A Wisdom Archive on equation

In mathematics, and particularly in analysis, an ordinary differential equation (or ODE) is an equation that involves the derivatives of an unknown function of one variable. A simple example of an ordinary differential equation is , where is an unknown function, and is its derivative. See differential calculus and integral calculus for basic calculus background. Important theorems in the field of ODEs include broad existence and uniqueness theorems and for ODEs in the plane, the Poincaré-Ben ... Including:

• Ordinary differential equation - Definition
• Ordinary differential equation - General application
• Ordinary differential equation - Existence and nature of solutions
• Ordinary differential equation - Types of differential equations with some history
• Ordinary differential equation - Linear ODEs with constant coefficients
• Ordinary differential equation - Linear ODEs with variable coefficient
• Ordinary differential equation - General solution method for first-order linear ODEs
• Ordinary differential equation - Linear PDEs
• Ordinary differential equation - First-order PDEs
• Ordinary differential equation - Singular solutions
• Ordinary differential equation - Reduction to quadratures
• Ordinary differential equation - The Fuchsian theory
• Ordinary differential equation - Lie's theory
• Ordinary differential equation - Bibliography

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In mathematics, an algebraic number relative to a field F is any element x of a given field K containing F such that x is a solution of a polynomial equation of the form: anxn + an−1xn−1 + ··· + a1x + a0 = 0 wh ... Including:

• Algebraic number - The field of algebraic numbers
• Algebraic number - Numbers defined by radicals
• Algebraic number - Algebraic integers
• Algebraic number - Special classes of algebraic number

Read more here: » Algebraic number: Encyclopedia - Algebraic number

Ad hoc is a Latin phrase which means "for this [purpose]." It generally signifies a solution that has been tailored to a specific purpose, such as a tailor-made suit, a handcrafted network protocol or a specific-purpose equation, as opposed to general solutions. It can also refer to an improvised and often impromptu event or solution "on an ad-hoc basis", as opposed to well-prepared ones. Ad hoc - Ad hoc computer network. In computer networking, ad-hoc is a connection method for wireles ... Including:

• Ad hoc - Ad hoc computer network
• Ad hoc - Ad hoc committee
• Ad hoc - Ad hoc hypothesis
• Ad hoc - Ad hoc pronunciation
• Ad hoc - Ad hoc querying

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ARIZ (russ. acronym of Алгоритм решения изобретательских задач) - Algorithm of Inventive Problems Solving is problem solving technique in form of list of (about 85) step-by-step procedures that incrementally evolves a complex problem to a point where it is simple to solve. See also Genrich Altshuller. Complex problems cannot be solved in just two steps. For those problems which are so complex, that they cannot be solved with any other tools, TRIZ includes the algorithm to fol ... Including:

• Algorithm of Inventive Problems Solving - Priciples of ARIZ
• Algorithm of Inventive Problems Solving - Framework for ARIZ
• Algorithm of Inventive Problems Solving - History

Read more here: » Algorithm of Inventive Problems Solving: Encyclopedia - Algorithm of Inventive Problems Solving

In mathematics, the catenary is the shape of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight). The slope of the chain is largest near the points of suspension because this part of the chain has the most weight pulling down on it. Toward the bottom, the slope of the chain decreases because the chain is supporting less weight. The word catenary is derived from the Latin word for "chain." The curve is also called the alysoid, funicular, and chainette. Gal ... Including:

• Catenary - The inverted catenary arch
• Catenary - Other uses of the term

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The activation energy in chemistry and biology is the threshold energy, or the energy that must be overcome in order for a chemical reaction to occur. Activation energy may otherwise be denoted as the minimum energy necessary for a specific chemical reaction to occur. The activation energy of a reaction is usually denoted by Ea. Known as the collisional model, there are three necessary requirements in order for a reaction to take place: Molecules must collide to react. If two molecules simply collide, h ... Including:

• Activation energy - Mathematical formulation
• Activation energy - Transition states

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Electrostatics is the branch of physics that deals with the forces exerted by a static (i.e. unchanging) electric field upon charged objects. Electrostatics - Overview. In electrostatics conditions of charge need not be 'static' and unchanging. Instead 'static' implies that the dynamic portion is being ignored, and we analyze frozen snapshots of the situation. In electrostatics we study e-fields, voltage, and charge but ignore any currents and magnetism which may also be present. Because of its relat ... Including:

• Electrostatics - Overview
• Electrostatics - The electrostatic approximation
• Electrostatics - Electrostatic potential
• Electrostatics - Fundamental concepts
• Electrostatics - Coulomb's law
• Electrostatics - The Electric field
• Electrostatics - Gauss's law
• Electrostatics - Poisson's equation
• Electrostatics - Laplace's equation
• Electrostatics - Static Charge generation
• Electrostatics - Charge separation by contact
• Electrostatics - Triboelectric series
• Electrostatics - Electrostatic generators
• Electrostatics - Charge neutralisation
• Electrostatics - 'Static' electricity

