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61 relations: Absement, Acceleration, Analytical Society, Antiderivative, Augustus De Morgan, ∂, Cartesian coordinate system, Chain rule, Cross product, Curl (mathematics), D'Alembert operator, Del, Dependent and independent variables, Derivative, Differential calculus, Differential equation, Differential operator, Divergence, Dot product, Euclidean space, Exterior derivative, Function (mathematics), Gottfried Wilhelm Leibniz, Gradient, Hessian matrix, Infinitesimal, Integral, Integral symbol, Inverse function, Isaac Newton, Jacobian matrix and determinant, Joseph-Louis Lagrange, Laplace operator, Leibniz–Newton calculus controversy, Leonhard Euler, Linear differential equation, Louis François Antoine Arbogast, Mathematical notation, Mathematical physics, Maxwell relations, Method of Fluxions, Minkowski space, Multivariable calculus, Nabla symbol, Non-standard analysis, Partial derivative, Physics, Prime (symbol), Product rule, Roman numerals, ..., Scalar field, Scalar multiplication, Second derivative, Tensor field, Thermodynamics, Third derivative, Time, Vector calculus, Vector field, Velocity, William Rowan Hamilton. Expand index (11 more) »
Absement
In kinematics, absement (or absition) is a measure of sustained displacement of an object from its initial position, i.e. a measure of how far away and for how long.
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Acceleration
In physics, acceleration is the rate of change of velocity of an object with respect to time.
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Analytical Society
The Analytical Society was a group of individuals in early-19th-century Britain whose aim was to promote the use of Leibnizian notation for differentiation in calculus as opposed to the Newton notation for differentiation.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.
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∂
The character ∂ (HTML element: ∂ or ∂, Unicode: U+2202) or \partial is a stylized d mainly used as a mathematical symbol to denote a partial derivative such as \frac (read as "the partial derivative of z with respect to x").
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Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
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Chain rule
In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions.
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Cross product
In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space \left(\mathbb^3\right) and is denoted by the symbol \times.
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Curl (mathematics)
In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space.
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D'Alembert operator
In special relativity, electromagnetism and wave theory, the d'Alembert operator (represented by a box: \Box), also called the d'Alembertian, wave operator, or box operator is the Laplace operator of Minkowski space.
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Del
Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential calculus
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.
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Differential equation
A differential equation is a mathematical equation that relates some function with its derivatives.
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Differential operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator.
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Divergence
In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.
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Dot product
In mathematics, the dot product or scalar productThe term scalar product is often also used more generally to mean a symmetric bilinear form, for example for a pseudo-Euclidean space.
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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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Exterior derivative
On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Gradient
In mathematics, the gradient is a multi-variable generalization of the derivative.
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Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Integral
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.
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Integral symbol
The integral symbol: is used to denote integrals and antiderivatives in mathematics.
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Inverse function
In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.
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Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
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Jacobian matrix and determinant
In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space.
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Leibniz–Newton calculus controversy
The calculus controversy (often referred to with the German term Prioritätsstreit, meaning "priority dispute") was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates) over who had first invented the mathematical study of change, calculus.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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Louis François Antoine Arbogast
Louis François Antoine Arbogast (4 October 1759 – 8 April 1803) was a French mathematician.
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Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas.
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Mathematical physics
Mathematical physics refers to the development of mathematical methods for application to problems in physics.
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Maxwell relations
Flow chart showing the paths between the Maxwell relations. ''P'': pressure, ''T'': temperature, ''V'': volume, ''S'': entropy, ''α'': coefficient of thermal expansion, ''κ'': compressibility, ''CV'': heat capacity at constant volume, ''CP'': heat capacity at constant pressure. Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials.
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Method of Fluxions
Method of Fluxions is a book by Isaac Newton.
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Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.
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Multivariable calculus
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.
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Nabla symbol
∇ The nabla symbol The nabla is a triangular symbol like an inverted Greek delta:Indeed, it is called anadelta (ανάδελτα) in Modern Greek.
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Non-standard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
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Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Prime (symbol)
The prime symbol (′), double prime symbol (&Prime), triple prime symbol (‴), quadruple prime symbol (⁗) etc., are used to designate units and for other purposes in mathematics, the sciences, linguistics and music.
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Product rule
In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.
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Roman numerals
The numeric system represented by Roman numerals originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages.
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Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space – possibly physical space.
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Scalar multiplication
In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra (or more generally, a module in abstract algebra).
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Second derivative
In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of.
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Tensor field
In mathematics and physics, a tensor field assigns a tensor to each point of a mathematical space (typically a Euclidean space or manifold).
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Thermodynamics
Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.
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Third derivative
In calculus, a branch of mathematics, the third derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing, used to define aberrancy.
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Time
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future.
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Vector calculus
Vector calculus, or vector analysis, is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3.
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Vector field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.
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Velocity
The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time.
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William Rowan Hamilton
Sir William Rowan Hamilton MRIA (4 August 1805 – 2 September 1865) was an Irish mathematician who made important contributions to classical mechanics, optics, and algebra.
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References
[1] https://en.wikipedia.org/wiki/Notation_for_differentiation
