We can abstract the derivative by saying the derivative of the function f (x) = x 2 is 2x. We can also make a generalized definition of the derivative using Zeno’s arrow example: ...

In the late 19th century, Karl Weierstrass invented a fractal-like function that was decried as nothing less than a “deplorable evil.” In time, it would transform the foundations of mathematics.

Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...

We generalize the notions of the fractional g-integral and g-derivative by introducing variable lower limit of integration. We discuss some properties and their relations. Finally, we give a ...