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In the scientific method, an experiment is a set of actions and observations, performed to support or falsify a hypothesis or research concerning phenomena. The experiment is a cornerstone in the empirical approach to knowledge. See the list of famous experiments for historically important scientific experiments. The word is derived from the Latin ex- + -periri, "from trying". Experiment - An experiment in baking. As a simple example, consider that many bakers have noticed that the amou ... Including:

• Experiment - An experiment in baking
• Experiment - Design of experiments
• Experiment - Controlled experiments
• Experiment - Natural experiments
• Experiment - Quasi-experiments
• Experiment - Field Experiments
• Experiment - Examples
• Experiment - Quotes
• Experiment - Literature

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In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of data. A number of different coefficients are used for different situations. The best known is the Pearson prod ... Including:

• Correlation - Pearson's product-moment coefficient
• Correlation - Mathematical properties
• Correlation - The sample correlation
• Correlation - Non-parametric correlation coefficients
• Correlation - Other measures of dependence among random variables
• Correlation - Copulas and correlation
• Correlation - Correlation matrices
• Correlation - Correlation does not imply causation

Read more here: » Correlation: Encyclopedia - Correlation

Determinism is the philosophical proposition that every event, including human cognition and action, is causally determined by an unbroken chain of prior occurrences. No mysterious miracles or wholly random events occur. If there has been even one indeterministic event since the beginning of time, then determinism is false. Determinism - Philosophy of determinism. The principal consequence of deterministic philosophy is that free will (except as defined in strict compatibilism) becomes an illusion. It is a ... Including:

• Determinism - Philosophy of determinism
• Determinism - The nature of determinism
• Determinism - Determinism in Western tradition
• Determinism - Determinism in Eastern tradition
• Determinism - Arguments against determinism
• Determinism - Argument from morality
• Determinism - Determinism quantum mechanics and classical physics
• Determinism - First cause
• Determinism - A multi-deterministic position
• Determinism - Modern perspectives on determinism
• Determinism - Scientific determinism and first cause
• Determinism - Determinism and generative processes

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Gravity is a force of attraction that acts between bodies that have mass. It is a physical phenomenon of fundamental importance, profoundly affecting the workings of the world around us and the universe beyond. Most familiarly, it is the gravitational attraction of the earth that endows objects with weight and causes them to fall to the ground when dropped. In fact, gravity is also the reason for the very existence of the earth, the sun and other celestial bodies; without it matter would not have coalesced into these bodies and ... Including:

• Gravity - Overview of the history of gravitational theory
• Gravity - Newton's law of universal gravitation
• Gravity - Acceleration due to gravity
• Gravity - Bodies with spatial extent
• Gravity - Vector form
• Gravity - Gravitational field
• Gravity - The Earth's gravity
• Gravity - Comparative gravities of the Earth Sun Moon and planets
• Gravity - Mathematical equations for a falling body
• Gravity - Gravitational potential
• Gravity - Acceleration relative to the rotating Earth
• Gravity - Gravity and astronomy
• Gravity - Self-gravitating system
• Gravity - Practical uses of gravity
• Gravity - Problems with Newton's theory
• Gravity - Theoretical concerns
• Gravity - Disagreement with observation
• Gravity - Newton's reservations
• Gravity - Einstein's theory of gravitation
• Gravity - Experimental tests
• Gravity - Comparison with electromagnetic force
• Gravity - Gravity and quantum mechanics
• Gravity - Alternative theories
• Gravity - Recent alternative theories
• Gravity - Historical alternative theories
• Gravity - Notes

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In astronomy, absolute magnitude is the apparent magnitude, m, an object would have if it were at a standard luminosity distance away from us. It allows the overall brightnesses of objects to be compared without regard to distance. The absolute magnitude uses the same convention as the visual magnitude, with a ~2.512 difference in brightness between step rates (because 2.5125 ≈ 100). The Milky Way, for example, has an absolute magnitude of about −20.5. So a quasar at an absolute magnitude of −25.5 is 100 ... Including:

• Absolute magnitude - Absolute Magnitude for stars and galaxies M
• Absolute magnitude - Computation
• Absolute magnitude - Apparent magnitude
• Absolute magnitude - Absolute Magnitude for planets H
• Absolute magnitude - Calculations
• Absolute magnitude - Apparent magnitude

Read more here: » Absolute magnitude: Encyclopedia - Absolute magnitude