, 100.000000028760, 100.000000028185, 100.000000027621, 100.000000027069, 100.000000026527, 100.000000025997, 100.000000025477, 100.000000024967, 100.000000024468, 100.000000023979, 100.000000023499, 100.000000023029, 100.000000022568, 100.000000022117, 100.000000021675, 100.000000021241, 100.000000020816, 100.000000020400, 100.000000019992, 100.000000019592, 100.000000019200, 100.000000018816, 100.000000018440, 100.000000018071, 100.000000017710, 100.000000017356, 100.000000017009, 100.000000016668, 100.000000016335, 100.000000016008, 100.000000015688, 100.000000015374, 100.000000015067, 100.000000014766, 100.000000014470, 100.000000014181, 100.000000013897, 100.000000013619, 100.000000013347, 100.000000013080, 100.000000012818, 100.000000012562, 100.000000012311, 100.000000012065, 100.000000011823, 100.000000011587, 100.000000011355, 100.000000011128, 100.000000010905, 100.000000010687, 100.000000010474, 100.000000010264, 100.000000010059, 100.000000009858, 100.000000009660, 100.000000009467, 100.000000009278, 100.000000009092, 100.000000008911, 100.000000008732, 100.000000008558, 100.000000008386, 100.000000008219, 100.000000008054, 100.000000007893, 100.000000007735, 100.000000007581, 100.000000007429, 100.000000007281, 100.000000007135, 100.000000006992, 100.000000006852, 100.000000006715, 100.000000006581, 100.000000006449, 100.000000006320, 100.000000006194, 100.000000006070, 100.000000005949, 100.000000005830, 100.000000005713, 100.000000005599, 100.000000005487, 100.000000005377, 100.000000005270, 100.000000005164, 100.000000005061, 100.000000004960, 100.000000004861, 100.000000004763, 100.000000004668, 100.000000004575, 100.000000004483, 100.000000004393, 100.000000004306, 100.000000004220, 100.000000004135, 100.000000004052, 100.000000003971, 100.000000003892, 100.000000003814, 100.000000003738, 100.000000003663, 100.000000003590, 100.000000003518, 100.000000003448, 100.000000003379, 100.000000003311, 100.000000003245, 100.000000003180, 100.000000003116, 100.000000003054, 100.000000002993, 100.000000002933, 100.000000002875, 100.000000002817, 100.000000002761, 100.000000002705, 100.000000002651, 100.000000002598, 100.000000002546, 100.000000002495, 100.000000002446, 100.000000002397, 100.000000002349, 100.000000002302, 100.000000002256, 100.000000002211, 100.000000002166, 100.000000002123, 100.000000002081, 100.000000002039, 100.000000001998, 100.000000001958, 100.000000001919, 100.000000001881, 100.000000001843, 100.000000001806, 100.000000001770, 100.000000001735, 100.000000001700, 100.000000001666]
N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
N_init = [310]
iterations = srange(0,1000)
for i in iterations:
n_new = N_init[i]+delta_t*N_prime(N_init[i])
N_init.append(n_new)

N_init

[310, 296.980000000000, 285.280175920000, 274.708823683811, 265.110012595538, 256.355549091768, 248.339026563575, 240.971352671938, 234.177341163668, 227.893082564044, 222.063892799217, 216.642696158172, 211.588738521600, 206.866554438199, 202.445131257937, 198.297227649087, 194.398814103406, 190.728610600512, 187.267702232202, 183.999217816980, 180.908059741867, 177.980675720791, 175.204865049201, 172.569613402804, 170.064951376861, 167.681832867035, 165.412030109646, 163.248042770840, 161.183018932555, 159.210686192764, 157.325291397025, 155.521547762334, 153.794588353902, 152.139925039591, 150.553412182172, 149.031214441877, 147.569778155110, 146.165805833263, 144.816233390950, 143.518209768061, 142.269078656416, 141.066362081196, 139.907745620655, 138.791065076137, 137.714294428666, 136.675534939243, 135.673005267842, 134.705032501517, 133.770043995300, 132.866559941106, 131.993186589811, 131.148610060381, 130.331590677434, 129.540957785281, 128.775604992201, 128.034485803824, 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107.571404317415, 107.408510998399, 107.249363571388, 107.093865645523, 106.941923746653, 106.793447210659, 106.648348081445, 106.506541013374, 106.367943177914, 106.232474174293, 106.100055943940, 105.970612688558, 105.844070791611, 105.720358743095, 105.599407067404, 105.481148254154, 105.365516691834, 105.252448604124, 105.141881988773, 105.033756558920, 104.928013686723, 104.824596349209, 104.723449076239, 104.624517900479, 104.527750309307, 104.433095198548, 104.340502827969, 104.249924778450, 104.161313910756, 104.074624325848, 103.989811326652, 