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39 relations: Antiderivative, Bridgman's thermodynamic equations, Chain rule, Closed and exact differential forms, Conservative vector field, Differentiable function, Differential (infinitesimal), Differential (mathematics), Differential calculus, Differential form, Differential geometry, Differential of a function, Differential topology, Enthalpy, Entropy, Exact differential equation, Gibbs free energy, Heat, Helmholtz free energy, If and only if, Inexact differential, Inexact differential equation, Integrating factor, Internal energy, Inverse functions and differentiation, Mechanical engineering, Multivariable calculus, Partial derivative, Pathological (mathematics), Permutation, Scalar field, Simply connected space, State function, Symmetry of second derivatives, Symplectic vector space, Thermodynamic equations, Thermodynamics, Triple product rule, Work (thermodynamics).
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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Bridgman's thermodynamic equations
In thermodynamics, Bridgman's thermodynamic equations are a basic set of thermodynamic equations, derived using a method of generating a large number of thermodynamic identities involving a number of thermodynamic quantities.
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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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Closed and exact differential forms
In mathematics, especially vector calculus and differential topology, a closed form is a differential form α whose exterior derivative is zero (dα.
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Conservative vector field
In vector calculus, a conservative vector field is a vector field that is the gradient of some function, known in this context as a scalar potential.
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Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
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Differential (infinitesimal)
The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity.
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Differential (mathematics)
In mathematics, differential refers to infinitesimal differences or to the derivatives of functions.
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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 form
In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.
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Differential geometry
Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.
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Differential of a function
In calculus, the differential represents the principal part of the change in a function y.
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Differential topology
In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds.
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Enthalpy
Enthalpy is a property of a thermodynamic system.
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Entropy
In statistical mechanics, entropy is an extensive property of a thermodynamic system.
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Exact differential equation
In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering.
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Gibbs free energy
In thermodynamics, the Gibbs free energy (IUPAC recommended name: Gibbs energy or Gibbs function; also known as free enthalpy to distinguish it from Helmholtz free energy) is a thermodynamic potential that can be used to calculate the maximum of reversible work that may be performed by a thermodynamic system at a constant temperature and pressure (isothermal, isobaric).
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Heat
In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions.
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Helmholtz free energy
In thermodynamics, the Helmholtz free energy is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature and volume.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Inexact differential
An inexact differential or imperfect differential is a specific type of differential used in thermodynamics to express the path dependence of a particular differential.
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Inexact differential equation
An inexact differential equation is a differential equation of the form The solution to such equations came with the invention of the integrating factor by Leonhard Euler in 1739.
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Integrating factor
In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials.
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Internal energy
In thermodynamics, the internal energy of a system is the energy contained within the system, excluding the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields.
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Inverse functions and differentiation
In mathematics, the inverse of a function y.
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Mechanical engineering
Mechanical engineering is the discipline that applies engineering, physics, engineering mathematics, and materials science principles to design, analyze, manufacture, and maintain mechanical systems.
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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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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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Pathological (mathematics)
In mathematics, a pathological phenomenon is one whose properties are considered atypically bad or counterintuitive; the opposite is well-behaved.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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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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Simply connected space
In topology, a topological space is called simply connected (or 1-connected, or 1-simply connected) if it is path-connected and every path between two points can be continuously transformed (intuitively for embedded spaces, staying within the space) into any other such path while preserving the two endpoints in question.
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State function
In thermodynamics, a state function or function of state is a function defined for a system relating several state variables or state quantities that depends only on the current equilibrium state of the system, for example a gas, a liquid, a solid, crystal, or emulsion.
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Symmetry of second derivatives
In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) refers to the possibility under certain conditions (see below) of interchanging the order of taking partial derivatives of a function of n variables.
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Symplectic vector space
In mathematics, a symplectic vector space is a vector space V over a field F (for example the real numbers R) equipped with a symplectic bilinear form.
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Thermodynamic equations
Thermodynamics is expressed by a mathematical framework of thermodynamic equations which relate various thermodynamic quantities and physical properties measured in a laboratory or production process.
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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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Triple product rule
The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial derivatives of three interdependent variables.
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Work (thermodynamics)
In thermodynamics, work performed by a system is the energy transferred by the system to its surroundings, that is fully accounted for solely by macroscopic forces exerted on the system by factors external to it, that is to say, factors in its surroundings.
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Full differential, Reciprocity relation.
References
[1] https://en.wikipedia.org/wiki/Exact_differential
