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VasujiVasuji
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algebra update
1 parent 851757e commit 3d1ee76

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+1818
-67
lines changed

‎2a. Arange-Oscillation.ipynb

+14-40
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"source": [
@@ -23,12 +23,12 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"$Y =Asin(\\omega t + \\phi)$"
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"$ Y = Asin(\\omega t + \\phi )$"
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]
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},
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{
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"cell_type": "code",
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" 5.999e+01])"
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]
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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"cell_type": "code",
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"metadata": {},
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" -0.28570267, -0.29527141])"
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},
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},
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"cell_type": "code",
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" 1.88401311e+02, 1.88432727e+02, 1.88464143e+02])"
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},
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"metadata": {},
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"output_type": "execute_result"
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}
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},
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"cell_type": "code",
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
@@ -129,12 +129,11 @@
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"'''create oscillation: Y = Asin(wt)| w = 2.pi.f'''\n",
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"ys = amp*np.sin(ts*(2*np.pi*freq))\n",
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"\n",
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"lb= \"amp: \"+str(amp) + \",freq:\"+str(freq) \n",
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"lb = \"amp: \" + str(amp) + \",freq:\" + str(freq) \n",
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"plt.plot(ts,ys, label = lb)\n",
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" \n",
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"plt.xlabel(\"Time in seconds\") \n",
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"plt.ylabel(\"Displacement\")\n",
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"plt.axis()\n",
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"plt.legend()\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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},
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"cell_type": "code",
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"execution_count": 15,
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"metadata": {},
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"outputs": [
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{
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"'''create a plot'''\n",
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"plt.plot(ts,ys, label= \"Superposed oscillation\")\n",
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"plt.legend()\n",
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"plt.show() "
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"plt.show()"
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]
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},
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{
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"-----------"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"fourierTransform = np.fft.fft(ys)/len(ys) # Normalize amplitude\n",
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"fourierTransform = fourierTransform[range(int(len(ys)/2))] # Exclude sampling frequency\n",
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"\n",
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"tpCount = len(ys)\n",
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"values = np.arange(int(tpCount/2))\n",
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"timePeriod = tpCount/fs\n",
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"frequencies = values/timePeriod\n",
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"\n",
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" \n",
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"\n",
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"# Frequency domain representation\n",
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"plt.title('Fourier transform depicting the frequency components')\n",
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"plt.scatter(frequencies, abs(fourierTransform))\n",
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"plt.xlabel('Frequency')\n",
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"plt.ylabel('Amplitude')\n",
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"plt.xlim(0.1,0.4)\n",
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"plt.show()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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},
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [],
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"source": [

‎2c. Arange-FourierSeries.ipynb

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@@ -340,17 +340,20 @@
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"plt.figure(figsize = [15,4])\n",
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"\n",
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"k = 1\n",
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"for n in [i for i in range(10) if i%2 !=0]:\n",
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"for n in [i for i in range(10) if i%2 != 0]:\n",
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" if n == 1:\n",
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" '''taking care of first term'''\n",
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" fi = (4/np.pi)*(1/n)*np.sin(n*np.pi*thetas/float(L))\n",
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" plt.plot(thetas,fi, label = \"first term\")\n",
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" ff = fi\n",
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" \n",
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" else:\n",
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" '''terms following first term'''\n",
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" fi = ff + (4/np.pi)*(1/n)*np.sin(n*np.pi*thetas/float(L))\n",
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" plt.plot(thetas,fi, label = \"sum of \"+str(k)+\" terms\")\n",
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" \n",
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" ff = fi\n",
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" \n",
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" k = k+1\n",
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" \n",
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"plt.legend()\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"#### Sum of all n-terms"
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"#### 3. Sum of all n-terms"
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]
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},
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{

‎3.Meshgrid.ipynb renamed to ‎3. Meshgrid.ipynb

+3-1
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"source": [
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"xs = np.arange(10)\n",
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"ys = np.arange(10)\n",
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"\n",
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"XG,YG = np.meshgrid(xs,ys)"
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]
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},
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"xs = np.arange(-3,3,1/ns)\n",
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"ys = np.arange(-3,3,1/ns)\n",
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"\n",
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"XG, YG = np.meshgrid(xs, ys, sparse=True) "
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"XG,YG = np.meshgrid(xs, ys, sparse=True) "
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]
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},
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"source": [
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"from matplotlib import cm\n",
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"from mpl_toolkits.mplot3d import Axes3D\n",
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"\n",
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"fig = plt.figure(figsize = [8,6])\n",
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"ax = fig.gca(projection='3d')\n",
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"\n",

‎3a. Meshgrid-SphericalHrmonics.ipynb

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"cell_type": "markdown",
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"source": [
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"## Meshgrid : ```mgrid```"
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"## Meshgrid : Spherical Harmonics"
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]
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"execution_count": 9,
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"ZG = RG * np.cos(thetas)\n",
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"\n",
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"'''normalization with maximum value'''\n",
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"NG = R/R.max()\n",
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"NG = RG/RG.max()\n",
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"\n",
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"'''plot figure'''\n",
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"fig = plt.figure(figsize = [8,8])\n",
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"ZG = RG * np.cos(thetas)\n",
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"'''normalization with maximum value'''\n",
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"NG = R/R.max()\n",
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"NG = RG/RG.max()\n",
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"'''plot figure'''\n",
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"fig = plt.figure(figsize = [8,8])\n",
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"ZG = RG * np.cos(thetas)\n",
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"'''normalization with maximum value'''\n",
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"NG = R/R.max()\n",
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"NG = RG/RG.max()\n",
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"'''plot figure'''\n",
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"fig = plt.figure(figsize = [8,8])\n",
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"ZG = RG * np.cos(thetas)\n",
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"'''normalization with maximum value'''\n",
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"NG = R/R.max()\n",
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"NG = RG/RG.max()\n",
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"'''plot figure'''\n",
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"fig = plt.figure(figsize = [8,8])\n",

‎5. Algebra.ipynb renamed to ‎4. Algebra.ipynb

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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"UsageError: Line magic function `%` not found.\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import seaborn as sns\n",
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"import matplotlib.pyplot as plt\n",
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"% matplotlib inline\n",
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"%matplotlib inline\n",
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"sns.set()"
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.1"
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"version": "3.7.3"
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},
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"widgets": {
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"state": {},

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