103.906831381235, 103.825642087322, 103.746202138099, 103.668471289245, 103.592410327140, 103.517981038206, 103.445146179325, 103.373869449299, 103.304115461301, 103.235849716278, 103.169038577275, 103.103649244629, 103.039649732010, 102.977008843271, 102.915696150075, 102.855681970266, 102.796937346957, 102.739434028313, 102.683144447988, 102.628041706203, 102.574099551437, 102.521292362708, 102.469595132418, 102.418983449746, 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100.002943639775, 100.002884765247, 100.002827068277, 100.002770525313, 100.002715113272, 100.002660809532, 100.002607591925, 100.002555438727, 100.002504328646, 100.002454240819, 100.002405154798, 100.002357050545, 100.002309908423, 100.002263709188, 100.002218433979, 100.002174064315, 100.002130582083, 100.002087969534, 100.002046209271, 100.002005284248, 100.001965177759, 100.001925873432, 100.001887355221, 100.001849607404, 100.001812614572, 100.001776361624, 100.001740833760, 100.001706016479, 100.001671895567, 100.001638457097, 100.001605687418, 100.001573573154, 100.001542101195, 100.001511258696, 100.001481033065, 100.001451411965, 100.001422383305, 100.001393935234, 100.001366056141, 100.001338734645, 100.001311959593, 100.001285720057, 100.001260005325, 100.001234804901, 100.001210108498, 100.001185906036, 100.001162187634, 100.001138943611, 100.001116164479, 100.001093840940, 100.001071963882, 100.001050524375, 100.001029513667, 100.001008923181, 100.000988744514, 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100.000003745214, 100.000003670309, 100.000003596903, 100.000003524965, 100.000003454466, 100.000003385377, 100.000003317669, 100.000003251316, 100.000003186289, 100.000003122564, 100.000003060112, 100.000002998910, 100.000002938932, 100.000002880153, 100.000002822550, 100.000002766099, 100.000002710777, 100.000002656562, 100.000002603430, 100.000002551362, 100.000002500335, 100.000002450328, 100.000002401321, 100.000002353295, 100.000002306229, 100.000002260104, 100.000002214902, 100.000002170604, 100.000002127192, 100.000002084648, 100.000002042955, 100.000002002096, 100.000001962054, 100.000001922813, 100.000001884357, 100.000001846670, 100.000001809736, 100.000001773542, 100.000001738071, 100.000001703309, 100.000001669243, 100.000001635858, 100.000001603141, 100.000001571078, 100.000001539657, 100.000001508864, 100.000001478686, 100.000001449113, 100.000001420130, 100.000001391728, 100.000001363893, 100.000001336615, 100.000001309883, 100.000001283685, 100.000001258012, 100.000001232851, 100.000001208194, 100.000001184031, 100.000001160350, 100.000001137143, 100.000001114400, 100.000001092112, 100.000001070270, 100.000001048864, 100.000001027887, 100.000001007329, 100.000000987183, 100.000000967439, 100.000000948090, 100.000000929129, 100.000000910546, 100.000000892335, 100.000000874488, 100.000000856999, 100.000000839859, 100.000000823061, 100.000000806600, 100.000000790468, 100.000000774659, 100.000000759166, 100.000000743982, 100.000000729103, 100.000000714521, 100.000000700230, 100.000000686226, 100.000000672501, 100.000000659051, 100.000000645870, 100.000000632953, 100.000000620294, 100.000000607888, 100.000000595730, 100.000000583815, 100.000000572139, 100.000000560696, 100.000000549482, 100.000000538493, 100.000000527723, 100.000000517168, 100.000000506825, 100.000000496689, 100.000000486755, 100.000000477020, 100.000000467479, 100.000000458130, 100.000000448967, 100.000000439988, 100.000000431188, 100.000000422564, 100.000000414113, 100.000000405831, 100.000000397714, 100.000000389760, 100.000000381965, 100.000000374325, 100.000000366839, 100.000000359502, 100.000000352312, 100.000000345266, 100.000000338360, 100.000000331593, 100.000000324961, 100.000000318462, 100.000000312093, 100.000000305851, 100.000000299734, 100.000000293739, 100.000000287865, 100.000000282107, 100.000000276465, 100.000000270936, 100.000000265517, 100.000000260207, 100.000000255003, 100.000000249903, 100.000000244905, 100.000000240006, 100.000000235206, 100.000000230502, 100.000000225892, 100.000000221374, 100.000000216947, 100.000000212608, 100.000000208356, 100.000000204189, 100.000000200105, 100.000000196103, 100.000000192181, 100.000000188337, 100.000000184570, 100.000000180879, 100.000000177261, 100.000000173716, 100.000000170242, 100.000000166837, 100.000000163500, 100.000000160230, 100.000000157026, 100.000000153885, 100.000000150807, 100.000000147791, 100.000000144835, 100.000000141939, 100.000000139100, 100.000000136318, 100.000000133592, 100.000000130920, 100.000000128301, 100.000000125735, 100.000000123221, 100.000000120756, 100.000000118341, 100.000000115974, 100.000000113655, 100.000000111382]
