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module1.html
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<!DOCTYPE HTML>
<!--
Dimension by HTML5 UP
html5up.net | @ajlkn
Free for personal and commercial use under the CCA 3.0 license (html5up.net/license)
-->
<html>
<head>
<title>Electrophysiological Signals - Module 1</title>
<meta charset="utf-8" />
<meta name="viewport" content="width=device-width, initial-scale=1, user-scalable=no" />
<link rel="stylesheet" href="assets/css/main.css" />
<noscript>
<link rel="stylesheet" href="assets/css/noscript.css" />
</noscript>
</head>
<body class="is-preload">
<script src="assets/js/slowloading.js"></script>
<!-- Wrapper -->
<div id="wrapper">
<!-- Header -->
<header id="header">
<div class="content">
<div class="inner">
<h1>Math Refresher <br> (Module 1)</h1>
<img src="images/coverart_math.png" alt="Cover art goes here!">
<p>Self-Paced online Module <br>(start with Part A)
</p>
</div>
</div>
<nav>
<ul>
<li><a href="#parta">Part A - Functions</a></li>
<li><a href="#partb">Part B - Calculus</a></li>
<li><a href="#partc">Part C - ODEs</a></li>
</ul>
</nav>
</header>
<!-- Main -->
<div id="main">
<!-- Part A -->
<article id="parta">
<h2 class="major">Part A - Functions</h2>
<!-- <span class="image main"><img src="images/pic01.jpg" alt="" /></span> -->
<p>
This first part of Module 1 is called Part A. It is made of three brief videos, lasting in total
<b>35
minutes</b>. They offer
an informal and elementary presentation, refreshing of the notion of a <b></i>mathematical
functions</b> that
you might have widely encountered in high school and, especially, during foundational courses (in
math and physics) of your academic training.
Ultimately, functions serve us as fundamental
metaphors and are pivotal for the progression of quantitative Neurobiology, Biophysics, and
<b>Bioengineering</b>.
<p>
<p>During our course, referring to and manipulating functions will be a powerful tool 1) to <b>precisely
identify</b>
the (bio)physical properties of neurons, synapses, and networks and 2) to
<b>predict or explain how they change</b> in time and/or space. We do NOT do math for the sake of
math! Should you initially feel differently, bear with me and trust my experience on
brushing
off your math background knowledge, aiming at further building up on it, and ultimately interested
in a <b>quantitative way of understanding neurobiology</b>.
</p>
<h3>A recomendation</h3>
<p>
While watching these videos (and attending classes too), please
<b>do
take notes</b> - despite the videos or overheads availability. Also do use <b>paper and
pen</b>, instead of a keyboard. Regaining your own confidence in
writing and
manipulating
mathematical symbols is of utmost importance.
Trust me: watching or listening passively this course will leave you no knowledge and you will
forget the course content very soon. It would be a pity as you are investing your precious time!
But be reassured: this (course) is neither special nor difficult, although it certainly departs from
old-fashioned
descriptive
and
qualitative treatment of biology. <b>Neuroscience, Bioengineering, and more in general Life Sciences,
have now
grown up into
quantitative disciplines, where skills in math, physics, and computers are necessary and not
optional.</b>
</p>
<h3>Let's dive into it</h3>
<p>Click on the image(s) below to watch the <b>videos</b> in a sequence.</p>
<p>Download if needed, the <b>overheads</b> from <a href="assets/pdf/Module1_PartA.pdf" target="_blank">
here</a>.
</p>
<span class=" image main"><a href="https://youtu.be/NsuqYK8jtWM" target="_blank"><img loading=" lazy"
src="https://i.ytimg.com/vi/NsuqYK8jtWM/hqdefault.jpg" alt="A1" /></a></span>
<p>
Let's now move away from abstract definitions. Let me help you developing a intuitive understanding
of the graph of
(some) functions. You might call it <b>algebra</b> of functions' graphs. In the next video below, we
will
play
with very simple manipulations to a mathematical function and understand how these are reflected
visually
on its graph. That's a convenient way to appreciate and understand functions.
