mgiugliano/functions_of_one_variable.ipynb

## functions_of_one_variable.ipynb
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    "kernelspec": {
      "name": "python3",
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    "language_info": {
      "name": "python"
    },
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            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 720x720 with 1 Axes>",
                  "image/png": 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xIlgCAICMvPbaa0l78t54443N1zlWVlbmsyxJ0g477CBJDU4s/s0330hyI68TmT9/vr788sus6njxxRf1t7/9TZJ022236dFHH1Xr1q01depUXX/99Y3uP2/ePEnS9ttvn1Ud+UKwBAAAGfn66699p3hjIpGIrrvuOkku4OVzRHjM/vvvL0mbB98kEhuR/cEHHyR8/uKLL86qBu98lWPHjtUpp5yiyspKXXvttZJcT2lsWqRkYs8PHz48q1ryhWAJAAAy0rlzZ5199tm6++67Nw8s+eabbzR27NjNA2KuueaagtR2wAEHSHIj0uvq6hJuc9hhh0lyNU6aNGlzD+u8efN00kkn6dFHH1XXrl0zOr61Vj/96U+1ZMkSDRo0yDdf5UUXXaSDDz5YmzZt0tixY7VmzZqEbdTV1WnmzJmSCJYAAKCZO+ecc1RZWakzzjhD5eXlqqioUP/+/fXoo49Kki677DKNHj26ILUddNBB6tGjh6qqqvTKK68k3Oaaa65Rr169tHbtWh177LFq3769unTpoq222koPP/ywrr32Wg0ZMiSj499000164YUX1KpVK40fP37zNZ+Su+XjAw88oB49emjevHk6++yzE7YxZcoUVVVVqWfPnhoxYkRGdeQbwRIAAGSkTZs2mjJliq677jptt9122rBhgzp37qyDDjpIzz77rK6++uqC1habvP0///lPwm0GDBigGTNm6PTTT988Qrtdu3Y64ogjNHny5JSnBAp6//33N+/7hz/8IeF8lb1799Z9990nY4zGjx+f8JKCWN2nnXZakxi4I0kmm+HzaFxlZaXN98SwAJq32KhV3r/T99lnnzWZQRDI3ty5c7XtttuqrKxMixYtUocOHQpdUsqqqqq0xRZbqLq6WnPmzNFWW22VUTvp/s4bY2ZaazMebUWPJQAAaJa22mornX766Vq7dq1uu+22QpeTlltvvVVr167Vz3/+84xDZSHQY5lj9FgCCBs9lpmjx7LlWbJkiX7wgx+offv2mjdvXpPotVy3bp0GDRqk9evX68svv1SvXr0ybivfPZbceQcAADRbvXr10oMPPqhZs2Zp/vz52nHHHQtdUqPmz5+vc889V7vuumtWobIQCJYAAKBZO/roo3X00UcXuoyU7bTTTtppp50KXUZGuMYSAAAAoSBYAgAAIBQESwAAAISCYAkAAIBQECwBAAAQCoIlAKBFYf5PtBSF+F0nWAIAWozS0lLV1dUVugwgL+rq6lRaWprXYxIsAQAtRllZmdatW1foMoC8WLduncrKyvJ6TIIlAKDFKC8v14oVK+i1RLNXV1enFStWqLy8PK/H5c47AIAWo1OnTqqpqdGCBQtUUVGhjh07qrS0dPP914GmzFqruro6rVu3TitWrFCHDh3UqVOnvNZAsAQAtBjGGPXs2VNr167VmjVrtHTpUnov0ayUlpaqrKxM3bt3V6dOnfL+oYlgCQBoUYwxKi8vz/spQqAl4BpLAAAAhIJgCQAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAIAACAUBEsAAACEgmAJAACAUBAsAQAAEAqCJQAAAEJBsAQAAEAoCJYAAAAIBcESAAAAoSBYAgAAIBQESwAAAISCYAkAAIBQECwBAAAQCoIlAAAAQkGwBAAAQCgIlgAAAAgFwRIAAAChIFgCAAAgFARLAAAAhIJgCQAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAJAU7JxozpK6ihJ69cXuBgA8CNYAkBTceONUrduWitprSSVl0vnn1/gogAgjmAJAE3BihXSJZdI69bF19XWSrfeKr3/fuHqAgAPgiUANAXvv++CZCLTp+e3FgBIgmAJAE1BQ72S9FgCKBIESwBoCmbN2vzlMklve58jWAIoEgRLAGgKPOHx/ehjs48+kjZtyndFAFAPwRIAil11tTR79ubFWdHHZuvXS59/nu+qAKAegiUAFLuPP5Yikc2L9XosJU6HAygKBEsAKHaB0Pi+pI8lqbQ0vnKWrw8TAAqCYAkAxc4bGtu31xxJ6yVp8OD4enosARQBgiUAFDtvaBwyRJtPiu+6a3z9rFmStfmsCgDqIVgCQDGrq5M+/DC+vMsuib9esUL65pv81QUACRAsAaCYzZkj1dTEl729lN6vJU6HAyg4giUAFLPgoJxkPZaJtgWAPCNYAkAx8/ZClpRIP/xhfLmiQurfP/G2AFAABEsAKGbesLjddlJZmf95b68lPZYACoxgCQDF7LPP4l8HT30H1y1YIFVV5b4mAEiCYAkAxaquTlq0KL48aFD9bYLrvvsutzUBQAMIlgBQrJYu9d3KUX361N8muI5gCaCACJYAUKy+/da/TLAEUOQIlgBQrIIhMZVgGQyjAJBHBEsAKFapBMuuXaV27ZLvAwB5RLAEgGLlDYnGSL1719/GGH/gJFgCKCCCJQAUK+9p7Z49pdatE29HsARQJAiWAFCsvCEx0WnwRM9xjSWAAiJYAkCxSjVY9u3r38fa3NUEAA0gWAJAsfIGS294DPKGzvXrpVWrclcTADSAYAkAxWjDBmnZsvhyqqfCJa6zBFAwBEsAKEbeWzlKBEsATQLBEgCKUSpzWMYET5MzgAdAgRAsAaAYpRMst9ii4X0BIE8IlgBQjIK9jg0N3unYUSovjy8TLAEUCMESAIqRNxy2aiV1797w9kySDqAIECwBoBh5w+EWW0gljbxde3s0ucYSQIEQLAGgGKU6OXqibeixBFAgBEsAKEbeXseGrq+M8QbLRYukSCT8mgCgEQRLAChG6fZYesNnXZ30/ffh1wQAjSBYAkCxWbvWPWLSPRUucTocQEEQLAGg2KQzh2WybRjAA6AAmk2wNMbsYIyZYoypNsZ8Z4z5ozGmtJF9rjTG2CSPSzzb3Zdkm8G5f2UAWpwwgiU9lgAKoFWhCwiDMaarpJclfSrpKElbS7pRLjhf1sCu90h6IbDuaEnjJD0fWD9b0mmBdfMzqxgAGhAMhakM3uHuOwCKQLMIlpLOktRe0jHW2jWSXjLGlEu60hjzl+i6eqy1CyUt9K4zxlwuaba1dlZg8ypr7Ts5qB0A/DLpsWzTRurRIz5oh2AJoACay6nwH0maHAiQj8iFzeGpNmKM6SbpYEkPh1seAKTBe31k+/ZS586p7ecNoFxjCaAAmkuwHCx3qnoza+3Xkqqjz6XqWEmtlThY7mCMWWOM2WCMmWaMSTmwAkBaglMNGZPafkySDqDAmkuw7CppVYL1K6PPpWqMpPestV8E1r8v6TeSjpT0Y0mlcqfbh2ZQKwA0zDsHZe/eqe/n3ZZ5LAEUQHO5xjJrxpgt5E6bjws+Z629ObDtc5I+kXSp3GCfYFtnSDpDkvr375+LcgE0Z8uWxb/u1i31/bzbLlsmWZt6bycAhKC59FiulJToIqSu0edScYIkI2lCYxtaa6slPSdptyTP32WtrbTWVvbo0SPFwwNAlDdYdu+e+n7ebTdskKqqwqsJAFLQXILlbAWupTTG9JNUpsC1lw0YI2matfabFLe30QcAhMfacIKl5G8HAPKguQTL5yUdaozp5Fl3oqQaSa81trMxZqCkYUpxNLgxpr2kwyXNTLdQAGjQmjXSpk3xZYIlgCakuQTLOyRtkDTJGDMieo3jlZL+5p2CyBjzpTHm3gT7j5G0SdJjwSeMMZ2NMW8YY840xhxkjDlR0lRJfSRdl4PXAqAlC4ZBgiWAJqRZDN6x1q40xhwk6VZJT8uNEL9JLlx6tZIb0R00RtIUa22id+ENkr6Xu4NPT0nrJb0tabi1dkYoLwAAYgiWAJqwZhEsJcla+6mk/2tkm4FJ1u/SwD7rJR2TVXEAkCqCJYAmrLmcCgeA5mH5cv9yOsGySxepxPO2HmwLAHKMYAkAxSSbHsvSUqmiInlbAJBjBEsAKCbeMFhamvp9wmO8QZRgCSDPCJYAUEyCd90pSfNtmmAJoIAIlgBQTDKdHD3RPgRLAHlGsASAYkKwBNCEESwBoJiEHSwtd54FkD8ESwAoJmEGy02b3C0iASBPCJYAUCwiEf/ck9kGS4nT4QDyimAJAMVi1SoXLmMIlgCaGIIlABSLbCZHT7YPwRJAHhEsAaBYECwBNHEESwAoFgRLAE0cwRIAikUYwbK8XGrVKnmbAJBDBEsAKBZhBEtjmCQdQMEQLAGgWHhDYJs2UseOmbVDsARQIARLACgWwcnRjcmsHYIlgAIhWAJAsfCGwG7dMm/Huy/BEkAeESwBoFhkezvHRPsSLAHkEcESAIpFLoLlihVSXV3mbQFAGgiWAFAschEsIxF3q0gAyAOCJQAUg02bpJUr48thBUuJ0+EA8oZgCQDFYMUK/zLBEkATRLAEgGKwfLl/OcxgGWwbAHKEYAkAxSCMu+4k25ceSwB5QrAEgGJAsATQDBAsAaAYhBksO3SQ2rZN3jYA5AjBEgCKQTD8ZXPnHWP8wfT77zNvCwDSQLAEgGLgHWDTrp3rdcyGN5gGR5wDQI4QLAGgGHjDX0VF9u152yBYAsgTgiUAFAOCJYBmgGAJAMXAeyo8m+srE7XBPJYA8oRgCQDFINc9ltZm3yYANIJgCQDFIJfBsrZWqqrKvk0AaATBEgAKzdrcBkuJ6ywB5AXBEgAKrbpa2rgxvkywBNBEESwBoNCCg2vCHryT6BgAkAMESwAotGBvIj2WAJoogiUAFBrBEkAzQbAEgEIjWAJoJgiWAFBouQiW7du7e44nOwYA5ADBEgAKLReDd4LtMHgHQB4QLAGg0Ly9iW3but7GMHC/cAB5RrAEgEILTo5uTDjtEiwB5BnBEgAKLey77iRqi2AJIA8IlgBQaARLAM0EwRIACs07sCasgTvBtpYvd/ckB4AcIlgCQKHlo8dy40Z3T3IAyCGCJQAUkrX5CZYSp8MB5BzBEgAKqaZG2rAhvkywBNCEESwBoJCCYS9X11gmOhYAhIxgCQCFFLwjTi57LLn7DoAcI1gCQCHl4j7hydqixxJAjhEsAaCQCJYAmhGCJQAUUi6DZfv27t7jyY4FACEjWAJAIeVy8I4x/vYIlgByjGAJAIXkHVDTpo1UVhZu+94eUAbvAMgxgiUAFFJwcnRjwm2f+4UDyCOCJQAUUq7uupOoTYIlgBwjWAJAIREsATQjBEsAKCRv2Atz4E6iNgmWAHKMYAkAheQdUJPrHsv166Xq6vCPAQBRBEsAKKR8ngoPHg8AQkawBIBCqalxvYgxBEsATRzBEgAKJZd33UnWJsESQA4RLAGgUIITlud68E6iYwJAiAiWAFAo9FgCaGYIlgBQKMHew3wES3osAeQQwRIACiUfp8LLyqS2bZMfEwBCRLAEgELJR7A0xt8uwRJADhEsAaBQvCGvbVvXu5gLBEsAeUKwBIBC8Ya8bt1c72IuECwB5AnBEgAKJRgsc4VgCSBPCJYAUCgESwDNDMESAArFG/K6d8/dcbxtr1ghRSK5OxaAFo1gCQCFUogey7o6afXq3B0LQItGsASAQohE/HfByVewlDgdDiBnCJYAUAirV/tPSRMsATQDBEsAKIRly/zLBEsAzQDBEgAKIR933UnWNsESQI4QLAGgEAiWAJohgiUAFEI+g2WXLv67+hAsAeQIwRIACiGfwbK0VOraNfmxASAkBEsAKARvuDPG9SrmEnffAZAHBEsAKARvuOva1fUq5hLBEkAeECwBoBDydTvHRMcITnUEACEhWAJAIeTrdo6JjkGPJYAcIVgCQCEQLAE0QwRLACiEQgbLmhr3AICQESwBoBAKGSyDxweAkBAsASDfqqv9PYYESwDNBMESAPItn5OjJzsGwRJADhAsASDfCJYAmimCJQDkG8ESQDNFsASAfCuGYMkk6QBygGAJAPlWiGDZrp1UVpa8BgAIAcESAPKtEMFS8t/WkWAJIAcIlgCQb95Q16GD603MB+6+AyDHCJYAkG/5nhw90bEIlgBygGAJAPlGsATQTBEsASDfCJYAmimCJQDkWzEEy1WrpLq6/B0bQItAsASAfPPOIVmoYGmttHJl/o4NoEUgWAJAPm3a5HoLYwoVLCUmSQcQOoIlgJbNWumaa6TevaUTT75t+CwAACAASURBVMx92Ar2EhYyWOb6OsuaGun889339swzXagG0KwRLAG0bLfdJl1+ubRkifToo1JlpTRrVu6Ot3Spf7lHj9wdKyh4rGAtYfr6a2m//aRbb3Xf27vukn7zm9wdD0BRIFgCaLleeUW64AL/ugULpL33lp54IjfHXLLEv9y7d26Ok0jwWMFawjJ9ugvoM2f6199yi3TPPbk5JoCiQLAE0DJ99ZV0/PGJR0bX1EgnnywtXhz+cYNhrlev8I+RTM+eDdcShtpa9339/vvEz59zjjRtWvjHBVAUCJYAWqZTT5VWrIgvH3ecNGJEfLm6WnrssfCPW8hg2aaN1LVr8lrCMGWK9M038eUhQ6Rzz40v19ZKY8dKGzeGf2wABUewBNDyfPyxv9ds992lBx6QnntO6t49vv6RR8I/tjfMlZZKFRXhH6Mh3iCbi2Dp/Z6VlEiTJ7tT4KNHx9cvXOi+1wCaHYIlgJbnwQf9y3feKbVvL7Vu7U7jxrz1lrvmMkze0+s9e7rwlU+5DJbr1/uvTf2//3PXdZaUuME7rVvHn3vggXCPDaAoECwBtCx1ddJDD8WXd9xR2m23+PKYMf7tH3003ON7w1w+T4MnOmbYwfKFF6Q1a+LL3u9l9+7S4YfHl595httKAs0QwRJAy/LKK9J338WXTzlFMia+vO++Up8+8eWHHw73+MUULMMenOT9XrVu7T/9LbnvdUxtrTRhQrjHB1BwBEsALYv3FKwx0o9/7H++pMRNlB7z/vvS55+Hd/xiCpbr1rlBSmFYt056+un48qGH1r9+dORI/zpOhwPNDsESQP6tXu0C28yZ0owZuZ2o22vdOmnSpPjyiBFS3771twueDg+rZ81a/2stdLCUwjsd/vTTbpqmmOD3UJLatvWvnz5dmjMnnOM3ZtUq9/s2c6b73Us2HRKArBAsAeTXiy9K/fq56xorK6U99nDhLh+9V5Mm+XvovKdmvfbYQxo0KL4cVrBcudKdAo5pTsHS+z1q104aNSrxdsHveXAgVS68+qrUv7/7fausdL97ffpI996b+2MDLQzBEkD+vPmmdPTR0tq1/vWbNkk/+5mbmiaXvNcAduhQ/xrAGGOkE06IL3/6aTg9XIW8606yY4YRLCMR6fXX48sjR0qdOiXeduhQaZtt4svjx7ue3Fz56CPpqKMS/8794he5mVIKaMEIlgDyY9YsNyrYe7rUq67OTVL+3nu5OX5VlTR1anz5qKNcuExm+HD/8vTp2ddQyMnRkx0zjGD5xReuNzYm+L3zCl7XOnduuNewei1c6EKud6S6l7XST34iPftsbo4PtEAES6ClWL1a+te/pLPPdqcfN2zI37EXLXKDOVavjq875BDpv//19wyuW+fC57ffhl/DK6/4X/MRRzS8/dCh/uV33sm+hmIIlrm4rWPwezNsWMPbB7/3uZgsvbra/S4tXBhft88+7nfu1FPj6zZtyu0HmkTq6tw1qeecI918c25uHQoUCMESaO4++8xN+t2rl3T66dIdd7jr3Pr3l664wg1qyLXf/94/aGXffd1E2qNGuZB74IHx5xYvlq66KvwavOGlpMQF3YZ06+Y/ZdtcgmW7dlLnzvHlsINlmzbSzjs3vP2uu/pfey56DG+7Tfrww/jy4MHSU0+537l77nG3lYxZv1765S9ze0pech9sbrrJ/V6NGiX985/SBRe4a4wPPZR7qKNZIFgCuWKtu3PLAw9Ijz8uPf+867nLpxkzXO/R44/X76FculS6+mr3fC4nqp41S7rvvvjy4MGut6aszC23aeMG1QweHN/mvvv895vOlrX+8LLXXqndStHb8/buu66nKRvenqmSEhdeCyHsSdK9lwnstpsb/d2QkhLpRz+KL7/xRvLT1ZmoqZFuvDG+3K2b+/8X+5mXlkr33y8ddFB8mzff9M8YELYNG9xrvvBCad48/3ORiBvUduCBrkc1n1audMeeNMndOOCll1wvLpAhgiWap0WL3JQiYc3Rl65XX3XhZZ99pJ/+1PUYjhwpbbml9Otfu1O+ufbee9LBBzf+B/vzz931huvXh1+DtdJFF/l7gm6+WerSxb9dly7StdfGl2trpRtuCK+OTz7xB9WRI1Pbzxss166VZs/Org5viOvRwwWcQggzWFZV+XsGGzsNHuO9C09trTRlSnZ1eN17r/91/fa30sCB/m1at5Zuv11q1Sq+btw4aePG8OqIiUSk007zX+ObyKZN7r3imWfCryGotla6/vp4b+mxx7rrTQ85xN2NauLE3PfgJqvrww+l+fMLc3xkz1rLI4eP3Xff3TZ7kYi1H3xg7SuvWDt9urUff2xtTU3+63jmGWuPOsraPn2sdW9J1rZta+2hh1p7yy3WrlmT+xpWrLD2yCPjx0/26NfP2mefzV0dH35obUWF/5iVldZOmGDtd99Z+7e/Wdu7t//544+3tq4u3Dqee85/jEMPTb5tXZ21O+wQ37ZdO2sXLw6njuuv99cxa1Zq+82c6d/vnnuyq+Pww+NtDRmScTOSrHv7ztBxx8Xr2HbbzNux1trXXvN/jx55JLX9Vq2ytlWr+H6nn55dHTEbNli75Zbxdrt0sXb16uTbn3eev/6//z2cOrwuucR/jI4drb38cmsXLLD2+eetPeww//Nt2rj1ufLuu9b+8IeNv0/tuae1c+fmro6YDRusve8+a485xtpOneLHr6iw9pBD3HNhvzc1prbW2s8+c9+rV191/9bW5reGApE0w2aRe9LfQfpS0jhJPbM5cNgPSTtImiKpWtJ3kv4oqTSF/TpL+reklZJWS/qPpG4JtjtK0keS1kv6VNKJqdSVk2C5ZIm148dbe9VV1v7kJ9YefbS1l11m7dNPW/v99+EfL5kvvnDH3Wqr+m9InTpZ+6tfWfvll7mv4+uv3fegsTfJgQOtffPN3NWxdKm1O+/ceB3ex333hV/HmjXWbr21/zh7710/WH/8sbWdO/u3u/zy8OrYtMnaHXeMt11S4gJvQx56yF/P734XTi3Dh8fb7NPHfRhKxcaNLuDG9v35z7Oro7Iy3tbBB2fcTNbB8txz43V07px5O9Za+5e/+H9m8+alvu8BB8T322KL1H8uDbnnHn89f/hDw9svXWpteXl8+4oK9wExLA884K+ntNTayZP929TWWnviif7tOnd2wTNsU6e6D9ypvkf17Wvt7Nnh1xEze7a1u+3WeB17723tRx/lro6YRYvc70yvXvVr6NXL/V2bOTP3dcSsXm3tSy9Ze8017gPhmDHW/v731v773+n9X0tDIYJlRFKdpA2SHpU0IpsCwnhI6hoNky9LOljSWZKqJF2Twr6TJc2TdKyk0ZLmSHojsM2+kjZJukXSgZJuiH4fDmms/VCD5ccfu0/1Db0plJRYe8op1n71VXjHDaqutva3v3XHauzNwBhrTzop3DdqrwcfdJ/+U32TLClxbxphf/L89ltrt9++/vHGjLF2xgzXo/vQQ/7e1Ngfmf/+N9xafvYz/zGGDk3eYzNlirWtW/vr+eCDcOp4+GF/Han0SNXW+kNxx47WLl+eXR0rV7rXlWk43Hff+L477ZRdLf36xds6+eSMm8k6WP7xj/6fTTZnGI45Jt5Or17phcNgKH3vvczrsNZ9mMnk9yfYo33VVdnVEbNkibVdu/rbvvfexNtu3Gjtscf6tx0+3L2msMyY4e8RlFyovuUWa99/333wO+88/3uCZG3Pno1/KExXJGLt3XdbW1aW+vt3q1bWXnttOB9AgmpqrL3wwvqvPdnjxz+2dtmy8OuIWbrU1eP9YJvo79kxx4TeYVKIYHm1pG+iwSoWMr+U9LtC9WJKuiTa41juWfe7aO9leQP77RV9g97fs25odN0Iz7rJkl4J7PucpGmN1RZKsFy2zPVMpvqfL/Yf8Kyzwg90r79u7TbbpFeLZG3//tZOmxZeHZGItX/6U/3jGGPtqFHuzefee90f7+ApYcm9gW/cGE4tS5ZY+4Mf+Nvv2dPad96pv+3q1daedpp/27Zt3amWMEyc6G97iy0a78UO9vAMG5b9aae6OhfCvK/x229T2zdYz003ZVfLo4/623viifT2v+gi/+9XQ6dVGxKJuFOcsbZ+85vM2rE2+2B5553+70mmPWORiPsdi7Vz1FHp7f/xx/46rrkmszpinn3W316qPd41Na5nLrZf167hXDpz8sn+esaNa3j7DRvq995df332dVjrega7d/e3fcghif9ffvGFtYMH+7etqHA/rzBEIv7/V7FHWZm1o0db+89/Wnvjje6DeaKOlDPOCLdzYPZsa3fZJf2/az17WvvYY+HVYa2169dbe8UV1nbokF4tBx8cWg9m3oOlO6ZKJB0h6WlJtYFezAn57sWU9LqkRwLr+kfffI9sYL8/SlqcYP1cSTdGv24raaOkswLbnBJ9zZ0bqi3rYDlxYuIu+dijd29rBw1K/ny/fuGElkjE2uuuS9xLuc021l55pbUvv+yuc7zttsTX75SWWvvnP2f/abOuztrzz6/f/i67uGs8g1assPaEE+pvP3q0eyPPxrp11u6xh7/dxk4d1dVZ+9Of+vcpL7f288+zq+Xbb+uH6BdfbHy/SMT9gfHud8cd2dUyaZK/vfPOS33fDRvcG3Zs3x13zO535pRT4m21bp1+YHj8cf9rmTIlszpWrvS385e/ZNaOtdkHyyef9Nfy7ruZtfP11/52/vSn9PaPRKwdMCC+/7BhmdURM3q0//0m1Q8z1lp7883+1/LnP2dXy8sv+9vbbjsXGhrz2WfWtm/v/53Ntid32TJ3KZC3ngMOaLinesmS+pf29O+f3vc0kUjE9cQF34/32y/xB5w5c6wdMaL+9kcd5c6eZWv8+MQhbsAAF+qfftr9LG+80drdd0/8d/ass1L72Tbm44/dtdfJ/p737ev+phuT+PkOHay99dasOwYKEix9DUh9JF0ePZ1ckF5MSUslXZlgfZWk3zaw36OSXk2w/llJz0a/3iH6Jn5AYJs9ouv3aKi2jIPlkiVuMEWiX54993SDMNaujW+/bJkLoYl+8Y2x9uKLMw9Rq1cnvoaxRw9XR6I/+pGIu44o+GYmWXvqqZnXsn594pB44YUNf4KNRKz917/8PUaSe12Z1lJbW3+gzoABqV2GUFvrela9++64owuqmairqx8OL7gg9f2/+MLfM9ClS+YDZyIRf69L69bp94j99rf+1/L225nVsmmTtd26xdsZMSL9NhYu9Ndy7bWZ1TJ7tr+dBx7IrB1rsw+W77zjr+WppzJr57HH/O1MnZp+G97rPY3J/Pdu0SL/YKB0e0+rqvwfaHr0cOsyUVNT/8zOK6+kvv9tt/n33X77zGvZtMkNmvO2t9tuqfW8L19e/4PzLrtk3psbibj3peD791VXNXzKPxJxp+uDgWrvvTO/VCYScZdFBWvp2tXa//wn+d+TV1+tf4Yq9nf5m28yr+WWWxKf9t56a/e3yxvoa2rc39fgoK/YY//93Xt6hrUUPFhubkgykg6VNDHac5m3Xsxor+kFCdYvlHRdA/u9JOnJBOsfkvRW9Ot9om/iuwS2+UF0fYPXWW4v2QOjfwRSfYyV7PcJflm+SLGtoyQ7L8H+MyS7XZq17C7ZOQnaGi/Zbins31myExLsP1WyXdOspVyyryRo69dptDFSsusD+z8p2dZp1iLJ3h5oZ5lkt01j/3aSfTPQxn8yqEOSPT/QzkeSbZtmG78PtHF/hrUcFmjnrgza2DbQxt0Z1rJPoJ3zMmznG08b/82wjf0CtRycYTthPAYEajk9w3Zu8LSxSbIdMmjjkEAtp2VYy28D7RyeQRsXBdr4ZYa1XBZo574M2ngm0MYtGdZyZaCduZLtkcb+3ST7eaCN55XZe+bfA+1YyZ6dxv7HSLYmsP/Hkt0yzTraSvahBLW8lmJb7SX71wT7L5X7G5NOLb0k+1yCtpZL9heSbdXI/kMkOz3B/lVyfxtL06hliGRfdl8XR7AMhK4+kl6VvwezTtLnks5QCqO1m3KwjL7GGZJm7B79IT8h2R808kPdR7LTEvyC1EV/idun8QtSLtkHkvyynZ/CL6uRe6PeGNh/g2TPTPM/juT+oG8KtDVXLrimsv9Ayb6foJaxGdRymOq/Of1Xsm3SaCP4plIj2b0zqKWPZBcH2vpVmm3sEHg96yX7wwxqaSPZTwK17JVBO96wvEmyW2XQhuTe5GPtrJVsxwzauD7wegZkWMtETxtfZ9jGcYFahmTYThiPdoFaLs2wnZc9bXyYYRttJLvG086kDNvxhp+FSu8PauzRUe4Doreddmm20V/ufTbWxjLJds+glp6SXRL4OR2WZhuHB/avluwuGdSyVYJaJqrxvyPexy2B/a1kz8iglv0luzLQzjdK/W/JILlOlmAtNyj935kjEtRi5QJ0Kh/sj5cLo8H9X5Js3zTqKJXsb6I/32Bbn0h2VCP795TsnXJZw7p1xRMs5a5rvEpucE+d4qFyptx1irHl/0nqEeJxl0r6Q4L1qZwKn5pgfaJT4cMD26R2Ktz7QzbG2gMPdCPhZs1yXdUffOCu3TjwwHq/EFZyF1C/9ZbN2MMP159SRnJz102aVP9ajE2b3GCHRNPm9OmTXS3PPlt/BHebNu60T0PX0D3yiH86EMm1k8r1g8m88EL9i8J/9KPGT/FEItZeeql/P2Oyu4B76lT/qOWSktTnuKypqf+zuvHGzGuZMsXf1q67pjcqNXhtZRYjn+399/vbuvvu9NvwDkDIYt7IeqOoMxkNesst/jYWLcq4nNgfhKx4Rweff376+0ci/mt6f/KTzGvxjoYuK0t/lPqrr/q/t7//fea1BH/W6V5rGbyEKZvrlZ96yt9Wr17uMqlUzJpV//323//OvJbp0/3XfkpuiqTG3h82brT2zDPr/z25667Ma/nww/ozbLRube1f/9rw9YVPPln/72FpqRvMlqk5c/wDFWOPAQPcIKTgtZeRiBsEu+ee9fdp06bx19CQzz+3dp99EmeJ3Xaz9uqr3fXUX33lsscjj7hLsgIj4QseLCWVSjpabpR0rSdQfi83Lc/W0e16SbpS0proNvdke2xPDa9Lejiwrl/0zbexwTuLEqz/SvUH75wZ2OYnSmXwTqIfcCqP0lJ3XWQYE40vWOCuuUh0nK5d3S/WL3/p/vVeSO99jBoVzhyZH3yQ+BhDhrjrNWNvUnV17oLpRNeZ9uwZzjxikyfXv6Zl8GBrP/008fbV1f7rwcJ4g4z561/9bXbs2Pgk3nV19a83Peig7Ed0eyfPTucP48aN/uvKSkuzm/+uqsr/gWLPPdPb//PP/a8jm7Dx3//628pkAM/vfx/f35isRrWGEiy914mdcEL6+wcH7vz1r5nXEvwQke7NA4Kjr7OZbm3VKv91ueXlqb/3BT+Y7bZb9tMFBUPZsGGNX2/57bf+SeIlN5I6W5MnJ75OPdn3Z9EiNyjHu70x2d9owFr3dy04cl1ynTSTJsWvnY9E3DyQ3jlTvX//gnOKZqKqyg3gSfS3s2dP12lx3nkuiHtnUfA+dtgh9Rs3NKSuzn2ITXdUeTEES0kDJV0r6VtPmIxImibpx5LaJNmvMrrdt9kUHmjzEkkrJHXyrLtIqU83tG+gPqv60w29HNj3GaUy3dDgwdbutVd6P9jjjst+hHDQpk1uFGo6cz5KLng11qOYruXL/XcgCR6vb1//RfTexx57hHsniJdeqh8uO3Z0d6aJ9QzU1bmpkrbbrn49//hHOHVEIvVHivftm/xi8EjETdQbfJPM9OJxrwUL/D0TFRWp9dDdequ/nnPOyb6Ws8/2t5nOG28wrCeaMSBVCxb428qkV/jnP4/v36NH5rVYa0MJlt6ejeHD09//6af935OXX868lu+/9884ceaZqe+7fLn///BBB2VeR8zf/+5/bb/6VeP7bNzovyGAFM78guvWuTNM3nZHjUr+wWTNmvpTFg0fnv0MGDFPP+0fJCW5ntQnn4zXtHq1u/lDMEQZk3wez0wsX27tEUck/lvRtasbxZ4sYFVWhj/B+BNPJJ7erqFHq1bW/vrX4Yxw91q0yIVd79mwxh7bbWftM8/YvAdLScdJelFuwvBYoFwt6TZJO6XYxneS6rIpPNBeV0mL5K6ZHCF3jeM6BSZIlxupfm9g3WS56YWOifa8fq7kE6T/XdIBkv6idCZIj0Tcm+5pp9U/pRt79OzpTiUlmvswTIsXuz/4jf2ytWnj/qjnaGZ/W1fnpiYJvkE19Bg3Lrw3R68330z8KbK01PWkJgvjN9wQbh0bNtT/VN2rV/3esU2b6p+ua9Uqu0sDgoLtjx7d8IeL1atdWIpt36lT6qfsGvLee/46zjor9X29d9vp3Tu7ntxIxI2Uj7WXyWlf7wwCWU60Hkqw9E5sPnhw+vtffbX/Z5PtGQ3vRPTp3B3pxhv9daR6S8mGbNjgv6NY69aN30Vs3Dh/HdlcGhD0ySf+3z/J3QghGEY++qh+L96222Z/k4GgiRMT/w1p29a9ZyYa3dyxo5u6K2yxEdXBntSGHueeG870QIl8/707O5Hsb733cfzxmY/eTtXnn7u/5cnORrZt6zqzJk3aPLdzIYJlxPN4T9IvJHVIs435YQbLaJs7SHpFUk00ZF6twCCh6HHvC6zrIndLx1Vyp+nHS+qeoP2jJX0sN8p9tqQxqdRVb7qhmhp3Td3Eie70zz33uNO6+b4P6ty57j/jcce58NK2rfu08qMfuds0LlyYvzrOOiv5m4Ixrgcinak6MrFoUfLLBYKPHj3Sn2Q7VStW1O8ZLSlx0ylNmuSu5Ux0Pc9DD4VbR01N/dtC3npr8u2DvafZTnTtNXRovN0OHVKfJiWbu+0k4g39mVyv6X0dWfaqhRIsvb3BXbumv7/3kom+fbOrxdr6d7+ZMaPxferq/Kf0e/UK78PnhAn+eg4/PPn79Asv+Lft1Mna774Lp46Y11+vf114v36uB/Dpp13QD14D2b177m6r+9ZbiafdSfRo6BKjsHzwgfsAnOzOOca4Sz7CON2cipUr3e/0qFHuPbuszP0/O/xwtz7sOxk1JhJxlyb9+9/u8dhjrjNi1ap6mxYiWFZHg9jQbA7cUh45uVd4c7RwoTv9fOGFbp7L4493PZpff52/GjZudHc88F5fFXwcc4y71VYuzZuX+PaQyR5ZTLTdoLff9vcot2njbvsWdNdd/nr69s18zr1E/v1vf/u33db4PsGaMp2n0csbnlu1Sr/Hw9tjcNJJWZUSSrC88kr/9yjd1+MNFSNHZleLtW5icG89F13U+D4vvujf59JLs68jJhKpP8Ai0Z18vvvO31svuUGTuTBxYvLJsYOP3r2zu/wjFevWuWsHk9XQoYPrOAjjLkapWrbMfQg+8UTXa/yrX7kBWLm833kzU4hg2SWbA7a0B8GyCdqwwd1B6Cc/cb1Uv/iF692dMSM396hNZO3axm/j2b69C5W5rCnYizRwoP9yjRdeqH9KbMKEcGuorvbfb3mnnRp+zZGI//Zs5eXhBN1gwE0UspOprfV/n37726xKCSVYBm+dmc4puTVr/PuGEegiEf81ihUVjV935r3TjjHWzp+ffR1e06fX7wH75z/jz8+ZU38C8TB6xxvy8MONX8d30EGZTzSfidmz3cjqc891xz7uOHdHm0xv+ICCynuw5EGwRJ7E7hbkvYex5E6Nn356fi5XqKurf9cOY9zxjzmm/qm3yy/PTR2//rX/OG+8kXzbt97yb/vLX4ZTQ/B6z3Smbpk7179vlrfMDCVYvvKKv6Z0Rse++aZ/37A+TPzjH/52778/+bYLF/rD+hFHhFNDUHDEekmJu2To/PPrX0u4ww7h9tYns3Klu6YzeGq8a1d3GUq2I9HRohEsi/xBsETWIhF3+v2dd9y0N2H3yjRmyRI3urKxU28//nHuek+DUweNGZN82+DUM599Fk4N69f7Lw1I55aZwftGZznFSSjBct48f03enrjGBG85GNYsFqtW+UfxDh2afNsrrvDXkO4URekIXjaQ6NGpkxs8k0+LF7uzK2+84aYYyve1+miWsg2WJQJQ3IyRevSQ9txTGjVKGjAgv8fv2VOaPl065pjk2xxwgHTvva7WXNh2W2nEiPjyhAnSjBn1t/v+e+nRR+PL//d/0uDB4dTQtq20/fbx5VmzUt933jz/8lZbhVNTNrbcUmrVKr4crLEhH3wQ/7qsTNp663Bq6txZOvnk+PK77yb+OS9aJP3tb/HlgQOlQw8Np4ZErrhCOvXU5M/vu6/0v/9JO+2UuxoS6dVLOvxwd/w+faQS/qSj8PgtBNC43r2liROlxx93X0tSly7SUUdJd9whvfiiC165dNFF8a+tlc47T4pE/Nv861/Sxo3x5XPOCbeGXXaJf/3BB66OVMydG/+6pETq3z/cujLRqpX/Q4q3xsZ4Q/WQIVJpaXh1BX9m//xn/W1+9ztp3br48oUXhltDkDHud2vCBGnsWBfoJKljR+kf/5Bee03abrvcHR9oQgiWAFJ37LHS/PnSl19Ky5ZJTz4pnXmm1Lp17o996KGuxzZm+nTp/vvjy6tXS7ffHl/u08e/fRh23jn+9cqV0jffpLafN7RtuaXUpk24dWVq0KD416kGy7o66aOP4sve70kYhgxxPXAx48e737mYN96QHnoovrzTTtLZZ4dbQyLGSCec4OpZtMjV9N137gMOPYXAZvxvAJCetm3dqc9c9hAlc9NN/p7RceNcwK2qcqcEv/46/twZZ4QfeL09lpL/lHBDvKeZi+E0eIy3llRPhX/xhVRTE18Ofk/C4O21XL/eXQaxaJG0YYMLcl633uo/pZ8Pxrje3k6d8ntcoAkgWAJoOrbayoXJmO+/d+v23FN68834+h49wj8NLtXvnUv1Oktvb2CxBsuVK92jMcHXHHaPpeR6xr3XK371lbTPPu4Sgg8/jK8fOvAPKQAAF0VJREFUO1YaPjz84wPIGMESQNMybpz/2sC1a6VPPokvd+nirvns0SP8Y3fvLvXtG19+773G91m71vWqxnhPPxdasJZUei29r9kY6Yc/DLcmyV0q8PzzblBOzLx50tKl8eUOHaQbbgj/2ACyQrAE0LSUlUmPPRYfROTVoYMLJLk4PRtTWRn/OtGI5aBiHBEeE6wllWDpfc3bb+8GsOTClltKU6a4a2WDOnRw1zp6Qz6AokCwBND07LGHO718773xU7HduklPPy0NG5bbY3uD5cKF0pIlDW8fHBRTzMGysQE8kYi/x9L7vciFrbZy4TLWczlokHTjje77HvbALAChyPMVzwAQkvbtpZ/9TDrtNBc0OneWystzf9xgmJo5Uxo5Mvn2wbBWTKfCu3Z137M1a9xyY8Hyq6/c6PuY3XfPXW0xgwdLs2e7Edj9+xdm0BiAlNFjCaBpM0bq1y8/oVKqH6YaOx3uDWtlZW7C+WJhjL/XsrFgGXytue6xjGnb1gVyQiVQ9AiWAJCOHj38E5w3FiyDUw3l6u5EmUpnyiHvay0pye21rACaJIIlAKTL21M3c2bD23p7AYvpNHiMt6b5890E6Ml4X+sOO7geWADwIFgCQLq8wfK779wjkUikeCdHj/HWVFsrfftt4u0iEX+wzNdpcABNCsESANIVvM4yWa/l4sXubjExxR4speSnw+fM8d+fm2AJIAGCJQCkK9VgWcwjwmOCNSUbwBN8jfkYEQ6gySFYAkC6unXzB7JkA3iKeQ7LmAED/AOKkgVL72ssLc3NrRwBNHkESwDIRPAOPNbW3yZ4WrkYeyzbtfPfwSbZqXBvsNxpJzePKAAEECwBIBPeYLlkSeIBPF99Ff+6d+/iHUXt7Un11hxTVye9/358mesrASRBsASATASvMZw+vf4277wT/3qbbXJbTza8tc2aJdXU+J//9FOpqiq+zPWVAJIgWAJAJior/XeCeeYZ//Pz5klffBFfPvDA/NSViQMOiH+9fr30xhv+54OvLdf3YwfQZBEsASATnTtLw4fHl596Stq0Kb48ebJ/+0MPzU9dmTj4YP9ysPYnnoh/3a8fd9wBkBTBEgAyNXp0/Ovly6Vp0+LLL74Y/7pzZ2no0PzVla5evfxh0RssFy6U/ve/+PLRRxffbSkBFA2CJQBk6uij/cuxnr3aWmnKlPj6gw6SWrXKX12Z8PaofvKJC5SS9OST/u28YRoAAgiWAJCpLbeU9tgjvvzEE27aoenTpTVr4uuL+TR4TLDGWI+r9zR4t27SfvvlryYATQ7BEgCy4e3B++Ybd4eapnR9Zcw++0gdOsSXX3zRnd5/7bX4uiOPLP6eVwAFRbAEgGwETw0/8YT/+srttnN3tyl2bdr4R66/9JIbkFRXF1/HaXAAjSBYAkA2Bg92j5h77/UPdjnkkPzXlClvrStWSJddFl/u0KH+6HEACCBYAkC2vD15S5b4b+/YFE6DxwRr9d5N6LDDuI0jgEYRLAEgWyef7J8sPaZtW//k48Vum22S38/81FPzWgqApolgCQDZ2mEHd3ea445zp8VLStxcj3/8o39ATLEzRvrTn1wgllzIPPJI6f77pSOOKGxtAJoEY72nbBC6yspKO2PGjEKXASCf1q93g15yFCpNdILynL1/57h+AMXLGDPTWluZ6f7MGwEAYWvXrtAVZKep1w+gYDgVDgAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAIAACAUBEsAAACEgmAJAACAUBAsAQAAEAqCJQAAAEJBsAQAAEAoCJYAAAAIBcESAAAAoSBYAgAAIBQESwAAAISCYAkAAIBQECwBAAAQCoIlAAAAQkGwBAAAQCgIlgAAAAgFwRIAAAChIFgCAAAgFARLAAAAhIJgCQAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAIAACAUBEsAAACEgmAJAACAUBAsAQAAEAqCJQAAAEJBsAQAAEAoCJYAAAAIBcESAAAAoSBYAgAAIBQESwAAAISCYAkAAIBQECwBAAAQCoIlAAAAQkGwBAAAQCgIlgAAAAgFwRIAAAChIFgCAAAgFARLAAAAhIJgCQAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAIAACAUBEsAAACEgmAJAACAUBAsAQAAEAqCJQAAAEJBsAQAAEAoCJYAAAAIBcESAAAAoSBYAgAAIBQESwAAAISCYAkAAIBQECwBAAAQCoIlAAAAQkGwBAAAQCgIlgAAAAgFwRIAAAChIFgCAAAgFARLAAAAhIJgCQAAgFAQLAEAABAKgiUAAABCQbAEAABAKAiWAAAACAXBEgAAAKEgWAIAACAUBEsAAACEgmAJAACAUBAsAQAAEAqCJQAAAEJBsAQAAEAoCJYAAAAIBcESAAAAoSBYAgAAIBQESwAAAISi2QRLY8wvjDFfGGPWG2NmGmMOSmGf+cYYm+SxhWe7RM+/k9tXBAAA0LS0KnQBYTDGjJV0h6QrJU2TdJqkZ4wxe1hrP25g19GS2gbW3S2pzlq7KLD+RkmPe5bXZlU0AABAM9MsgqVcoLzfWnu1JBljXpO0q6SLJZ2cbCdr7fveZWNMb0nbS/p9gs3nW2vppQQAAEiiyZ8KN8ZsJWlbSY/G1llrI5Iek/SjNJs7Qe578khoBQIAALQQTT5YShoc/Xd2YP1nkiqMMT3SaGuMpLettQsSPHelMWaTMWaZMeZfxpiKTIoFAABorprDqfCu0X9XBdav9Dz/fWONGGMGSBom6VcJnr5f0tPRdiolXS5pZ2PMUGttXSZFAwAANDdFGSyNMZ0lbdHYdtbaYC9lNsZIishzSt1znFM9i68bYz6T9JykIyU9GdzeGHOGpDMkqX///iGWCAAAULy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        },