N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
N_init = [1001]
iterations = srange(0,1000)
for i in iterations:
n_new = N_init[i]+delta_t*N_prime(N_init[i])
N_init.append(n_new)

N_init

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138.586104025479, 137.516604460197, 136.484773248948, 135.488850048164, 134.527181351652, 133.598212474201, 132.700480248425, 131.832606361761, 130.993291268969, 130.181308622853, 129.395500172359, 128.634771082835, 127.898085638185, 127.184463288966, 126.492975014325, 125.822739969016, 125.172922389735, 124.542728737612, 123.931405056082, 123.338234525369, 122.762535196709, 122.203657891059, 121.660984248489, 121.133924915797, 120.621917861011, 120.124426804538, 119.640939757605, 119.170967659540, 118.714043106149, 118.269719162150, 117.837568251254, 117.417181118006, 117.008165856026, 116.610146997748, 116.222764661136, 115.845673749263, 115.478543198964, 115.121055275073, 114.772904907045, 114.433799065025, 114.103456172635, 113.781605553980, 113.467986912571, 113.162349840024, 112.864453352561, 112.574065453498, 112.290962720022, 112.014929912705, 111.745759606289, 111.483251840418, 111.227213789043, 110.977459447369, 110.733809335238, 110.496090215965, 110.264134829681, 110.037781640327, 109.816874595469, 109.601262898195, 109.390800790383, 109.185347346678, 108.984766278569, 108.788925747981, 108.597698189861, 108.410960143231, 108.228592090260, 108.050478302897, 107.876506696658, 107.706568691177, 107.540559077155, 107.378375889372, 107.219920285432, 107.065096429938, 106.913811383826, 106.765974998579, 106.621499815071, 106.480300966810, 106.342296087350, 106.207405221671, 106.075550741320, 105.946657263132, 105.820651571348, 105.697462542978, 105.577021076233, 105.459260021891, 105.344114117456, 105.231519923967, 105.121415765344, 105.013741670149, 104.908439315639, 104.805451974023, 104.704724460808, 104.606203085141, 104.509835602066, 104.415571166593, 104.323360289516, 104.233154794887, 104.144907779086, 104.058573571405, 103.974107696090, 103.891466835772, 103.810608796230, 103.731492472426, 103.654077815763, 103.578325802511, 103.504198403351, 103.431658553994, 103.360670126828, 103.291197903551, 103.223207548752, 103.156665584396, 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100.000000173059, 100.000000169598, 100.000000166206, 100.000000162882, 100.000000159624, 100.000000156432, 100.000000153303, 100.000000150237, 100.000000147232, 100.000000144288]
#4.a
N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
listpop= [10]
count = srange(0,100,.1)
for i in iterations:
n_new = listpop[i]+delta_t*N_prime(listpop[i])
listpop.append(n_new)
list_plot(zip(count,listpop), axes_labels=["time","population"])

N_prime(n) = 0.2*n*(1-(n/100))
delta_t = .1
listpop= [10]
count = srange(0,100,.1)
for i in iterations:
n_new = listpop[i]+delta_t*N_prime(listpop[i])
listpop.append(n_new)
list_plot((count,listpop), axes_labels=["time","population"])
# If you omit "zip" it would not display a graph, but rather a 3-d object. The object being displayed is a cube.

3D rendering not yet implemented
#5
def euler(differentialeq,initialval,stepsize,numsteps):
vals = [initialval]
tfinal= numsteps*stepsize
for i in srange(0,tfinal,stepsize):
vals.append(differentialeq(vals[-1])*stepsize+vals[-1])
return vals
euler(.2*x*(1-x/100),10,.1,100)

[10, 10.1800000000000, 10.3628735200000, 10.5486531608817, 10.7373714073976, 10.9290606065975, 11.1237529455809, 11.3214804285737, 11.5222748533262, 11.7261677868336, 11.9331905403773, 12.1433741438903, 12.3567493196484, 12.5733464552916, 12.7931955761805, 13.0163263170940, 13.2427678932773, 13.4725490708478, 13.7056981365714, 13.9422428670207, 14.1822104971285, 14.4256276881541, 14.6725204950778, 14.9229143334436, 15.1768339456718, 15.4343033668624, 15.6953458901155, 15.9599840313958, 16.2282394939672, 16.5001331324319, 16.7756849164029, 17.0549138938481, 17.3378381541397, 17.6244747908507, 17.9148398643370, 18.2089483641508, 18.5068141713282, 18.8084500206003, 19.1138674625768, 19.4230768259530, 19.7360871797947, 20.0529062959569, 20.3735406116931, 20.6979951925157, 21.0262736953681, 21.3583783321730, 21.6943098338204, 22.0340674146637, 22.3776487375901, 22.7250498797374, 23.0762652989248, 23.4312878008740, 23.7901085072900, 24.1527168248781, 24.5191004153711, 24.8892451666427, 25.2631351649825, 25.6407526686093, 26.0220780824990, 26.4070899346026, 26.7957648535318, 27.1880775477853, 27.5840007865921, 27.9835053824450, 28.3865601753961, 28.7931320191857, 29.2031857692746, 29.6166842728451, 30.0335883608386, 30.4538568420897, 30.8774464996198, 31.3043120891448, 31.7344063398528, 32.1676799575012, 32.6040816298816, 33.0435580346936, 33.4860538498691, 33.9315117663792, 34.3798725035564, 34.8310748269554, 35.2850555687743, 35.7417496508515, 36.2010901102477, 36.6630081274186, 37.1274330569767, 37.5942924610362, 38.0635121451277, 38.5350161966658, 39.0087270259437, 39.4845654096256, 39.9624505367008, 40.4423000568551, 40.9240301312145, 41.4075554854027, 41.8927894648554, 42.3796440923231, 42.8680301274912, 43.3578571286387, 43.8490335162540, 44.3414666385172, 44.8350628385566]
#6
f(N) = .2*N(1-(N/100))
N = [10]
h = .1
for i in srange (0,100,h):
Nnew = N[-1] + f(N[-1])*h
N.append(Nnew)
tlist = srange(0,100,h)
zip(tlist,N)

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(2.60000000000000, 10.4668318698491), (2.70000000000000, 10.4847385034751), (2.80000000000000, 10.5026415557744), (2.90000000000000, 10.5205410274633), (3.00000000000000, 10.5384369192578), (3.10000000000000, 10.5563292318739), (3.20000000000000, 10.5742179660276), (3.30000000000000, 10.5921031224344), (3.40000000000000, 10.6099847018099), (3.50000000000000, 10.6278627048695), (3.60000000000000, 10.6457371323285), (3.70000000000000, 10.6636079849021), (3.80000000000000, 10.6814752633051), (3.90000000000000, 10.6993389682524), (4.00000000000000, 10.7171991004588), (4.10000000000000, 10.7350556606387), (4.20000000000000, 10.7529086495066), (4.30000000000000, 10.7707580677767), (4.40000000000000, 10.7886039161631), (4.50000000000000, 10.8064461953799), (4.60000000000000, 10.8242849061408), (4.70000000000000, 10.8421200491596), (4.80000000000000, 10.8599516251497), (4.90000000000000, 10.8777796348247), (5.00000000000000, 10.8956040788977), (5.10000000000000, 10.9134249580820), (5.20000000000000, 10.9312422730903), (5.30000000000000, 10.9490560246357), (5.40000000000000, 10.9668662134308), (5.50000000000000, 10.9846728401881), (5.60000000000000, 11.0024759056201), (5.70000000000000, 11.0202754104389), (5.80000000000000, 11.0380713553569), (5.90000000000000, 11.0558637410858), (5.99999999999999, 11.0736525683376), (6.09999999999999, 11.0914378378239), (6.19999999999999, 11.1092195502563), (6.29999999999999, 11.1269977063463), (6.39999999999999, 11.1447723068050), (6.49999999999999, 11.1625433523437), (6.59999999999999, 11.1803108436732), (6.69999999999999, 11.1980747815045), (6.79999999999999, 11.2158351665482), (6.89999999999999, 11.2335919995148), (6.99999999999999, 11.2513452811149), (7.09999999999999, 11.2690950120587), (7.19999999999999, 11.2868411930563), (7.29999999999999, 11.3045838248177), (7.39999999999999, 11.3223229080527), (7.49999999999999, 11.3400584434711), (7.59999999999999, 11.3577904317824), (7.69999999999999, 11.3755188736961), (7.79999999999999, 11.3932437699213), (7.89999999999999, 11.4109651211673), (7.99999999999999, 11.4286829281431), (8.09999999999999, 11.4463971915575), (8.19999999999999, 11.4641079121192), (8.29999999999999, 11.4818150905367), (8.39999999999999, 11.4995187275186), (8.49999999999999, 11.5172188237731), (8.59999999999999, 11.5349153800084), (8.69999999999999, 11.5526083969324), (8.79999999999998, 11.5702978752530), (8.89999999999998, 11.5879838156779), (8.99999999999998, 11.6056662189148), (9.09999999999998, 11.6233450856710), (9.19999999999998, 11.6410204166539), (9.29999999999998, 11.6586922125706), (9.39999999999998, 11.6763604741280), (9.49999999999998, 11.6940252020332), (9.59999999999998, 11.7116863969928), (9.69999999999998, 11.7293440597134), (9.79999999999998, 11.7469981909015), (9.89999999999998, 11.7646487912633), (9.99999999999998, 11.7822958615050), (10.1000000000000, 11.7999394023327), (10.2000000000000, 11.8175794144523), (10.3000000000000, 11.8352158985694), (10.4000000000000, 11.8528488553897), (10.5000000000000, 11.8704782856186), (10.6000000000000, 11.8881041899615), (10.7000000000000, 