{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Day 3: Functions\n", "\n", "\n", "\n", "**Goals**: \n", "\n", "- Review Linear, Exponential, and Harmonic Functions\n", "- Understand parameters of each function type\n", "- Use Functions to approximate data" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
\n", "

A Movie About Functions

\n", "\n", "
\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML\n", "\n", "HTML('''\n", "
\n", "

A Movie About Functions

\n", "\n", "
\n", "''')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear Functions: College Debt\n", "\n", "Returning to our example of paying down college debt, we examine the relationship between time and balance for a student who faces no compound interest.\n", "\n", "- Start with 40,000 dollars debt\n", "- Pay 500 dollars a month until no debt left\n", "\n", "**QUESTIONS**:\n", "\n", "1. Make a table of values for the first five months:\n", "\n", "| Month | Balance | Amount Paid |\n", "| ----- | ------- | ----------- |\n", "| 0 | 40000 | 0 |\n", "| 1 . | . | . |\n", "| 2 . | . | . |\n", "| 3 . | . | . |\n", "| 4 | . | . |\n", "| 5 . | . | . |\n", "\n", "2. What would the balance in month 10 be?\n", "\n", "3. How much would be paid in month 20?\n", "\n", "4. Can you generalize this to a function that takes as input the number of months and returns the balance in the account?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Linear Functions: Experiment\n", "\n", "A general form of the linear function would be:\n", "\n", "$$f(x) = ax + b$$\n", "\n", "Use the interaction below to answer the following questions:\n", "\n", "1. What does the parameter $a$ control about the graph? What is the difference between the cases where:\n", " - $a < 0$\n", " - $a = 0$\n", " - $a > 0$\n", " \n", "2. What does the parameter $b$ control about the graph? What is the difference between cases where:\n", " - $b < 0$\n", " - $b = 0$\n", " - $b > 0$\n", " \n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import ipywidgets as widgets\n", "from ipywidgets import interact" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def f(x, a, b):\n", " return a*x + b" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(-10, 10, 1000)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def linear_plot(a, b):\n", " plt.figure(figsize = (15, 6))\n", " plt.plot(x, f(x, a, b))\n", " plt.grid()\n", " plt.ylim(-10, 10)\n", " plt.xlim(-10, 10)\n", " plt.axvline(color = 'black')\n", " plt.axhline(color = 'black')\n", " plt.title(f'a = {a}\\nb = {b}', loc = 'right', fontsize = 20)\n", " return plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f27518ea8c064da38c2a76ae629374ec", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=2, description='a', max=10, min=-10), IntSlider(value=3, description='b'…" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "A = interact(linear_plot, a = widgets.IntSlider(2, min = -10, max = 10), b = widgets.IntSlider(3, min = -10, max = 10));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Quadratic Growth\n", "\n", "Use the image below to answer the following questions.