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            "_view_name": "OutputView",
            "layout": "IPY_MODEL_8df3d2d704b142a1adabcf912062892d",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 720x720 with 1 Axes>",
                  "image/png": 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            "style": "IPY_MODEL_fa7a4689c31847989d121508d12e966b",
            "value": -5
          }
        },
        "343f769207e0447a8533a6d6db60c3cc": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "FloatSliderModel",
          "model_module_version": "1.5.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/controls",
            "_model_module_version": "1.5.0",
            "_model_name": "FloatSliderModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/controls",
            "_view_module_version": "1.5.0",
            "_view_name": "FloatSliderView",
            "continuous_update": true,
            "description": "b",
            "description_tooltip": null,
            "disabled": false,
            "layout": "IPY_MODEL_fa26c23d56ed4e0a820d8073d5806102",
            "max": 1.5,
            "min": -1.5,
            "orientation": "horizontal",
            "readout": true,
            "readout_format": ".2f",
            "step": 0.1,
            "style": "IPY_MODEL_1808ec08a8ff46d69007b09cb64a3743",
            "value": 0
          }
        },
        "249004c0c6384f2d856b3d3028f5d26c": {
          "model_module": "@jupyter-widgets/output",
          "model_name": "OutputModel",
          "model_module_version": "1.0.0",
          "state": {
            "_dom_classes": [],
            "_model_module": "@jupyter-widgets/output",
            "_model_module_version": "1.0.0",
            "_model_name": "OutputModel",
            "_view_count": null,
            "_view_module": "@jupyter-widgets/output",
            "_view_module_version": "1.0.0",
            "_view_name": "OutputView",
            "layout": "IPY_MODEL_dcf3f103fdc146c5be8dc6e1d3c0cb5f",
            "msg_id": "",
            "outputs": [
              {
                "output_type": "display_data",
                "data": {
                  "text/plain": "<Figure size 720x720 with 1 Axes>",
                  "image/png": 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        "<a href=\"https://colab.research.google.com/gist/mgiugliano/77b29ff1243db057bbcf2c4b081d9ecd/functions_of_one_variable.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# **First: go to Runtime-menu and click on 'Run All'**\n",
        "\n",
        "# **Principles of Computational Neuroscience**\n",
        "# Mathematical Refresher - Functions of one variable\n",
        "\n",
        "##### *An Introductory Course Offered to (under)grad Neuroscience students at UniTs and SISSA, Trieste (SISSA)*\n",
        "\n",
        "A (mathematical) **function** can be intuitively imagined as the physical box depicted in the sketch below: as an element is offered as input, an element is istantaneously produced as an output. However, for a specific input element $x$ only one output element $y$ is associated. In order to emphasise such a precise correspondence between input and output, the output element is sometimes also written as $f(x)$ and reads as \"*function of $x$*\".\n",
        "\n",
        "<hr>\n",
        "\n",
        "## Definitions and representations\n",
        "\n",
        "\n",
        "![Image of a function](https://upload.wikimedia.org/wikipedia/commons/3/3b/Function_machine2.svg)\n",
        "\n",
        "### Independent and depenedent variables\n",
        "\n",
        "Instead of specifying one by one the elements when dealing with inputs $x$ and output  $y$ (or $f(x)$) elements, we have used here generic symbols. These denote \"[**variables**](https://en.wikipedia.org/wiki/Variable_(mathematics)\", which are identifiers (or *containers*) that can assume distinct values (or contain distinct elements). Sometimes the input variable $x$ is called *independent*, to distinguish it from the output $f(x)$ that is, by definition, dependent on the specific element of $x$ and it cannot take artibatry values. We note that the use of letters $x$, $y$, and $f$ is completely arbitrary: those or other letters can (and will) be used interchangably, provided that references and consistency are maintained. \n",
        "\n",
        "### Definition of a function of one (input) variable\n",
        "\n",
        "Summarising, a mathematical function is a relation or a correspondence between two sets of elements, with an important property: for each element of the input set there is exactly one (and only one) corresponding element in the output set. Such correspondences can be **graphically** represented, as depicted in the example below, identifying for all elements of the input set the corresponding elements of the output set by means of **arrows**. \n",