11.9057265691235), (10.8000000000000, 11.9233454238096), (10.9000000000000, 11.9409607547249), (11.0000000000000, 11.9585725625739), (11.1000000000000, 11.9761808480614), (11.2000000000000, 11.9937856118918), (11.3000000000000, 12.0113868547694), (11.4000000000000, 12.0289845773985), (11.5000000000000, 12.0465787804830), (11.6000000000000, 12.0641694647269), (11.7000000000000, 12.0817566308340), (11.8000000000000, 12.0993402795078), (11.9000000000000, 12.1169204114519), (12.0000000000000, 12.1344970273696), (12.1000000000000, 12.1520701279641), (12.2000000000000, 12.1696397139385), (12.3000000000000, 12.1872057859957), (12.4000000000000, 12.2047683448385), (12.5000000000000, 12.2223273911696), (12.6000000000000, 12.2398829256913), (12.7000000000000, 12.2574349491062), (12.8000000000000, 12.2749834621164), (12.9000000000000, 12.2925284654240), (13.0000000000000, 12.3100699597309), (13.1000000000000, 12.3276079457389), (13.2000000000000, 12.3451424241498), (13.3000000000000, 12.3626733956649), (13.4000000000000, 12.3802008609858), (13.5000000000000, 12.3977248208136), (13.6000000000000, 12.4152452758495), (13.7000000000000, 12.4327622267943), (13.8000000000000, 12.4502756743489), (13.9000000000000, 12.4677856192141), (14.0000000000000, 12.4852920620902), (14.1000000000000, 12.5027950036778), (14.2000000000000, 12.5202944446771), (14.3000000000000, 12.5377903857881), (14.4000000000000, 12.5552828277110), (14.5000000000000, 12.5727717711454), (14.6000000000000, 12.5902572167912), (14.7000000000000, 12.6077391653478), (14.8000000000000, 12.6252176175148), (14.9000000000000, 12.6426925739913), (15.0000000000000, 12.6601640354765), (15.1000000000000, 12.6776320026694), (15.2000000000000, 12.6950964762688), (15.3000000000000, 12.7125574569736), (15.4000000000000, 12.7300149454822), (15.5000000000000, 12.7474689424931), 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(67.6000000000004, 21.3823563213759), (67.7000000000004, 21.3980798501116), (67.8000000000004, 21.4138002341416), (67.9000000000004, 21.4295174740948), (68.0000000000004, 21.4452315706000), (68.1000000000004, 21.4609425242858), (68.2000000000004, 21.4766503357810), (68.3000000000004, 21.4923550057138), (68.4000000000004, 21.5080565347127), (68.5000000000004, 21.5237549234057), (68.6000000000004, 21.5394501724211), (68.7000000000004, 21.5551422823866), (68.8000000000004, 21.5708312539301), (68.9000000000004, 21.5865170876793), (69.0000000000004, 21.6021997842618), (69.1000000000003, 21.6178793443049), (69.2000000000003, 21.6335557684361), (69.3000000000003, 21.6492290572824), (69.4000000000003, 21.6648992114709), (69.5000000000003, 21.6805662316286), (69.6000000000003, 21.6962301183823), (69.7000000000003, 21.7118908723586), (69.8000000000003, 21.7275484941841), (69.9000000000003, 21.7432029844853), (70.0000000000003, 21.7588543438884), (70.1000000000003, 21.7745025730196), (70.2000000000003, 21.7901476725050), (70.3000000000003, 21.8057896429705), (70.4000000000003, 21.8214284850419), (70.5000000000003, 21.8370641993449), (70.6000000000003, 21.8526967865051), (70.7000000000003, 21.8683262471478), (70.8000000000003, 21.8839525818983), (70.9000000000002, 21.8995757913820), (71.0000000000002, 21.9151958762237), (71.1000000000002, 21.9308128370484), (71.2000000000002, 21.9464266744810), (71.3000000000002, 21.9620373891461), (71.4000000000002, 21.9776449816683), (71.5000000000002, 21.9932494526720), (71.6000000000002, 22.0088508027814), (71.7000000000002, 22.0244490326209), (71.8000000000002, 22.0400441428143), (71.9000000000002, 22.0556361339858), (72.0000000000002, 22.0712250067590), (72.1000000000002, 22.0868107617576), (72.2000000000002, 22.1023933996053), (72.3000000000002, 22.1179729209254), (72.4000000000002, 22.1335493263412), (72.5000000000002, 22.1491226164759), (72.6000000000002, 22.1646927919526), (72.7000000000001, 22.1802598533942), (72.8000000000001, 22.1958238014235), (72.9000000000001, 22.2113846366633), (73.0000000000001, 22.2269423597359), (73.1000000000001, 22.2424969712640), (73.2000000000001, 22.2580484718697), (73.3000000000001, 22.2735968621753), (73.4000000000001, 22.2891421428029), (73.5000000000001, 22.3046843143743), (73.6000000000001, 22.3202233775115), (73.7000000000001, 22.3357593328360), (73.8000000000001, 22.3512921809694), (73.9000000000001, 22.3668219225332), (74.0000000000001, 