</p>
<p>Click on the image to watch the <b>second video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/Ut-j2Z-2R-Y" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/Ut-j2Z-2R-Y/hqdefault.jpg" alt="A2" /></a></span>
<p>If you feel brave, or perhaps intrigued by those sort of interactive manipulations, you can play a
bit with
<a href="http://www.mathsisfun.com/data/function-grapher.php
" target="_blank"><b>this web site</b></a> or with the interactive notebook below (hint: click on <i>Open in
Colab</i>
button).
For both, you need curiosity and a web browser. For the latter, you might perhaps be tempted to look
behind the scenes
on how I built the code on what is Google Colab and how it works. Fear nothing! You can't break
things!
</p>
<a href="https://colab.research.google.com/gist/mgiugliano/77b29ff1243db057bbcf2c4b081d9ecd/functions_of_one_variable.ipynb"
target="_blank"><img loading="lazy" src="https://colab.research.google.com/assets/colab-badge.svg"
alt="Open in Colab Button" /></a>
<!-- <code data-gist-id="77b29ff1243db057bbcf2c4b081d9ecd"></code> -->
<p>Let's now go to the final video of this part. Click on the image to watch the <b>third and last
video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/pitTusmO_VY
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/pitTusmO_VY/hqdefault.jpg" alt="A3" /></a></span>
<p>Now you should have a bit of familiarity with some notable functions. They are so simple to remember
qualitatively and sketch on paper, when needed: straight lines, exponentials, and logarithms.
</p>
<!-- ---------------------------------------------------------------------- -->
</article>
<!-- Part B -->
<article id="partb">
<h2 class="major">Part B - Calculus</h2>
<!-- <span class="image main"><img src="images/pic01.jpg" alt="" /></span> -->
<h3>Let's dive into it</h3>
<p>Click on the image(s) below to watch the <b>videos</b> in a sequence.</p>
<p>Download if needed, the <b>overheads</b> from <a href="assets/pdf/Module1_PartB.pdf" target="_blank">
here</a>.
</p>
<span class="image main"><a href="https://youtu.be/vselE0s9W4k
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/vselE0s9W4k/hqdefault.jpg" alt="B1" /></a></span>
<p>Click on the image to watch the <b>second video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/wuz5491zDvY
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/wuz5491zDvY/hqdefault.jpg" alt="B2" /></a></span>
</article>
<!-- Part C -->
<article id="partc">
<h2 class="major">Part C - O.D.E., Dirac & Euler</h2>
<!-- <span class="image main"><img src="images/pic01.jpg" alt="" /></span> -->
<h3>Let's dive into it</h3>
<p>Click on the image(s) below to watch the <b>videos</b> in a sequence.</p>
<p>Download if needed, the <b>overheads</b> from <a href="assets/pdf/Module1_PartC.pdf" target="_blank">
here</a>.
</p>
<span class="image main"><a href="https://youtu.be/WC3S66s78MM
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/WC3S66s78MM/hqdefault.jpg" alt="C1" /></a></span>
<p>Click on the image to watch the <b>second video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/Y-05RwPzh8E
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/Y-05RwPzh8E/hqdefault.jpg" alt="C2" /></a></span>
<p>Click on the image to watch the <b>third video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/8L1gcO-FF4Q
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/8L1gcO-FF4Q/hqdefault.jpg" alt="C3" /></a></span>
<p>Click on the image to watch the <b>fourth video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/OTcGjgrfB_8
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/OTcGjgrfB_8/hqdefault.jpg" alt="C4" /></a></span>
<p>Click on the image to watch the <b>fifth video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/64U1EtcSAwk
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/64U1EtcSAwk/hqdefault.jpg" alt="C5" /></a></span>
<p>Click on the image to watch the <b>sixth video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/xElVPr9ZU8I
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/xElVPr9ZU8I/hqdefault.jpg" alt="C6" /></a></span>
<p>Click on the image to watch the <b>seventh video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/Zxe8Yg7XveE
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/Zxe8Yg7XveE/hqdefault.jpg" alt="C7" /></a></span>
<p>Click on the image to watch the <b>eight video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/SnFRv4cTE-w
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/SnFRv4cTE-w/hqdefault.jpg" alt="C8" /></a></span>
<p>Click on the image to watch the <b>last video</b> below.
</p>
<span class="image main"><a href="https://youtu.be/pQZPi6671ak
" target="_blank"><img loading="
lazy" src="https://i.ytimg.com/vi/pQZPi6671ak/hqdefault.jpg" alt="C9" /></a></span>
</article>
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