Awesome Fractals by Silvia Cordedda -- For the ones not familiar with fractals, a fractal is an image built with math, a repetition of the same geometric module over and over, with different dimensions, according to a mathematical function.
The Weierstrass function is a function that is continuous everywhere (there are no discontinuous jumps in value), but differentiable nowhere (it is smooth nowhere). If you zoom in far enough, most continuous functions will look smooth, or at least be...
When a supersonic jet flies by, a sonic boom is produced. The booming sound is a shock wave. Shock waves occur in other situations as well, such as in plasma. Shock waves produce damage. Its mathematical modeling is a challenge. For example, how to use differentiable function theory of calculus to handle a phenomena that has discontinuity. Some brilliant ideas in the talk from Professor Yuxi Zheng. For More information please visit http://www.yu.edu
In mathematics, the directional derivative of a multivariate differentiable function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. #Glogster #DirectionalDerivative
This activity engages the students in studying several continuous, non-continuous, differentiable, and non-differentiable functions to decide what conditions must be met to guaranteed the conclusions of the mean value theorem.
Zooming in on two different functions show students the difference between function that a differentiable and those that are not. In part II students investigate a second function for differentiability.