\n", "\n", "1. Draw the next image in the sequence.\n", "2. Complete the table of values below:\n", "\n", "| n | purple boxes | yellow boxes |\n", "| --- | -------- | ----------- |\n", "| 1. | . | . |\n", "| 2. | . | . |\n", "| 3. | . | . |\n", "| 4. | . | . |\n", "| 5. | . | . |\n", "\n", "3. Do you see a pattern to how the purple boxes are growing? Explain.\n", "\n", "4. Do you see a pattern to how the yellow boxes are growing? Explain.\n", "\n", "5. Describe a rule that would predict the number of purple squares given any value of $n$. Plot your results on the interval $1 \\leq n \\leq 100$. What shape does this graph resemble?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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9n81aMzjHgu4PtZa+ZuvYh5MynR7/OMerNaPU43doqDXDWn0wctYEzAAAAAAkJ2+lWmqtwrol1VpG5YQVyrVmWOV0S1skPLby/uzZgxkAAABYa32mfU2dntyT40wzLf3sWn5vXXRuf9Ln2vVaD/frSikXtmKsl3DjZi3bu0fGsavp+36ubWenK6NhMbYL6utsv+V66JhNUq9d7+f6laTbH3fG9S7dvDk3znMEzAAAAMBa289eV9LZuuEuTDMp+xnPrbJ940Zy/bODubYuJaMMjfUSxplkemQFc0mtJWWubZRBugyM7YJqanYzTo6M7ctfOTrWpd9wzN61SfpjV+Fbeg8AAADwgCspfXL8CsVbulgJurwyObFHUouxXVrJySu+F+nD3REwAwAAAJAu3e6dHi8p05JufF713C+6dJNyQsjcZbB3XvXcT0q6O45bSerA2J45ATMAAAAAKekmxwV2JWU6yHDnjleq41gl3e5xK2m7DMZduv3zrul+UFJql247t1l9PwuXhztJOXFlPnfHHswAAADAWusy3C4pcxnHQRgqWFrQJPsXp5leHGQwrum2a/qNJGWYYUq6aZdunJSUlN1RRldXXe866dMPa+qgpuzV1FFShyVdBhnULoP9W1tjDDO43mXw5qrrXRc1yST7j5QMUtLt1tSNmjoYZHjwgchgfCtc3siGY3YJffphP5sD3tJlcOO4/gJmAAAAYK1dzOUvd+nmwpAP5h/4/zbLlu0cFvRiff6ZF/P5P3S4raRMN3Nh7uJom9l65SPl23/mfKtbb5+pn/jHt3PzGw63DTOaDDOay+WeyNO/8u7y/t8+3+rW16ROul/Jz/+JI811KxePLrTvP1Y+/tPnVNZ94ZX64lNX89KHDrftZefl4/rbIgMAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCbDVRcAAADraJL9987fn9TfqJ98/6rqYTHj7D1V019IkppsJhns7fXZ3U3flTJJySRJfvpnb37Hz/3t7Y+ttFju6M0b083JpD6aJDUZ1JpRN6ndzk6fUjLtujJOUq++Nr30ff/Oy9+74nI5wfZ2vzGZWgQHsI4EzAAA0KCmbh1t2c/4wmqqYVE1dXMWLNetJIMk6WvqdJoyTU3XZdx12bux3V/e3i0bKy6XO9jdq8NaM6o1G7VmI0mpg9S+T0mSaV8vDLrsTCYlr73RP7LicgHgvuXTQQAA4AHz9XD5qL7PRl8zOueCaHSwcnkzmYXKRx7spn0u3PYxAODUCJgBAIAHRk1GOSZcfqvPNJvnVA53qfbZunOHdH1frUQHgDMkYAYAAB4g9cRtAmtSar1zCM09oWSBv2m9lgBwtuzBDAAADfayM111DSxvnL3aZ1oPtz33+VKHw/ldFEbdsA5K5zW+h037Orw57udey1JSX/pKP9evKyUbndcSAM6KgBkAABrUVKsi11BNrTV1Lk3e2yvZ25vfp3cjg1pSvMb3sD41By/b3Gs3PvJaDtL143ReSwA4I7bIAAAAHhgl3ThJvVOfLt3+SX1YvZKSMnut7qR2s9ccADgjAmYAAOCBUVJqSbd3/OPpBxnunmdNtCspe0npj3t8kMG43OFxAODu2SIDAAB4oHTp9mtK36ffSmqXJCWpJd1EuLxeSkq6dDdr6mZNPzrU3g8y2C2x9zIAnDUBMwAANLiYy186fH+Q0c47867nVlUPi/linv34OHvvuHW/ppZhRnWYYcqhrXsfzuOffCiPfHUlRbKQN3PtsZfz5e+8db+mpqRkM1ulpLy1xckgwzefzjN/azVVsqireeWZ/ew9tOo6AFiegBkAABoMMpzbZmEjG9tPlHe/sqp6WMxX6gu7k+xPDrcNM5wOMpy7CNylXLnm9bzH1eRr+crca1lS3vZaDjPa81re+96s197RZ7q56joAWJ49mAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaDJcdQEALG6S8fsP3381Lz/zan2lX1U9cMs0+5s1/eNJUpNRUoeTvu+2d2pKybQrZa8k9asvT678C//aS//iquuFJNkbV+fCAPeJScZ/X5dubl7/7XzqvallVSWtncnbz+dGJaVMM01JpknZS1J3s3P5M/X/dT63hN3sPFbTX6hJSbKRZDgb166WZD8p+0lyNS9956v1lW9fbbXro6bm0DE7SLKR1ME0kyRlWpK9pPRJ4phdVu1q+rmFyfsZP3pcbyfVAGukHpm3a2TL3Bv69KODk7qtpI4OmmvtU2oy6kvdGHTZKbVMd/bq1iprBQDuPzUZ3uZcWeaxhJp+4zbnc/0saMooqRslZacmkz5T53NLODg+R0m9kLd2E6i3xnYjqZOSstOnH5U4V17ULGDOILOx3cwswK+z2zqsyUZJdpPsO2ZPxei4B2yRAQCcltGhP0bm1XTTPhdSYxkRAMC96/jzuaSrqRdKnM+1qVs5PocbzoJmGnSHwuWjSp2N++Cca3rgCJgBgFNSN+/8cLppf+wfLAAArNwJ53OzkFkQurQ6yokhZ92I8L7BseHyLUV4f/YEzADAaRhksRNiqwcAAO5JtYvzubOyyJiVxPUhGiyQbVbH7Blz4AKskd1s23SZe9I0kzrOXj3ctn+91F/+5fnzvVJKRhk4jgGAU7WXnVoOLuZFm2kmOXo+l5TsZ7/Ot3QZZWSsl7CX3dpnOjeOXbqUdHNtgwzrwLnywmqScXZLnf3zLZNM6tGuG9k0rndpkvHRcX2LgBlgvfjmCfeo0ufIipe+1oz359sG6WpSHMcAwCmrxTnGXXvb+dzBZdTm2rpkGn+XLKXc5ly5ptYcGduSYmyXUjP7O2RuhXJ9+zFb+hjX03DsNxwMLgBw10pKSrrxnfukdif0AQBgNWbnc8X53BkoKfs5ssr2qC7dfkm5Yx/e7qRjNkm6DPbPo5YHmYAZADgVJWUvs1UXt1O7DHZ9dRUA4N5V0p1wPjfcFYIur6TULoOdOzzeDzLcPc+a7hcl3eQgwL+tLoNxSTc5z5oeRLbIAABORUlJl267pm7U1FFSS0lqSZl2Ge4JlwEA7m3z53P9KMmh87nBXknnfK7RwRjeqOm36sGWDiXpSwaTQbq9Vde3zroMdmv6SZ+6ebDtSC0pfZfBuBMunwsBM8AauZSHnj98/0oe+crjeeqrq6oHbnk1Lz39Ur70XUea+81sdeXQVl3DbLz6vnz45863Ori9L+S3fu+qawDgdFzMQ8916TYOt70nH/i1YTZs57Cgq/nKe17Oi995pPlt53OjbF59Jt/4f51vdevtuXz2H97N9rsPtw0ynI4yOrx3cB7NE598PO967nyrW1/TTLrfzN/75w+31dS6lQulHLk8zAfzzf/L+Va33t7I1SfeyNX3HW7by84rx/UXMAOskS7d3NfVRtnYu1IevrmqeuCW6/X1t21/cbBKY67fIIOpY5Z7RVe7474CDMCa6dJNj54rX8yVm5tlS8C8oGv11UXP5/adzy1nULv9o2PbpZuWdHMp6Cibu8Z2cZM66W5zzNYug6MXo+uN63K265tXjs6pd1oNbg9mAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoImAGQAAAACAJgJmAAAAAACaDFddAAAArKP9jD905H4+Xf/ut66qHhazl92H+/SbB3e3kjqYZpIkfUmZJNlPkpfype95uX55vKo6OVmf6bBP/9jB3WFSR0npZq9nmZZknKTfy+6jn65/919ZYakAcF8TMAMAAA+aQVIvJCmzu6UmGdbUYZJhSdlZYW0srW4lGR38uyYpSe3q11/L/RUWBwD3PVtkAAAAD5JyEEiWYx4f1mTjPAvirozyVrj8NqXOPkjwdy8AnCFvtAAAwAOjzsLIE/4OqgLmtXHia1VmW2cAAGdFwAwAADxIFtkmsCzYj9UqWeBv2uq1BIAz5Y0WAAAa7GZ71SXQYC+7tc90rm0/4xzdMWOUUboMzrEyltVnWvay+7b2/SNbLnfpMrLrCQCcGSuYAQCAB0iZntwntaSbnHkp3JWS0iepC/TzWgLAGRIwAwAAD4ySMk7S36lPl258TuVwl0q6vTs/nur1BICzJWAGAAAeGCUlXQa7OWbla0mZDDIQSK6JkrJ/3ArlWbg83C0pJ65yBgDa2YMZAAB4oJSUaZfBzZp+s2a20XJJ6bt0+126/aP7MXPvKikpGezU9MOaulFTS5ltcTLtMhgfbKMBAJwhATMAADS4kkeePXx/I5s3PlS++VOrqofFfLr+0j+5m52nDreNsjEdZDh3Rb+n8t6//VT5hufPtzqW8bv1K09+Pp/7w4fbSsp0MxfmXstRNt74aPm9P3m+1bGs5+vnPrqTm4+tug4AlmeLDAAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgiYAQAAAABoImAGAAAAAKCJgBkAAAAAgCYCZgAAAAAAmgxXXQAAAADA3Zhm8kRNNzrc9uU8+/tK7fpV1bRudrP9cE29fHC3JHVYU0qfPkmmJZkmyTjj+vn6Gx9fWaFraD/77zo0tl1Sh3361PQ1KZOk1iS5ltc+vFu337HCUtdKn74cGtfMjtkM+vQ5OF4ntx5wzC5nP+ML00yuHG6bvjWcbydgBgAAANZan/6xHMk4buT6oysqZy1NM9moqReTDJK6laQrSV/Td0lSU/ZLsjvNZPBm3vjG1Va7XiaZPFRTt5K6mWQjSWr6vp+NbS0pu2d+4dkAAAeNSURBVEkme9l5epzdx1da7Bqps/8uZhbabyUZJKk1famzLpOSspdk6pi9ewfH623ZIgMAAACAZBbUXcht86I6moWktPl6uHxEqbMxH5xzQfeRY8dveDC25ZwLeuAImAEAAABITg7jRvFt+BaD3D5cfovwvlXdzJ3zza6eMPbcPQEzAAAAACUL5UR1dHIf5tVFQvkuVjG3WGBsq3E9Yz51AgAAANbafsbTklvbrtJimsnGJPtHLopYUlP7+ZYugwz3z7O2dTfOODXTuXHs02eayVxbl0G6DIztgmpqJtlPkqMX8zwyF5QyzMi43qXJkeP1MAEzAAAAsNb6TAYlnYzjLvSZlmmmR1cw15o6t2XGIINaUqxiXkLNtB4d2z59X9LNtY1mH5IY2wXV1EzTJ6mHx7HWI9u8lJRJl8643qX69vnhLbbIAAAAAHjAzVaAl+kC/SbnUc/9pKQ7cfVsSelLyrErRLm9RY7HLp1j9owJmAEAAABIl273hMf3hXXLm4XH3d6d+gwyvOPYc3slZS93COZLSt+lG59nTQ8iATMAAAAAB2Hc4OZtArs6yGBvkIEQtFFJGd8uZC5JP8xwuyywepy3Kynp0m3fbiVzl25/mNHNIztmcAbsTwQAAACstVG2vnZ0j9WLufxysdp2Ybu5+diNXPtIktTU60kdJCmjbKakTMrBGsVBBtcv5eHPrrLWdfNGrn6kZPxYktTUUlOHXbp+mI0yG9tZALqViy9sZOuVlRa7Vmq5mpe+4+DOmzW1q6mDUTbSZTA9tOVIfSiPfWpVVa6jSfYu72XvkSPNV4/rL2AGAAAA1tpmtl7v0m0cbnt/PvJrm2XLV+MX9GJ9/pmd3HzmcFtJmW7mwuBw22a2Xv3G8i3CuiV8pn7i8e30W4fbhhlNhhnN5XKP5Z0vvLu8/7fPt7r1NamT7vX87seONNetXDy6ZLl3zC7nlfriU1fz0ofmW+uxAbMtMgAAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaCJgBgAAAACgiYAZAAAAAIAmAmYAAAAAAJoImAEAAAAAaDJcdQEAtJtkf/NGvXZ51XXAfva2FulXUzvHLPer3vG9FmrqQots9jP2HnuP28vuhUX6ee9ZD336wWk/53bevLRf9zZO+3nvV5OMFz2fG/idWk6fulD+NvHes5Q+k0UXzhbjupxJxpvL9F86YN7L7uXn6+c+uuz/B0Ayyf5CJ22LupFrT93ItadO8zmhxST7C/2RP8n+hS/md771rOuBVZhkfNHxfe+bZHJpkX5v5NVnruf1d5x1PbSbZrLQH7/TTDb8bj6YvpovfNOqa1gn+xlfXLCf87klTbK/ULh5PW+8+0auP3zW9dwvaurCfR2zZ2vpgLnPdGMnNx87i2IAAAAAAFgf9mAGAAAAAKCJgBkAAAAAgCYu8gewRqaZ3Fh1DXA700z6PtPdw20lpU4yKYfbupSdkuI45r5gTl5PfaY7faZzFxObZlJrUuZ71ps1A6/xPWyayWSR956Ssuu95/43zeRmTTdedR3rrM+0Lng+53dqSdNMHu4z3Zhv6/qkTOZ71m3vPYurqTl6zNYkk8wPa0lql8643qVppnvHPVZqPX5D7GEZ/dub2XKVRYAztJvta9M6/fOrrgMAAABgWXcMmAEAAAAA4Dj2YAYAAAAAoImAGQAAAACAJgJmAAAAAACaCJgBAAAAAGgiYAYAAAAAoMn/D24osmxmjbqtAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n0 = np.array([[0]])\n", "n1 = np.array([[0, 0], [0, 1]])\n", "n2 = np.array([[0, 0, 0], [0, 0, 0], [0, 1, 1]])\n", "n3 = np.array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 1, 1, 1]])\n", "fig, ax = plt.subplots(nrows = 1, ncols = 4, figsize = (20, 6))\n", "for index, array in enumerate([n0, n1, n2, n3]):\n", " ax[index].pcolor(array, edgecolors = 'black', linewidth = 