22.3823485581487), (74.1000000000001, 22.3978720884371), (74.2000000000001, 22.4133925140194), (74.3000000000001, 22.4289098355166), (74.4000000000000, 22.4444240535495), (74.5000000000000, 22.4599351687388), (74.6000000000000, 22.4754431817050), (74.7000000000000, 22.4909480930687), (74.8000000000000, 22.5064499034501), (74.9000000000000, 22.5219486134694), (75.0000000000000, 22.5374442237467), (75.1000000000000, 22.5529367349019), (75.2000000000000, 22.5684261475550), (75.3000000000000, 22.5839124623254), (75.4000000000000, 22.5993956798330), (75.5000000000000, 22.6148758006970), (75.6000000000000, 22.6303528255369), (75.7000000000000, 22.6458267549718), (75.8000000000000, 22.6612975896208), (75.9000000000000, 22.6767653301028), (76.0000000000000, 22.6922299770368), (76.1000000000000, 22.7076915310414), (76.1999999999999, 22.7231499927352), (76.2999999999999, 22.7386053627367), (76.3999999999999, 22.7540576416641), (76.4999999999999, 22.7695068301358), (76.5999999999999, 22.7849529287698), (76.6999999999999, 22.8003959381840), (76.7999999999999, 22.8158358589964), (76.8999999999999, 22.8312726918246), (76.9999999999999, 22.8467064372862), (77.0999999999999, 22.8621370959987), (77.1999999999999, 22.8775646685795), (77.2999999999999, 22.8929891556458), (77.3999999999999, 22.9084105578147), (77.4999999999999, 22.9238288757031), (77.5999999999999, 22.9392441099280), (77.6999999999999, 22.9546562611060), (77.7999999999999, 22.9700653298538), (77.8999999999998, 22.9854713167878), (77.9999999999998, 23.0008742225245), (78.0999999999998, 23.0162740476800), (78.1999999999998, 23.0316707928704), (78.2999999999998, 23.0470644587118), (78.3999999999998, 23.0624550458201), (78.4999999999998, 23.0778425548109), (78.5999999999998, 23.0932269863000), (78.6999999999998, 23.1086083409027), (78.7999999999998, 23.1239866192345), (78.8999999999998, 23.1393618219107), (78.9999999999998, 23.1547339495463), (79.0999999999998, 23.1701030027564), (79.1999999999998, 23.1854689821559), (79.2999999999998, 23.2008318883594), (79.3999999999998, 23.2161917219818), (79.4999999999998, 23.2315484836374), (79.5999999999998, 23.2469021739406), (79.6999999999997, 23.2622527935058), (79.7999999999997, 23.2776003429471), (79.8999999999997, 23.2929448228785), (79.9999999999997, 23.3082862339140), (80.0999999999997, 23.3236245766672), (80.1999999999997, 23.3389598517519), (80.2999999999997, 23.3542920597815), (80.3999999999997, 23.3696212013696), (80.4999999999997, 23.3849472771293), (80.5999999999997, 23.4002702876739), (80.6999999999997, 23.4155902336163), (80.7999999999997, 23.4309071155696), (80.8999999999997, 23.4462209341465), (80.9999999999997, 23.4615316899596), (81.0999999999997, 23.4768393836217), (81.1999999999997, 23.4921440157449), (81.2999999999997, 23.5074455869418), (81.3999999999997, 23.5227440978244), (81.4999999999996, 23.5380395490048), (81.5999999999996, 23.5533319410950), (81.6999999999996, 23.5686212747068), (81.7999999999996, 23.5839075504519), (81.8999999999996, 23.5991907689418), (81.9999999999996, 23.6144709307880), (82.0999999999996, 23.6297480366018), (82.1999999999996, 23.6450220869945), (82.2999999999996, 23.6602930825771), (82.3999999999996, 23.6755610239606), (82.4999999999996, 23.6908259117558), (82.5999999999996, 23.7060877465735), (82.6999999999996, 23.7213465290241), (82.7999999999996, 23.7366022597183), (82.8999999999996, 23.7518549392664), (82.9999999999996, 23.7671045682785), (83.0999999999996, 23.7823511473649), (83.1999999999995, 23.7975946771354), (83.2999999999995, 23.8128351582000), (83.3999999999995, 23.8280725911683), (83.4999999999995, 23.8433069766501), (83.5999999999995, 23.8585383152548), (83.6999999999995, 23.8737666075917), (83.7999999999995, 23.8889918542702), (83.8999999999995, 23.9042140558994), (83.9999999999995, 23.9194332130882), (84.0999999999995, 23.9346493264456), (84.1999999999995, 23.9498623965803), (84.2999999999995, 23.9650724241010), (84.3999999999995, 23.9802794096161), (84.4999999999995, 23.9954833537342), (84.5999999999995, 24.0106842570635), (84.6999999999995, 24.0258821202121), (84.7999999999995, 24.0410769437880), (84.8999999999995, 24.0562687283993), (84.9999999999994, 24.0714574746536), (85.0999999999994, 24.0866431831586), (85.1999999999994, 24.1018258545220), (85.2999999999994, 24.1170054893511), (85.3999999999994, 24.1321820882532), (85.4999999999994, 