        "\n",
        "![Image of a function](https://upload.wikimedia.org/wikipedia/commons/d/df/Function_color_example_3.svg)\n",
        "\n",
        "The same can be done by enumerated explicitly all the correspondences in a **table**, by listing for each possible input element $x$ its corresponding $y=f(x)$.\n",
        "\n",
        "| $x$   |   $y$    |\n",
        "|:-----:|:---------:|\n",
        "| :     |    :      |\n",
        "| -2     |   -4       |\n",
        "| -1     |   -2       |\n",
        "| 0     |   0       |\n",
        "| 1     |   2       |\n",
        "| 2     |   4       |\n",
        "| 3     |   6       |\n",
        "| 4     |   8       |\n",
        "| 5     |   9       |\n",
        "| 6     |   10      |\n",
        "| 7     |   12      |\n",
        "| :     |    :      |\n",
        "\n",
        "As the input set is composed by many elements, the above representations might be a bit cumbersome leading to very crowded graphs or lengthy tables. Moreover, if the input and output sets are numerical (e.g. real [numbers](https://en.wikipedia.org/wiki/Number)), another and more intuitive graphical representation can be also provided in terms of a **plot**, as a collection of coloured points in the [*Cartesian plane*](https://en.wikipedia.org/wiki/Cartesian_coordinate_system) $x,\\ y$. There, every possible point is specified rigorously by two coordinates $(x,y)$ but, instead of being choosen or addressed arbitrarily as in a game of [*Battleship*](https://en.wikipedia.org/wiki/Battleship_(game)), they are now reflecting the correspondences mentioned above. Thus, one accurately adjusts the vertical coordinate $y$ corresponding to the horizontal coordinate $x$, according to the function $y=f(x)$. The curve composed by all those points is referred to as the [*graph*](https://en.wikipedia.org/wiki/Graph_of_a_function) of the function. \n",
        "\n",
        "![Image of a function](https://upload.wikimedia.org/wikipedia/commons/f/f8/Polynomialdeg2.svg)\n",
        "\n",
        "Finally, a numerical function may  sometimes also be specificed by a mathematical expression, like $f(x) = 2x$ (as for the function tabulated above) or like $f(x) = x^2 - x - 2$ (as for the function, a parabula, whose plot is given above).\n",
        "\n",
        "As this is not at all a course in mathematics, our goal is to turn such (high-school) elementary concepts just refreshed into more intuitive concepts. An efforts is requested to link mathematical formulations to graphs, so that formulae will perhaps no longer  appear \"dry\". Few notable operation on functions should be appreciated and mastered visually and the following subsections aims precisely at that.\n"
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      "source": [
        "### Some 'graphical algebra' for your eyes and intuition\n",
        "\n",
        "Below you will find computer-code (currently hidden) for interactive plotting of a sample function $f(x) = {sin(x)}/{x}$. This function is called *sinc* and it was chosen for this example, only because of its shape:   it *goes up and down* and it has only certain symmetries. \n",
        "\n",
        "Having launched the code (i.e. as *Run All* from the menu above), user interface *sliders* appears: they allow the user to explore (in this case) elementary algebraic operations (e.g. addition, multiplication) on the function graph, interactively. \n",
        "\n",
        "We first start by changing the numerical value of a fixed numerical parameter $a$ that is simply added to the function. This value can be added *inside* (i.e. to the independent variable) or *outside*, as discussed in the online lectures. So the user will have two sliders, which can be used one to explore how the value of $a$ (and of $b$) affects the graph of the (new) function $f(x +   a) + b$.\n",
        "\n",
        "The reader might then appreciate that adding (or subtracting) a constant *outside* the graph of the function **translates vertically**  upwards (or downwards). If adding (or subtracting) a constant *inside* the graph of the function **translates horizontally** towards the left (or the right). \n",
        "\n",
        "The computer code can be made visibile by clicking on *Show code* and then made hidden again by right-mouse clicking and then selecting *Form --> Hide code*. You can execute it but otherwise safely ignore it for the moment. As in the task of approaching a foreign language however, the best among you will try reading it and *making sense* of it. That won't certaily kill you, if you try!\n"
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        "#@title\n",
        "# The following commands import a couple of libraries\n",
        "from google.colab import output           # this is for the \"widgets\"\n",
        "output.enable_custom_widget_manager()     # this is for the \"widgets\"\n",
