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The sphere (surface of a ball ) is a two-dimensional manifold since it can be represented by a collection of two-dimensional maps. In mathematics (specifically in differential geometry and topology ), a smooth manifold is a subset of Euclidean space which is locally the graph of a smooth (perhaps vector-valued) function. A more general topological manifold can be described as a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold. Thus, a line and a circle are one-dimensional manifolds, a plane and sphere (the surface of a ball ) are two-dimensional manifolds, and so on into high-dimensional space . More formally, every point of an n -dimensional manifold has a neighborhood homeomorphic to an open subset of the n -dimensional space R n . Although manifolds resemble Euclidean spaces near each point ("locally"), the global structure of a manifold may be more complicated.
Manifold
Math Help
This algebra reference sheet contains the following algebraic operations addition, subtraction, multiplication, and division. It also contains associative, commutative, and distributive properties. There are example of arithmetic operations as well as properties of exponents, radicals, inequalities, absolute values, complex numbers, logarithms, and polynomials. This sheet also contains many common factoring examples. There is a description of the quadratic equation as well as step by step instruction to complete the square.
Calculus Online Book
Understanding Calculus Understanding Calculus is a complete online introductory book that focuses on concepts. Integrated throughout the e-book are many engineering applications aimed at developing the student's scientific approach towards problem solving. The book has as much to do with calculus as with philosophy.Fundamental Theorem of Calculus, proof way.
(Submitted on 26 Sep 2008) Abstract: A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and Stokes' theorem are discussed, as well as the new theory of monogenic functions, which generalizes the concept of an analytic function of a complex variable to higher dimensions.
area depsribed and proofed that integral over area works. does anyone knows explanation by common sense ? That tiny fractions of space summed together works, but is there any deeper side in it by Mar 30
Math Gems
The binomial theorem expands powers of sums. The binomial coefficient is the number of ways to choose k objects from a set of n objects, regardless of order. The golden ratio, phi. The ratio of a whole to its larger part equals the ratio of the larger part to the smaller. phi is irrational and algebraic.
A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed! Background information on every chapter: see " Details ".
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Pauls Online Math Notes
Algebra Cheat Sheet - This is as many common algebra facts, properties, formulas, and functions that I could think of. There is also a page of common algebra errors included. Currently the cheat sheet is four pages long. Algebra Cheat Sheet (Reduced) - This is the same cheat sheet as above except it has been reduced so that it will fit onto the front and back of a single piece of paper. It contains all the information that the normal sized cheat sheet does. Trig Cheat Sheet - Here is a set of common trig facts, properties and formulas.Info. « hd fractals
fractalus.com A site dedicated to fractal art, information, and software. Artwork by Damien M. Jones, Sharon Webb, Alice Kelley, Linda Allison, Kerry Mitchell, Sylvie Gallet, and Margaret and Jack Valero are on display at the site; it is also the home for three fractal contests, various fractal programs, and the Infinite Fractal Loop. The Spanky... Read More »
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Introduction to Scilab
1. About Scilab Scilab is a freely distributed open source scientific software package, first developed by researchers from INRIA and ENPC, and now by the Scilab Consortium. It is similar to Matlab, which is a commercial product. Yet it is almost as powerful as Matlab.
GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable.
Octave
Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. Here are a few examples, plus a few other negations; it works for many of the others as well. In mathematics, sometimes we need to enclose expressions in brackets or braces or parentheses. Some of these work just as you'd imagine in LaTeX; type ( and ) for parentheses, [ and ] for brackets, and | and | for absolute value.