Differential
Encyclopedia
Mathematics
- Differential (mathematics)Differential (mathematics)In mathematics, the term differential has several meanings.-Basic notions:* In calculus, the differential represents a change in the linearization of a function....
comprises multiple related meanings of the word, both in calculus and differential geometry, such as an infinitesimal change in the value of a function - Differential algebraDifferential algebraIn mathematics, differential rings, differential fields, and differential algebras are rings, fields, and algebras equipped with a derivation, which is a unary function that is linear and satisfies the Leibniz product law...
- Differential calculusDifferential calculusIn mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus....
- Differential of a functionDifferential of a functionIn calculus, the differential represents the principal part of the change in a function y = ƒ with respect to changes in the independent variable. The differential dy is defined bydy = f'\,dx,...
, represents a change in the linearization of a function - Differential (infinitesimal) (e.g. dx, dy, dt etc.) are interpreted as infinitesimals
- Differential topologyDifferential topologyIn mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.- Description :...
, in multivariable calculus, the differential of a smooth map between Euclidean spaces or differentiable manifolds is the approximating linear map between the tangent spaces, called pushforward (differential)
- Differential of a function
- Differential geometry, exterior differential, or exterior derivativeExterior derivativeIn differential geometry, the exterior derivative extends the concept of the differential of a function, which is a 1-form, to differential forms of higher degree. Its current form was invented by Élie Cartan....
, is a generalization to differential formDifferential formIn the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better definition for integrands in calculus...
s of the notion of differential of a function on a differentiable manifold - Differential (coboundary), in homological algebra and algebraic topology, one of the maps of a cochain complex
- Differential cryptanalysisDifferential cryptanalysisDifferential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultant difference at the output...
, a pair consisting of the difference, usually computed by XOR, between two plaintexts, and the difference of the corresponding ciphertexts
Natural sciences and engineering
- Differential (mechanical device), as part of a powertrain and car, the device that allows each of the driving wheels to rotate at different speeds
- Limited slip differentialLimited slip differentialA limited slip differential is a type of differential gear arrangement that allows for some difference in angular velocity of the output shafts, but imposes a mechanical bound on the disparity...
- Electronic differentialElectronic DifferentialThe main purpose of the electronic differential is to replace the mechanical differential in multi-drive systems, providing the required torque for each driving wheel and allowing different wheel speeds. When cornering, the inner and outer wheels rotate at different speeds, because the inner...
, an electric motor controller which substitutes its mechanical counterpart with significant advantages in electric vehicle application - Differential signalingDifferential signalingDifferential signaling is a method of transmitting information electrically by means of two complementary signals sent on two separate wires. The technique can be used for both analog signaling, as in some audio systems, and digital signaling, as in RS-422, RS-485, Ethernet , PCI Express and USB...
, in electronics, applies to a method of transmitting electronic signals over a pair of wires to improve noise immunity
Social sciences
- SemanticSemantic differentialSemantic differential is a type of a rating scale designed to measure the connotative meaning of objects, events, and concepts. The connotations are used to derive the attitude towards the given object, event or concept.-Semantic differential:...
and structural differentialStructural differentialThe Structural differential is a physical chart or three-dimensional model illustrating the abstracting processes of the human nervous system. In one form, it looks like a pegboard with tags. Created by Alfred Korzybski, and awarded a U.S. patent on May 26, 1925, it is used as a training device in...
s in psychology - Quality spread differentialQuality Spread DifferentialQuality Spread Differential arises during an interest rate swap in which two parties of different levels of creditworthiness experience different levels of interest rates of debt obligations...
, in finance - Compensating differentialCompensating differentialCompensating differential is a term used in labor economics to analyze the relation between the wage rate and the unpleasantness, risk, or other undesirable attributes of a particular job...
, in labor economics
Medicine
- Differential diagnosisDifferential diagnosisA differential diagnosis is a systematic diagnostic method used to identify the presence of an entity where multiple alternatives are possible , and may also refer to any of the included candidate alternatives A differential diagnosis (sometimes abbreviated DDx, ddx, DD, D/Dx, or ΔΔ) is a...
, the characterization of the underlying cause of pathological states based on specific tests - Differential WBC countComplete blood countA complete blood count , also known as full blood count or full blood exam or blood panel, is a test panel requested by a doctor or other medical professional that gives information about the cells in a patient's blood...
,the enumeration of each type of white blood cells either manually or using automated analyzers
Other
- Differential hardeningDifferential hardeningDifferential hardening is a method used in forging swords and knives to increase the hardness of the edge without making the whole blade brittle. To achieve this, the edge is cooled more rapidly than the spine by adding a heat insulator to the spine before quenching. Clay or another material is...
, in metallurgy - Differential rotationDifferential rotationDifferential rotation is seen when different parts of a rotating object move with different angular velocities at different latitudes and/or depths of the body and/or in time. This indicates that the object is not solid. In fluid objects, such as accretion disks, this leads to shearing...
, in astronomy - Differential centrifugationDifferential centrifugationDifferential centrifugation is a common procedure in microbiology and cytology used to separate certain organelles from whole cells for further analysis of specific parts of cells. In the process, a tissue sample is first homogenised to break the cell membranes and mix up the cell contents...
, in cell biology - Differential scanning calorimetryDifferential scanning calorimetryDifferential scanning calorimetry or DSC is a thermoanalytical technique in which the difference in the amount of heat required to increase the temperature of a sample and reference is measured as a function of temperature. Both the sample and reference are maintained at nearly the same temperature...
, in materials science - Differential signalling, in communications
- Differential GPSDifferential GPSDifferential Global Positioning System is an enhancement to Global Positioning System that provides improved location accuracy, from the 15-meter nominal GPS accuracy to about 10 cm in case of the best implementations....
, in technology