        "\n",
        "#widget modules\n",
        "from ipywidgets import interact, interactive  # this is for the \"widgets\"\n",
        "import ipywidgets as widgets                  # this is for the \"widgets\"\n",
        "\n",
        "#mathematics, arrays, and plotting \n",
        "import matplotlib.pyplot as plt           # this is for plotting\n",
        "import numpy as np                        # this is for math and arrays\n",
        "\n",
        "# These are \"global\" variables and I initialise to 0, for the moment\n",
        "x = np.zeros(50)\n",
        "y = np.zeros(50)"
      ]
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      "cell_type": "code",
      "source": [
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title(a,b):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "\n",
        "  a_sign = '+' if (a>=0) else '-'   # I prepare a character +/- for a\n",
        "  b_sign = '+' if (b>=0) else '-'   # I do the same for b\n",
        "\n",
        "  if (a==0.0 and b!=0.0):\n",
        "      title_text = 'f(x) {sign2} {valueb:,.1f}'.format(sign2=b_sign, valueb=abs(b))\n",
        "  elif (a!=0.0 and b==0.0):\n",
        "      title_text = 'f(x {sign1} {valuea:,.1f})'.format(sign1=a_sign, valuea=abs(a))\n",
        "  elif (a==0.0 and b==0.0):\n",
        "      title_text = 'f(x)'.format(sign1=a_sign, valuea=abs(a))\n",
        "  else:\n",
        "    title_text = 'f(x {sign1} {valuea:,.1f}) {sign2} {valueb:,.1f}'.format(sign1=a_sign, valuea=abs(a), sign2=b_sign, valueb=abs(b))\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_label(a,b):    # This is a utility function to nicely format a legend\n",
        "  mylabel = 'f(x + a) + b'\n",
        "  return mylabel\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def plot_my_function(a, b):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-50,50)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-1.5,1.5)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-50, 50, 5))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-1.5, 1.5, 5))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title(a,b) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  sinc_function(a, b)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label=create_label(a,b))                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def sinc_function(a, b):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x + a) + b,  (a,b parameters)\n",
        "  x = np.linspace(-50,50,num=200) # First the array containing the 'x'\n",
        "  y = np.sin(x+a)/(x+a) + b       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function,a=(-50.0,50.0), b=(-5.0,5.0))\n",
        "output = interactive_plot.children[-1]\n",
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        "### Some more 'graphical algebra' for your eyes and intuition\n",
        "\n",
        "We now try to multiply the function for a number. This number can be multiplied *inside* (i.e. to the independent variable) or *outside*, as discussed in the online lectures. So the user will have two sliders, which can be used one to explore how the value of $a$ (and of $b$) affects the graph of the (new) function $f(x *  a) * b$.\n",
        "\n",
        "The reader might then appreciate that multiplying *inside* the function by a constant, the graph of the function **scales vertically** proportionally depending on its local value. In other words, it is as if the numerical labels on the vertical axis must be altered if one wants to keep the shape of the function unaltered. In addition, if the multiplier is larger or smaller than one, the scaling will be effectively *zooming in or out* respectively. Finally, if the number is negative (e.g. say $-1$), the plot is **flipped** symmetrically with respect to the horizontal axis.\n",
        "\n",
        "Instead,  multiplying the the function *outside* by a constant value makes the graph of the function **scaling horizontally** and proportionally, depending on its local value. In other words, it is as if the numerical labels on the horizontal axis must be changed in oder to keep the shape of the function unaltered. In addition, if the multiplier is larger or smaller than one, scaling will be effectively *zooming in or out* respectively. Finally, if the number is negative (e.g. say $-1$), the plot is **flipped** symmetrically with respect to the vertical axis. This of course cannot be appreciated in the specific example of the function we have chosen, as the *sinc* is symmetrical with respect to the vertical axis, so a flip won't be noticeable.\n",
        "\n",
        "Once again, the computer code can be made visibile by clicking on *Show code* and then made hidden again by right-mouse clicking and then selecting *Form --> Hide code*. You can execute it but otherwise safely ignore it for the moment. As in the task of approaching a foreign language however, the best among you will try reading it and *making sense* of it. That won't certaily kill you, if you try!"
