Thursday, November 12th, 2009
How to Identify Fractals
Description
A detailed tutorial on fractals. Step by step tutorial including several examples and a helpful visual example of fractals for reference.
Overview
A fractal is a geometric shape that can easily be split into parts. Each part is really just a small version of the whole. Fractals are often very rough or fractured looking shapes, which is how they got their name. The common features of a fractal is that it has a fine structure at small scales, it is an irregular shape, it is self-similar, and it has a recursive definition as well as a simple one. One of the most famous and well-known fractals is the Mandelbrot set.
Tags: fine, fractal, fractured, Geometry, irregular, Mandelbrot, parts, resursive, rough, scale, self, self-similar, shape, similar, simple, small, structure, version
Posted in Geometry | No Comments »
Thursday, November 5th, 2009
Overview of the Dominated Convergence Theorem
Description
A detailed tutorial on the dominated convergence theorem. Step by step tutorial including several examples of the dominated convergence theorem for reference.
Overview
Unlike the monotone convergence theorem, the dominated convergence theorem only has one form. The official name of the theorem is Lebesgue’s Dominated Convergence Theorem, but most people just call it the dominated convergence theorem. It is considered to be a special version of the Fatou-Lebesque theorem, so Fatou’s lemma is used in direct proofs of this theorem. This theorem is also closely related to the bounded convergence theorem.
Tags: bounded proof, Calculus, convergence, direct, dominated, Fatou, form, Lebesque, lemma, monotone, special, theorem, version
Posted in Calculus | No Comments »