24.1473556518356), (85.5999999999994, 24.1625261807052), (85.6999999999994, 24.1776936754691), (85.7999999999994, 24.1928581367340), (85.8999999999994, 24.2080195651066), (85.9999999999994, 24.2231779611936), (86.0999999999994, 24.2383333256014), (86.1999999999994, 24.2534856589363), (86.2999999999994, 24.2686349618045), (86.3999999999994, 24.2837812348121), (86.4999999999994, 24.2989244785651), (86.5999999999994, 24.3140646936694), (86.6999999999993, 24.3292018807307), (86.7999999999993, 24.3443360403546), (86.8999999999993, 24.3594671731465), (86.9999999999993, 24.3745952797119), (87.0999999999993, 24.3897203606559), (87.1999999999993, 24.4048424165838), (87.2999999999993, 24.4199614481005), (87.3999999999993, 24.4350774558108), (87.4999999999993, 24.4501904403197), (87.5999999999993, 24.4653004022316), (87.6999999999993, 24.4804073421512), (87.7999999999993, 24.4955112606827), (87.8999999999993, 24.5106121584306), (87.9999999999993, 24.5257100359989), (88.0999999999993, 24.5408048939917), (88.1999999999993, 24.5558967330129), (88.2999999999993, 24.5709855536663), (88.3999999999993, 24.5860713565556), (88.4999999999992, 24.6011541422843), (88.5999999999992, 24.6162339114558), (88.6999999999992, 24.6313106646735), (88.7999999999992, 24.6463844025406), (88.8999999999992, 24.6614551256601), (88.9999999999992, 24.6765228346349), (89.0999999999992, 24.6915875300680), (89.1999999999992, 24.7066492125620), (89.2999999999992, 24.7217078827195), (89.3999999999992, 24.7367635411429), (89.4999999999992, 24.7518161884347), (89.5999999999992, 24.7668658251970), (89.6999999999992, 24.7819124520320), (89.7999999999992, 24.7969560695416), (89.8999999999992, 24.8119966783277), (89.9999999999992, 24.8270342789920), (90.0999999999992, 24.8420688721362), (90.1999999999992, 24.8571004583618), (90.2999999999991, 24.8721290382701), (90.3999999999991, 24.8871546124625), (90.4999999999991, 24.9021771815400), (90.5999999999991, 24.9171967461037), (90.6999999999991, 24.9322133067544), (90.7999999999991, 24.9472268640931), (90.8999999999991, 24.9622374187203), (90.9999999999991, 24.9772449712365), (91.0999999999991, 24.9922495222423), (91.1999999999991, 25.0072510723378), (91.2999999999991, 25.0222496221234), (91.3999999999991, 25.0372451721989), (91.4999999999991, 25.0522377231645), (91.5999999999991, 25.0672272756199), (91.6999999999991, 25.0822138301647), (91.7999999999991, 25.0971973873987), (91.8999999999991, 25.1121779479212), (91.9999999999990, 25.1271555123316), (92.0999999999990, 25.1421300812292), (92.1999999999990, 25.1571016552129), (92.2999999999990, 25.1720702348819), (92.3999999999990, 25.1870358208349), (92.4999999999990, 25.2019984136707), (92.5999999999990, 25.2169580139880), (92.6999999999990, 25.2319146223852), (92.7999999999990, 25.2468682394607), (92.8999999999990, 25.2618188658128), (92.9999999999990, 25.2767665020397), (93.0999999999990, 25.2917111487393), (93.1999999999990, 25.3066528065095), (93.2999999999990, 25.3215914759482), (93.3999999999990, 25.3365271576530), (93.4999999999990, 25.3514598522215), (93.5999999999990, 25.3663895602511), (93.6999999999990, 25.3813162823390), (93.7999999999989, 25.3962400190825), (93.8999999999989, 25.4111607710787), (93.9999999999989, 25.4260785389245), (94.0999999999989, 25.4409933232167), (94.1999999999989, 25.4559051245521), (94.2999999999989, 25.4708139435272), (94.3999999999989, 25.4857197807385), (94.4999999999989, 25.5006226367823), (94.5999999999989, 25.5155225122550), (94.6999999999989, 25.5304194077525), (94.7999999999989, 25.5453133238710), (94.8999999999989, 25.5602042612062), (94.9999999999989, 25.5750922203539), (95.0999999999989, 25.5899772019099), (95.1999999999989, 25.6048592064695), (95.2999999999989, 25.6197382346282), (95.3999999999989, 25.6346142869813), (95.4999999999988, 25.6494873641239), (95.5999999999988, 25.6643574666510), (95.6999999999988, 25.6792245951577), (95.7999999999988, 25.6940887502387), (95.8999999999988, 25.7089499324886), (95.9999999999988, 25.7238081425021), (96.0999999999988, 25.7386633808736), (96.1999999999988, 25.7535156481975), (96.2999999999988, 25.7683649450678), (96.3999999999988, 25.7832112720788), (96.4999999999988, 25.7980546298244), (96.5999999999988, 25.8128950188984), (96.6999999999988, 25.8277324398946), (96.7999999999988, 25.8425668934067), (96.8999999999988, 25.8573983800280), (96.9999999999988, 