- Vector calculus - From Wikipedia, the free encyclopedia
Vector calculus (also called vector analysis) is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. It consists of a suite of formulas and problem solving techniques very useful for engineering and physics. Vector analysis has its origin in quaternion analysis, and was formulated by the American scientist, J. Willard Gibbs [1]. It concerns vector fields, which associate a vector to every point in space, and scalar fields, which associate a scalar to every point in space. For example, the temperature of a swimming pool is a scalar field: to each point we associate a scalar value of temperature. The water flow in the same pool is a vector field: to each point we associate a velocity vector.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: The summary of gradient, curl and divergence is particularly good. - Differential Equations - Wikibooks, collection of open-content textbooks
This book aims to lead the reader through the topic of differential equations, a vital area of modern mathematics and science. It is hoped that this book will provide information about the whole area of differential equations, but for the moment it will concentrate on the simpler equations.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: This stuff I found to be rather good: http://en.wikibooks.org/wiki/Differential_Equations/First_Order - Wiki - From Wikipedia, the free encyclopedia
A wiki (IPA: [ˈwɪ.kiː] <WICK-ee> or [ˈwiː.kiː] <WEE-kee>[1]) is a type of website that allows users to easily add, remove, or otherwise edit and change some available content, sometimes without the need for registration. This ease of interaction and operation makes a wiki an effective tool for collaborative authoring. The term wiki can also refer to the collaborative software itself (wiki engine) that facilitates the operation of such a website (see wiki software), or to certain specific wiki sites, including the computer science site (and original wiki), WikiWikiWeb, and the online encyclopedias such as Wikipedia. The first wiki, WikiWikiWeb, is named after the "Wiki Wiki" line of Chance RT-52 buses in Honolulu International Airport, Hawaii.
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in Computing > World Wide Web > Collaboration Tools by 9 users - Bijection - wikipedia
In mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the property that, for every y in Y, there is exactly one x in X such that f(x) = y. Alternatively, f is bijective if it is a one-to-one correspondence between those sets; i.e., both one-to-one (injective) and onto (surjective).[1] (See also Bijection, injection and surjection.)
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups - Bijection, injection and surjection - Wikipedia
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: Need to learn this. - Fixed point property - Wikipedia
In mathematics, a topological space X has the fixed point property if all continuous mappings from X to X have a fixed point.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
Note: In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function... http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29 - Fixed-point theorem - Wikipedia
In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics. The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups - Range (mathematics) - Wikipedia
In mathematics, the range of a function is the set of all "output" values produced by that function. Sometimes it is called the image, or more precisely, the image of the domain of the function....The range should not be confused with the codomain B. The range is a subset of the codomain, but is not necessarily equal to the codomain, since there may be elements of the codomain which are not elements of the range. The codomain is sometimes taken to be the range, but more often is some standard set, such as the real numbers or the complex numbers, which contains the range. A function whose range equals its codomain is called onto or surjective.
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in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups
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