10, alpha = 0.4)\n", " ax[index].set_title(f'$n$ = {index + 1}', fontsize = 20, loc = 'left')\n", " ax[index].axis('off')\n", "plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Experiment: Quadratic\n", "\n", "In general, a quadratic function can be written in three canonical forms: \n", "\n", "- **Standard Form**:\n", "\n", "$$y = ax^2 + bx + c$$\n", "\n", "- **Factored Form**:\n", "\n", "$$y = a(x - b)(x - c)$$\n", "\n", "- **Vertex Form**:\n", "\n", "$$y = a(x - b)^2 + c$$\n", "\n", "Your goal is to describe the effect of each of the parameters $a, b, \\text{and} c$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def f(x, a, b, c):\n", " st = 'Standard'\n", " return a*x**2 + b*x + c\n", "\n", "def f2(x, a, b, c):\n", " st = 'Factored'\n", " return a*(x - b)*(x - c)\n", "\n", "def f3(x, a, b, c):\n", " st = 'Vertex'\n", " return a*(x - b)**2 + c\n", "\n", "\n", "def quad_plotter(a, b, c):\n", " st = [f'${a}x^2 + {b}x + {c}$', f'${a}(x - {b})(x - {c})$', f'${a}(x - {b})^2 + {c}$']\n", " fig, ax = plt.subplots(nrows = 1, ncols = 3, figsize = (20, 8))\n", " for i, func in enumerate([f, f2, f3]):\n", " ax[i].plot(x, func(x, a, b, c))\n", " ax[i].set_ylim(-4,4)\n", " ax[i].grid(True)\n", " ax[i].axvline(color = 'black')\n", " ax[i].axhline(color = 'black')\n", " ax[i].set_title(f'{st[i]}', fontsize = 20, loc = 'right')\n", " return plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "53d34697977e4037acf3a951d690f76d", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=1, description='a', max=5, min=-5), IntSlider(value=1, description='b', …" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = np.linspace(-10, 10, 1000)\n", "interact(quad_plotter, a = widgets.IntSlider(1, min = -5, max = 5), b = widgets.IntSlider(1, min = -5, max = 5), c = widgets.IntSlider(1, min = -5, max = 5))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exponential Functions\n", "\n", "1. Suppose we know that a population of fish produces 1 new baby for every 10 existing fish each year. Use this and a starting population of 500 fish to complete the table below.\n", "\n", "| Year | Population | Population Change | \n", "| ----- | --------- | -------------- |\n", "| 0 . | 500 . | na |\n", "| 1 | . | . |\n", "| 2 | . | . | \n", "| 3 . | . | . |\n", "| 4 . | . | . |\n", "| 5 . | . | . |\n", "\n", "2. What will the population be in year 10? Explain.\n", "\n", "3. When will the population reach 10,000? Explain." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Experiment: Exponential Function\n", "\n", "Typically, we will represent an exponential function as:\n", "\n", "$$y = ab^{cx}$$\n", "\n", "As before, your goal is to describe the effects of varying the different parameters." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "def f(x, a, b, c):\n", " return a*b**(c*x)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def exp_plotter(a, b, c):\n", " plt.figure(figsize = (15, 5))\n", " plt.plot(x, f(x, a, b, c))\n", " plt.ylim(0, 20)\n", " plt.grid()\n", " plt.title('$f(x) = ab^{cx}$', loc = 'right', fontsize = 20)\n", " return plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "1eb1ae110623463d9410756f0f5be3de", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='a', max=15.0, min=-5.0), FloatSlider(value=1.0, desc…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "interact(exp_plotter, a = widgets.FloatSlider(1, min = -5, max = 15), \n", " b = widgets.FloatSlider(1, min = 0.1, max = 5), \n", " c = widgets.FloatSlider(1, min = -1, max = 1))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Harmonic Functions\n", "\n", "The image below is the largest Ferris Wheel in the world, located in Las Vegas. This wheel has a height of 550 feet and a diameter of 520 feet, and takes 30 minutes to complete 1 full rotation. Use this information to complete the table below. \n", "\n", "
\n", " \n", "
\n", " \n", " \n", "\n", "| time (in minutes) | height above ground |\n", "| ---- | ------ |\n", "| 0 . | . 0 . |\n", "| 7.5 | |\n", "| 15 . | . |\n", "| 22.5 . | . |\n", "| 30 . | . |\n", "\n", "\n", "1. What height will the rider be at time 45 minutes? 90?\n", "\n", "2. Draw a graph of the riders height ($y$-axis) against time ($x$-axis).\n", "\n", "3. Why do we call these \"harmonic\" functions?\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Experiment: Sine and Cosine Functions\n", "\n", "We have two basic trigonometric functions, the $\\sin$ and $\\cos$. Typically, we can express these as:\n", "\n", "$$A\\sin(Bx + c) + D \\quad \\text{or} \\quad A\\cos(Bx + c) + D$$\n", "\n", "You know the drill by now; what does each of the parameters control?" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "x = np.linspace(-4*np.pi,4*np.pi, 1000)\n", "def sin_plot(x, a, b, c, d):\n", " return a*np.sin(b*x + c) + d\n", "\n", "def cos_plot(x, a, b, c, d):\n", " return a*np.cos(b*x + c) + d\n", "\n", "def trig_plot(a, b, c, d):\n", " title = [f'$f(x) = {a}\\sin({b}x + {c}) + {d}$', f'$g(x) = {a}\\cos({b}x + {c}) + {d}$']\n", " fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (16, 6))\n", " for i, axs in enumerate([sin_plot, cos_plot]):\n", " ax[i].plot(x, axs(x, a, b, c, d))\n", " ax[i].grid(True)\n", " ax[i].set_ylim(-10, 10)\n", " ax[i].set_title(title[i], fontsize = 18, loc = 'right')" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "97eb929aba4e435a858eb85b1fc17a88", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(FloatSlider(value=1.0, description='a', max=10.0, min=-10.0, step=0.25), FloatSlider(val…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "interact(trig_plot, a = widgets.FloatSlider(1, min = -10, max = 10, step = 0.25),\n", " b = widgets.FloatSlider(1, min = -10, max = 10, step = 0.25),\n", " c = widgets.FloatSlider(1, min = -10, max = 10, step = 0.25),\n", " d = widgets.FloatSlider(1, min = -10, max = 10, step = 0.25))" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weather in Central Park\n", "\n", "The data below is from temperature readings in Central Park. These range from 1870 to present, and we have the first few rows of the data as well as plots for the first and last five years of the dataset. Use the plots to answer the following questions:\n", "\n", "1. What kind of function would be appropriate for a model of temperatures in central park?\n", "\n", "2. Use what you've learned from the experiments above to determine what you think are reasonable parameters for a model of temperatures. We will imagine that each year the temperature cycles are consistent, and where $x$ is the index of the date sequence for the year, i.e. $f(\\text{day of year}) = \\text{max temperature}$ \n", "\n", "3. What does your model approximate the temperature on the 200th day of the year to be?\n", "\n", "4. The real temperature on the 200th day of the year in 2019 was 91 degrees. How close was your approximation?" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "df = pd.read_csv('data/2017018.csv')" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "temps = df.loc[:, ['NAME', 'DATE', 'TMAX', 'PRCP']]\n", "temps['DATE'] = pd.to_datetime(temps.DATE)\n", "temps.set_index('DATE', inplace = True)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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NAMETMAXPRCP
DATE
1870-01-01NY CITY CENTRAL PARK, NY US430.08
1870-01-02NY CITY CENTRAL PARK, NY US541.18
1870-01-03NY CITY CENTRAL PARK, NY US410.00
1870-01-04NY CITY CENTRAL PARK, NY US350.00
1870-01-05NY CITY CENTRAL PARK, NY US340.00
\n", "
" ], "text/plain": [ " NAME TMAX PRCP\n", "DATE \n", "1870-01-01 NY CITY CENTRAL PARK, NY US 43 0.08\n", "1870-01-02 NY CITY CENTRAL PARK, NY US 54 1.18\n", "1870-01-03 NY CITY CENTRAL PARK, NY US 41 0.00\n", "1870-01-04 NY CITY CENTRAL PARK, NY US 35 0.00\n", "1870-01-05 NY CITY CENTRAL PARK, NY US 34 0.00" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "temps.head()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(nrows = 1, ncols = 2, figsize = (16, 5))\n", "temps['TMAX'][:365*5].plot(ax = ax[0])\n", "ax[0].grid(True)\n", "temps['TMAX'][-365*5:].plot(ax = ax[1])\n", "plt.grid()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }