curve

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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Determining the length of an irregular arc segment—also called rectification of a curve—was historically difficult. Although many methods were used for specific curves, the advent of calculus led to a general formula that provides closed form solutions in some cases. Length of an arc - Modern methods. Consider a function such that and (its derivative with respect to x) are continuous on [a,b]. The length s of the arc bounded by < ...

Including:

• Length of an arc - Modern methods
• Length of an arc - Historical methods
• Length of an arc - Ancient
• Length of an arc - 1600s
• Length of an arc - Integral form

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Walter William (Billy) Pierce (born April 2, 1927 in Detroit, Michigan) is a former starting pitcher in Major League Baseball. From 1945 through 1964, Pierce played for the Detroit Tigers (1945, 1948), Chicago White Sox (1949-61) and San Francisco Giants (1962-64). A diminutive left handed listed at 5 ft 10 in (1.78 m), 160 pounds (73 kg), Pierce has been considered one of the greatest pitchers in Chicago White Sox history. Billy Pierce - Career. Having never thrown a pitch in the minor leagues, Pier ...

Including:

• Billy Pierce - Career
• Billy Pierce - Highlights
• Billy Pierce - Inside the numbers

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Fundamental theorem | Function | Limits of functions | Continuity | Mean value theorem | Vector calculus | Tensor calculus Product rule | Quotient rule | Chain rule | Implicit differentiation | Taylor's theorem | Related rates Integration by substitution | Integration by parts | Integration by trigonometric substitution | Integration by disks | Integration by cylindrical shells | Improper integrals | Lists of integrals Integral and differential calculus is a central branch of mathematics, developed from algebra an ...

Including:

• Calculus - Differential calculus
• Calculus - Integral calculus
• Calculus - Foundations
• Calculus - Fundamental theorem of calculus
• Calculus - Applications
• Calculus - History
• Calculus - Footnotes

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In mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of 'expansion' and 'contraction'. Anosov diffeomorphisms were introduced by D. V. Anosov, who proved that their behaviour was in an appropriate sense generic (when they exist at all). Three closely related definitions must be distinguished: If a differentiable map f on ...

Including:

• Anosov diffeomorphism - Anosov flow on tangent bundles of Riemann surfaces
• Anosov diffeomorphism - Lie vector fields
• Anosov diffeomorphism - Anosov flow
• Anosov diffeomorphism - Geometric interpretation of the Anosov flow
• Anosov diffeomorphism - Historical references
• Anosov diffeomorphism - Modern references

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An Angle (from the Lat. angulus, a corner, a diminutive, of which the primitive form, angus, does not occur in Latin; cognate are the Lat. angere, to compress into a bend or to strangle, and the Greek ἀγκύλος (angulοs) crooked, curved; both connected with the Aryan or Indo-European root ank-, to bend) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. Angles provide a means of expressing the difference ...

Including:

• Angle - Units of measure for angles
• Angle - Conventions on measurement
• Angle - Types of angles
• Angle - Some facts
• Angle - A formal definition
• Angle - Angles in different contexts
• Angle - Angles in Riemannian geometry
• Angle - Angles in astronomy
• Angle - Angles in maritime navigation

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Gottfried Wilhelm von Leibniz (also Leibnitz) (July 1 (June 21 Old Style) 1646, Leipzig – November 14, 1716, Hanover) was a German polymath, deemed a genius in his lifetime and since, and the last true polyhistor. Trained as a lawyer and active as a diplomat and librarian, he wrote on philosophy, science, mathematics, theology, history, and comparative philology, even writing verse. Through his service to two major German noble houses, he played a major role in the European ...

Including:

• Gottfried Leibniz - Life
• Gottfried Leibniz - Early life and education
• Gottfried Leibniz - Career
• Gottfried Leibniz - Writings
• Gottfried Leibniz - Posthumous reputation
• Gottfried Leibniz - Philosopher
• Gottfried Leibniz - Metaphysics
• Gottfried Leibniz - Theodicy and optimism
• Gottfried Leibniz - Symbolic thought
• Gottfried Leibniz - Characteristica Universalis Universal characteristic and Calculus Ratiocinator
• Gottfried Leibniz - Formal logic
• Gottfried Leibniz - Mathematician
• Gottfried Leibniz - Topology
• Gottfried Leibniz - The dispute over who first invented the calculus
• Gottfried Leibniz - Science and technology
• Gottfried Leibniz - The vis viva
• Gottfried Leibniz - Information technology
• Gottfried Leibniz - Philology
• Gottfried Leibniz - The Sinophile
• Gottfried Leibniz - Works
• Gottfried Leibniz - Secondary literature
• Gottfried Leibniz - Quotes

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In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way one follows the curve. Spiral - Two-dimensional spirals. A two-dimensional spiral may be described using polar coordinates by saying that the radius r is a continuous monotonic function of θ. The circle would be regarded as a degenerate case (the function not being strictly monotonic, but rather constant). Some of the more import ...

Including:

• Spiral - Two-dimensional spirals
• Spiral - Three-dimensional spirals
• Spiral - Spherical spiral

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Benoit Paul Émile Clapeyron (February 26, 1799 - January 28, 1864) was an French engineer and physicist, one of the founders of thermodynamics. Émile Clapeyron - Life. Born in Paris, Clapeyron studied at the École polytechnique and the École des Mines, before leaving for Saint Petersburg in 1820 to teach at the École des Travaux Publics. He returned to Paris only after the Revolution of July 1830, supervising the construction of the first railway line connecting Paris to Versailles and Saint-Ger ...