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        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "# Note how we modified only a portion of the above code, by redefining some\n",
        "# useful functions\n",
        "\n",
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title2(a,b):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "\n",
        "  a_sign = '' if (a>=0) else '-'   # I prepare a character +/- for a\n",
        "  b_sign = '' if (b>=0) else '-'   # I do the same for b\n",
        "\n",
        "  if (a==1.0 and b!=1.0):\n",
        "      title_text = '{sign2}{valueb:,.1f} f(x)'.format(sign2=b_sign, valueb=abs(b))\n",
        "  elif (a!=1.0 and b==1.0):\n",
        "      title_text = 'f({sign1}{valuea:,.1f} x)'.format(sign1=a_sign, valuea=abs(a))\n",
        "  elif (a==1.0 and b==1.0):\n",
        "      title_text = 'f(x)'.format(sign1=a_sign, valuea=abs(a))\n",
        "  else:\n",
        "    title_text = '{sign2}{valueb:,.1f} f({sign1}{valuea:,.1f} x)'.format(sign1=a_sign, valuea=abs(a), sign2=b_sign, valueb=abs(b))\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_label2(a,b):    # This is a utility function to nicely format a legend\n",
        "  mylabel = 'b  f(a x)'\n",
        "  return mylabel\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "# THE CODE HERE IS IDENTICAL TO plot_my_function(). IT IS REPEATED TO AVOID\n",
        "# FORCING YOU TO EXECUTE ONE CELL AT THE TIME TO MAKE THIS NOTEBOOK WORKING FINE\n",
        "def plot_my_function2(a, b):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-50,50)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-1.5,1.5)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-50, 50, 5))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-1.5, 1.5, 5))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title2(a,b) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  sinc_function2(a, b)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label=create_label2(a,b))                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def sinc_function2(a, b):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x * a) * b,  (a,b parameters)\n",
        "  x = np.linspace(-50,50,num=200) # First the array containing the 'x'\n",
        "  y = np.sin(x*a)/(x*a) * b       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function2,a=(-3.0,5.0), b=(-3.0,5.0))\n",
        "output = interactive_plot.children[-1]\n",
        "interactive_plot"
      ],
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      "cell_type": "markdown",
      "source": [
        "## Notable functions and their graphs\n",
        "\n",
        "### The function \"*constant*\": $f(x) = a$\n"
      ],
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        "id": "YJeCdMCL0H62"
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      "source": [
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "# Note how we modified only a portion of the above code, by redefining some\n",
        "# useful functions\n",
        "\n",
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title3(a):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "  title_text = '{valuea:,.1f}'.format(valuea=a)\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "# THE CODE HERE IS IDENTICAL TO plot_my_function(). IT IS REPEATED TO AVOID\n",
        "# FORCING YOU TO EXECUTE ONE CELL AT THE TIME TO MAKE THIS NOTEBOOK WORKING FINE\n",
        "def plot_my_function3(a):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-50,50)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-1.5,1.5)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-50, 50, 5))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-1.5, 1.5, 5))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title3(a) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  constant_function(a)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label='a')                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def constant_function(a):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x * a) * b,  (a,b parameters)\n",
        "  x = np.linspace(-50,50,num=200) # First the array containing the 'x'\n",
        "  y = np.ones(200) * a       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function3,a=(-1.5,1.5))\n",
        "output = interactive_plot.children[-1]\n",
        "interactive_plot"
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        {
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              "interactive(children=(FloatSlider(value=0.0, description='a', max=1.5, min=-1.5), Output()), _dom_classes=('wi…"
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      "cell_type": "markdown",
      "source": [
        "### The function *straight line*: $f(x) = m x + a$"
      ],
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        "id": "J2ecOAZ82onc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "# Note how we modified only a portion of the above code, by redefining some\n",
        "# useful functions\n",
        "\n",
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title4(a,b):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "\n",
        "  title_text = '{valuea:,.1f} x +  {valueb:,.1f}'.format(valuea=a, valueb=b)\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "# THE CODE HERE IS IDENTICAL TO plot_my_function(). IT IS REPEATED TO AVOID\n",
        "# FORCING YOU TO EXECUTE ONE CELL AT THE TIME TO MAKE THIS NOTEBOOK WORKING FINE\n",
        "def plot_my_function4(a, b):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-50,50)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-1.5,1.5)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-50, 50, 5))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-1.5, 1.5, 5))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title4(a,b) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  straight_line(a, b)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label='a x + b')                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def straight_line(a, b):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x * a) * b,  (a,b parameters)\n",
        "  x = np.linspace(-50,50,num=200) # First the array containing the 'x'\n",
        "  y = x*a + b       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function4,a=(-0.5,0.5), b=(-30.0,30.0))\n",
        "output = interactive_plot.children[-1]\n",
        "interactive_plot"
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      "outputs": [
        {
          "output_type": "display_data",
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              "interactive(children=(FloatSlider(value=0.0, description='a', max=0.5, min=-0.5), FloatSlider(value=0.0, descr…"
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      "cell_type": "markdown",
      "source": [
        "### The function *exponential*: $f(x) = e^{x/a} + b$\n"
      ],
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      }
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      "cell_type": "code",
      "source": [
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "# Note how we modified only a portion of the above code, by redefining some\n",
        "# useful functions\n",
        "\n",
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title5(a,b):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "\n",
        "  title_text = 'exp(x/{valuea:,.1f}) +  {valueb:,.1f}'.format(valuea=a, valueb=b)\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "# THE CODE HERE IS IDENTICAL TO plot_my_function(). IT IS REPEATED TO AVOID\n",
        "# FORCING YOU TO EXECUTE ONE CELL AT THE TIME TO MAKE THIS NOTEBOOK WORKING FINE\n",
        "def plot_my_function5(a, b):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-50,50)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-1.5,1.5)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-50, 50, 5))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-1, 4, 6))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title5(a,b) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  exponential(a, b)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label='exp(x/a) + b')                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def exponential(a, b):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x * a) * b,  (a,b parameters)\n",
        "  x = np.linspace(-50,50,num=200) # First the array containing the 'x'\n",
        "  y = np.exp(x/a) + b       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function5,a=(-20.0,10.0), b=(-1.5,1.5))\n",
        "output = interactive_plot.children[-1]\n",
        "interactive_plot"
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      "source": [
        "### The function *logarithm*: $f(x) = log(a x)$\n"
      ],
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      "cell_type": "code",
      "source": [
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "# Note how we modified only a portion of the above code, by redefining some\n",
        "# useful functions\n",
        "\n",
        "#@title\n",
        "# This is the interesting part!\n",
        "\n",
        "\n",
        "# We first create a Python-procedure (called 'function') to make a nice \n",
        "# plot of x-y points... This function \"calls\" another function (see below):\n",
        "# sinc_function() and passes to it two arguments 'a' and 'b', that the function\n",
        "# received as input on a first place...\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def create_title6(a,b):    # This is a utility function to nicely format a title\n",
        "  title_text = ''   # I need a title on the graph and I want it to change so that\n",
        "                    # it does not annoy you and propely place +/- the parameters\n",
        "\n",
        "  title_text = 'log({valuea:,.1f} x) +  {valueb:,.1f}'.format(valuea=a, valueb=b)\n",
        "\n",
        "  return title_text\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "# THE CODE HERE IS IDENTICAL TO plot_my_function(). IT IS REPEATED TO AVOID\n",
        "# FORCING YOU TO EXECUTE ONE CELL AT THE TIME TO MAKE THIS NOTEBOOK WORKING FINE\n",
        "def plot_my_function6(a, b):     # This is the function to be called \"interactively\"\n",
        "\n",
        "  plt.figure(figsize=(10, 10), frameon=False, facecolor='white') # Create a fig\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # PURELY AESTHETICS - NOTHING TO REALLY UNDERSTAND\n",
        "  plt.rc('font', size=25)        # Set the default text font size\n",
        "  plt.rc('axes', titlesize=25)   # Set the axes title font size\n",
        "  plt.rc('axes', labelsize=30)   # Set the axes labels font size\n",
        "  plt.rc('xtick', labelsize=15)  # Set the font size for x tick labels\n",
        "  plt.rc('ytick', labelsize=15)  # Set the font size for y tick labels\n",
        "  plt.rc('legend', fontsize=25)  # Set the legend font size\n",
        "  plt.rc('figure', titlesize=30) # Set the font size of the figure title\n",
        "\n",
        "  plt.xlim(-0.5,4)               # Set the vertical axis 'boundaries'\n",
        "  plt.ylim(-5,10)               # Set the horizontal axis 'boundaries'\n",
        "    \n",
        "  plt.axhline(color='black', linewidth=2) # Makes the x-axis thick and black\n",
        "  plt.axvline(color='black', linewidth=2) # Makes the y-axis thick and black\n",
        "  plt.xticks(np.linspace(-1, 4, 6))     # Where to display the 'ticks'\n",
        "  plt.yticks(np.linspace(-5, 10, 7))   # Where to display the 'ticks'\n",
        "\n",
        "  plt.xlabel(\"x\", fontsize=25)            # Add a label on the x-axis\n",
        "  plt.ylabel(\"y\", fontsize=25)            # Add a label on the y-axis\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  #-----------------------------------------------------------------------------\n",
        "  # THIS IS ALSO FOR AESTHETICS ONLY: I WANT A 'COOL' TITLE. CAN YOU GET IT?\n",
        "\n",
        "  title_text = create_title6(a,b) # A ah! I am using my own function!\n",
        "  #-----------------------------------------------------------------------------\n",
        "\n",
        "  plt.title(title_text)         # The title is now finally set\n",
        "\n",
        "  logarithm(a, b)           # The mathematical function to plot is called\n",
        "\n",
        "  # The command to plot the graph is launched\n",
        "  plt.plot(x, y,linewidth=3.5, color='red', label='log(a x) + b')                \n",
        "  plt.legend(loc=\"upper right\")   # Can you guess what this does?\n",
        "  \n",
        "  #ax = plt.gca()\n",
        "  plt.show()\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "#-------------------------------------------------------------------------------\n",
        "def logarithm(a, b):      # This function updates the global variables\n",
        "  global x, y                 # This command allows 'x' and 'y' to be altered\n",
        "  # Remember: we are after a (generic) function f(x * a) * b,  (a,b parameters)\n",
        "  x = np.linspace(0.00001,4.5,num=200) # First the array containing the 'x'\n",
        "  y = np.log(a*x) + b       # then the array containing the 'y'\n",
        "#-------------------------------------------------------------------------------\n",
        "\n",
        "\n",
        "\n",
        "# Here is the 'magic' of the Python libraries for interactive plots...\n",
        "# Try to see if you get what this does \n",
        "interactive_plot = interactive(plot_my_function6,a=(0,5), b=(-1.5,1.5))\n",
        "output = interactive_plot.children[-1]\n",
        "interactive_plot"
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