Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]
The power of math: 17 Equations That Changed the World - a one table summary of the book by Ian Stewart FRS. Business Insider gives its interpretation of the importance of each equation. Brain pickings (2012) on this book and equations, and another extract from the book. [more inside]
Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]
How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.
Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]
There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.
Calculus of Averages - Newton and Archimedes did not possess this knowledge. No mathematics professor today can provide this knowledge and depth of understanding. Author John Gabriel maintains a blog, Friend of Wisdom, and contributes articles such as Are real numbers uncountable? to Google's Knol project.
MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.