Including:

• Émile Clapeyron - Life
• Émile Clapeyron - Work
• Émile Clapeyron - Thermodynamics
• Émile Clapeyron - Other work
• Émile Clapeyron - Honors

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A line, or straight line, can be described as an (infinitely) thin, (infinitely) long, perfectly straight curve (the term curve in mathematics includes "straight curves"). In Euclidean geometry, exactly one line can be found that passes through any two points. The line provides the shortest connection between the points. Three or more points that lie on the same line are called collinear. Two different lines can either be parallel and never meet, or may intersect at one and only one point. Two planes intersect in at most one line). Lines in a Cartesian plane can be describe ...

Including:

• Line mathematics - Line segment
• Line mathematics - Ray

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In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. Vector fields are often used in physics to model for example the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point. In the rigorous mathematical treatment, (tangent) vector fields are defined on manifolds as sections of the manifold's tangent bundle. V ...

Including:

• Vector field - Definition
• Vector field - Notes
• Vector field - Examples
• Vector field - Gradient field
• Vector field - Central field
• Vector field - Curve integral
• Vector field - Flow curves
• Vector field - Difference between scalar and vector field
• Vector field - Example 3

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In mathematics, a continuous function is a function in which arbitrarily small changes in the input produce arbitrarily small changes in the output. If small changes in the input can produce a broken jump in the changes of the output (or the value of the output is not defined), the function is said to be discontinuous (or to have a discontinuity). The context in this entry is real-valued functions on the real domain or on topological or metric spaces other than the complex numbers; for complex-valued functions see comple ...

Including:

• Continuous function - Real-valued continuous functions
• Continuous function - Epsilon-delta definition
• Continuous function - Heine definition of continuity
• Continuous function - Examples
• Continuous function - Facts about continuous functions
• Continuous function - Continuous functions between metric spaces
• Continuous function - Continuous functions between topological spaces
• Continuous function - Continuous functions between partially ordered sets

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A contour line (also level set, isopleth, isogram or isarithm) for a function of two variables is a curve connecting points where the function has a same particular value. A contour map is a map showing contour lines. The gradient of the function is always perpendicular to the contour lines. When the lines are close together the gradient is large: the variation is steep. If adjacent contour lines are of the same width, the direction of the gradient cannot be determined from the contour lines alone. However if contour lines rotate through three or more widths the direction of the grad ...

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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 mathematics, a conic section (or just conic) is a curve formed by intersecting a cone (more precisely, a right circular conical surface) with a plane. The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties. Conic section - Types of conics. Two well-known conics are the circle and the ellipse. These arise when the intersection of cone and plane is a closed curve. The circle is a special case of the ellipse in which ...

Including:

• Conic section - Types of conics
• Conic section - Conics as point loci
• Conic section - Eccentricity
• Conic section - Conics in analytic geometry
• Conic section - Semi-latus rectum and polar coordinates
• Conic section - Properties
• Conic section - Applications
• Conic section - Dandelin spheres
• Conic section - Derivation
• Conic section - Derivation of the parabola
• Conic section - Derivation of the ellipse
• Conic section - Derivation of the hyperbola

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A cone is a basic geometrical shape: see cone (solid). Several things have also been called "cones" on account of their shape: A volcanic cone is a mountain formed by material ejected from a volcanic vent. In relativity, the light cone of an event consists of all spacetime events that can interact with it. The scaly fruit-like reproductive bodies of certain plants, especially conifers and cycads, are called cones: see conifer cone. In vertebrate anatomy, a cone cel ...

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A chord of a curve is a geometric line segment whose endpoints both lie on the curve. A secant or a secant line is the line extension of a chord. Chord geometry - Chords of a circle. Among properties of chords of a circle are the following: Chords are equidistant from the center if and only if their lengths are equal. A chord's perpendicular bisector passes the center. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then ...

Including:

• Chord geometry - Chords of a circle
• Chord geometry - Chords in Trigonometry

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Work (abbreviated W) is the energy transferred by a force to a moving object. Work is a scalar quantity, but it can be positive or negative. Work is associated with a change in energy, but not all changes in energy can be readily analysed in terms of work. In addition, not all forces do work. For instance, a centripetal force in uniform circular motion does not transfer energy; the kinetic energy of the object undergoing the motion remains constant. Mechanical work - Definition. Note: Reade ...

Including:

• Mechanical work - Definition
• Mechanical work - Units
• Mechanical work - Simpler formulae
• Mechanical work - Types of work
• Mechanical work - PV work
• Mechanical work - Mechanical energy
• Mechanical work - Conservation of mechanical energy

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Chloracne is an acne-like eruption of blackheads, cysts, and pustules associated with over-exposure to certain halogenic aromatic hydrocarbons, such as chlorinated dioxins and dibenzofurans. The lesions are most frequently found on the cheeks, behind the ears, in the armpits and groin region. The condition was first described in German industrial workers in 1897 by Von Bettman, and was initially believed to be caused by exposure to toxic chlorine (hence the name "chloracne"). It was only in the mid-1950s that chloracne was associated with aromatic hydrocarbons[1]. The substances that may cause chloracn ...

Including:

• Chloracne - Etiology and progression
• Chloracne - Treatment
• Chloracne - Related conditions
• Chloracne - Notable cases

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Charles Wilber(n) "Bullet" Rogan, a.k.a. "Bullets" or "Bullet Joe" (July 28, 1893 - March 4, 1967), born in Oklahoma City, Oklahoma, played baseball in the United States Army and the Negro Leagues from 1911 to 1938. He won more games than any other pitcher in Negro League history, and was elected to the National Baseball Hall of Fame in 1998. Considered one of the greatest pitchers of his day, Rogan relied on a sharp curve that broke almost straight down, an excellent fastball, and a no-windup delivery. Early in his career he o ...

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