25.8722269003520), (97.0999999999988, 25.8870524549719), (97.1999999999988, 25.9018750444809), (97.2999999999987, 25.9166946694720), (97.3999999999987, 25.9315113305381), (97.4999999999987, 25.9463250282720), (97.5999999999987, 25.9611357632664), (97.6999999999987, 25.9759435361137), (97.7999999999987, 25.9907483474065), (97.8999999999987, 26.0055501977370), (97.9999999999987, 26.0203490876975), (98.0999999999987, 26.0351450178799), (98.1999999999987, 26.0499379888763), (98.2999999999987, 26.0647280012786), (98.3999999999987, 26.0795150556783), (98.4999999999987, 26.0942991526672), (98.5999999999987, 26.1090802928366), (98.6999999999987, 26.1238584767781), (98.7999999999987, 26.1386337050827), (98.8999999999987, 26.1534059783417), (98.9999999999986, 26.1681752971460), (99.0999999999986, 26.1829416620866), (99.1999999999986, 26.1977050737542), (99.2999999999986, 26.2124655327394), (99.3999999999986, 26.2272230396329), (99.4999999999986, 26.2419775950250), (99.5999999999986, 26.2567291995060), (99.6999999999986, 26.2714778536661), (99.7999999999986, 26.2862235580953), (99.8999999999986, 26.3009663133837)]
#7
def euler(differentialeq,initialval,stepsize,maxsize):
nvals = [initialval]
count = srange(0, maxsize)
for i in count:
a = differentialeq(nvals[-1])
nvals.append(nvals[-1]+a*stepsize)
return zip(count, nvals)
differentialeq(n) = .2*n(1-n/100)
euler(differentialeq,10,.1,100)
list_plot(zip(count,listpop),axes_labels= ["time","state values"])

[(0, 10), (1, 10.0180000000000), (2, 10.0359964000000), (3, 10.0539892007200), (4, 10.0719784028799), (5, 10.0899640071993), (6, 10.1079460143978), (7, 10.1259244251950), (8, 10.1438992403099), (9, 10.1618704604619), (10, 10.1798380863698), (11, 10.1978021187525), (12, 10.2157625583287), (13, 10.2337194058171), (14, 10.2516726619359), (15, 10.2696223274035), (16, 10.2875684029380), (17, 10.3055108892575), (18, 10.3234497870796), (19, 10.3413850971222), (20, 10.3593168201028), (21, 10.3772449567387), (22, 10.3951695077474), (23, 10.4130904738459), (24, 10.4310078557511), (25, 10.4489216541799), (26, 10.4668318698491), (27, 10.4847385034751), (28, 10.5026415557744), (29, 10.5205410274633), (30, 10.5384369192578), (31, 10.5563292318739), (32, 10.5742179660276), (33, 10.5921031224344), (34, 10.6099847018099), (35, 10.6278627048695), (36, 10.6457371323285), (37, 10.6636079849021), (38, 10.6814752633051), (39, 10.6993389682524), (40, 10.7171991004588), (41, 10.7350556606387), (42, 10.7529086495066), (43, 10.7707580677767), (44, 10.7886039161631), (45, 10.8064461953799), (46, 10.8242849061408), (47, 10.8421200491596), (48, 10.8599516251497), (49, 10.8777796348247), (50, 10.8956040788977), (51, 10.9134249580820), (52, 10.9312422730903), (53, 10.9490560246357), (54, 10.9668662134308), (55, 10.9846728401881), (56, 11.0024759056201), (57, 11.0202754104389), (58, 11.0380713553569), (59, 11.0558637410858), (60, 11.0736525683376), (61, 11.0914378378239), (62, 11.1092195502563), (63, 11.1269977063463), (64, 11.1447723068050), (65, 11.1625433523437), (66, 11.1803108436732), (67, 11.1980747815045), (68, 11.2158351665482), (69, 11.2335919995148), (70, 11.2513452811149), (71, 11.2690950120587), (72, 11.2868411930563), (73, 11.3045838248177), (74, 11.3223229080527), (75, 11.3400584434711), (76, 11.3577904317824), (77, 11.3755188736961), (78, 11.3932437699213), (79, 11.4109651211673), (80, 11.4286829281431), (81, 11.4463971915575), (82, 11.4641079121192), (83, 11.4818150905367), (84, 11.4995187275186), (85, 11.5172188237731), (86, 11.5349153800084), (87, 11.5526083969324), (88, 11.5702978752530), (89, 11.5879838156779), (90, 11.6056662189148), (91, 11.6233450856710), (92, 11.6410204166539), (93, 11.6586922125706), (94, 11.6763604741280), (95, 11.6940252020332), (96, 11.7116863969928), (97, 11.7293440597134), (98, 11.7469981909015), (99, 11.7646487912633)]
#8
EulersX= euler(-2.1*x,1,1,10)
list_plot(EulersX,axes_labels=["Time","X"],plotjoined=True)
# Oscillation occurs within the positive values as it becomes increasingly more positive and negative as the value time goes on.

#9
f(x)=-2.1*x
def euler(diffeq,initial,f,time):
newn=[diffeq]
hold=[]
for i in srange(0,initial,time):
hold.append(i)
newn.append(newn[-1]+(.1*f(newn[-1])))
return list_plot(zip(newn,hold),plotjoined=true)
euler(10,10,f,.5)
#Using a function thats takes a final time instead of a number of steps as an input