The Beauty of Calculus [video]
Very nice lecture that connects calculus to the laws of nature. I've always thought applied math has a leg up on abstract math because of the connections to real-world ideas.<p>I encourage anyone who liked the talk to try out some of the calculations on their own using <a href="https://live.sympy.org/" rel="nofollow">https://live.sympy.org/</a> which is an online REPL with build in calculus function like integrate, diff, limit, summation, etc.  Here is an example:<p><pre><code>   >>> summation((1/2)**(2*n), [n,0,oo])
   4/3
</code></pre>
via <a href="https://live.sympy.org/?evaluate=summation((1%2F2)**(2*n)%2C%20%5Bn%2C0%2Coo%5D)%0A%23--%0A" rel="nofollow">https://live.sympy.org/?evaluate=summation((1%2F2)**(2*n)%2C...</a>   note the answer is an exact rational number (class 'sympy.core.numbers.Rational) and not a float approximation 1.33333...<p>For a quick tutorial on how to use SymPy, check "Taming math and physics using SymPy" which is avail in printable format <a href="https://minireference.com/static/tutorials/sympy_tutorial.pdf#page=5" rel="nofollow">https://minireference.com/static/tutorials/sympy_tutorial.pd...</a> or notebook <a href="https://nbviewer.jupyter.org/github/minireference/sympytut_notebooks/blob/master/notebooks/Calculus.ipynb" rel="nofollow">https://nbviewer.jupyter.org/github/minireference/sympytut_n...</a>