Solving Newton’s Law of Cooling Using Maxima

In my previous post, I introduced setting up Maxima, a powerful symbolic computation system, to work with Emacs. This post provides a real example of using Maxima.

I was motivated by this interesting post, introducing the use of Newton’s Law of Cooling in the ranking algorithm of Reddit.  This post (in Chinese) explains more about the derivation of Newton’s Law. I believe the author is good at calculus.  But how if you forgot calculus?  In this case, Maxima would save you!  The following figure illustrates how I use Maxima to derive the Law:

Using Maxima with Mac OS X in Emacs imaxima Mode

Maxima is a computer algebra system written in common lisp.  For me, it is an alternative to Mathematica. To install maxima with Mac OS X, I use Homebrew:

brew update && brew upgrade && brew install maxima

Then, open the ~/.emacs file and add two lines to load imaxima mode:

(add-to-list 'load-path "/usr/local/Cellar/maxima/5.25.1/share/maxima/5.25.1/emacs")
(require 'maxima)

In Emacs, launch Maxima in imaxima mode by M-x imaxima. Then you can do what ever you want!