Sometimes you’re lazy. You’re sitting there at your computer surfing the internet, hanging ten minutes out to the eternal, when you get sucked back out of your wormhole by a tedious task that your boss wants you to perform. They hand you a little slip of paper with some algebraic symbols on it and say, “Hey bud, you … More Mathematical Induction

This weeks blog post is going to build off of last week’s blog post about linearization. Today we are going to investigate an algorithm devised by Isaac Newton and Joseph Raphson that allows people and calculators to estimate the roots (translation: where ) of functions with startling precision. The first step of Newton’s method is to … More Newton’s Method

A simple way to estimate the value of a function at a certain point is to use linear approximation.  Check out the graph of below. It’s really easy to evaluate this function at , but it’s harder to evaluate this function around . With really complicated functions it is difficult and sometimes impossible to compute … More Linearization

This week I started taking Robert Ghrist’s Calculus: Single Variable on Coursera. The class started on an atypical topic: Taylor Series. In this post I’d like to answer a very basic question: Why are Taylor Series important? Answer: Taylor Series are important because they allow you to approximate functions. I’m sure there are many other reasons … More Taylor Series