This push to confine the study of mass behaviour to the measurements of parameters involved in differential equations has led sociology perilously close to the reduction of the word `` mass '' to mean a small group in which certain relations between all pairs of individuals in such a group can be studied.

Since the removal force is a function of coating thickness, a differential transformer pickup has been incorporated into the instrument to accurately measure film thickness.

Connes has applied his work in areas of mathematics and theoretical physics, including number theory, differential geometry and particle physics.

The differential operator must be understood to be an abstract operator, acting on kets, that has the effect of differentiating wavefunctions once the expression is projected into the position basis:

It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus.

The notation ∇ × F has its origins in the similarities to the 3 dimensional cross product, and it is useful as a mnemonic in Cartesian coordinates if we take ∇ as a vector differential operator del.

It has applications that include probability, statistics, computer vision, image and signal processing, electrical engineering, and differential equations.

Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds.

Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis and other areas.

A recent study argues that the force of Berkeley's criticisms has been overestimated ; that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof ; and that Leibniz's system for differential calculus was free of logical contradictions.

The ability of cells to do this has been proposed to arise from differential cell adhesion by Malcolm Steinberg through his Differential Adhesion Hypothesis.

The main difference is that notation symbols are differential rather than absolute, i. e. they indicate pitch change ( rise or fall ), and the musician has to deduce correctly, from the score and the note they are singing presently, which note comes next.

Since ω is a differential two-form the skew-symmetric condition implies that M has even dimension.

This function evolves according to a differential equation ( generically called the Schrödinger equation ), and this equation has solutions that follow the form of the wave equation.

Because of its enormous economic importance, CAD has been a major driving force for research in computational geometry, computer graphics ( both hardware and software ), and discrete differential geometry.

If redistribution of wealth via such mechanisms has differential efficiency

Every question and method about differential equations has a discrete equivalent for difference equations.

It has also been speculated that organisms may take advantage of differential mutation rates associated with epigenetic features to control the mutation rates of particular genes.

The use of infinitesimals to compute rates of change was developed significantly by Bhāskara II ( 1114 – 1185 ); indeed, it has been argued that many of the key notions of differential calculus can be found in his work, such as " Rolle's theorem ".

If Parkinson's disease has been excluded, the differential diagnosis or list of potential causes for Parkinsonism syndrome includes:

The constraints arise almost always because the differential equations must obey a set of boundary conditions, and the boundary has a non-trivial homotopy group, preserved by the differential equations.

Although the issue of existence and uniqueness of solutions of ordinary differential equations has a very satisfactory answer with the Picard – Lindelöf theorem, that is far from the case for partial differential equations.

The Cauchy – Kowalevski theorem states that the Cauchy problem for any partial differential equation whose coefficients are analytic in the unknown function and its derivatives, has a locally unique analytic solution.

Although α and − α produce the same differential equation, it is conventional to define different Bessel functions for these two orders ( e. g., so that the Bessel functions are mostly smooth functions of α ).

Since this is a second-order differential equation, there must be two linearly independent solutions.

For non-integer α, the functions J < sub > α </ sub >( x ) and J < sub >− α </ sub >( x ) are linearly independent, and are therefore the two solutions of the differential equation.

These linear combinations are also known as Bessel functions of the third kind ; they are two linearly independent solutions of Bessel's differential equation.

This role as a sink for CO < sub > 2 </ sub > is driven by two processes, the solubility pump and the biological pump .< ref > The former is primarily a function of differential CO < sub > 2 </ sub > solubility in seawater and the thermohaline circulation, while the latter is the sum of a series of biological processes that transport carbon ( in organic and inorganic forms ) from the surface euphotic zone to the ocean's interior.

The differential map provides the link between the two alternate definitions of the cotangent bundle given above.

In mathematics, the Cauchy – Riemann differential equations in complex analysis, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which must be satisfied if we know that a complex function is complex differentiable.

The result of the Sun's differential rotation is that the active regions always arise in two bands parallel to the equator and their extension increases during the periods of maximum of the solar cycle, while they almost disappear during each minimum.

This is an inherently global view, though, because there is no way for the differential topologist to tell whether the two objects are the same ( in this sense ) by looking at just a tiny ( local ) piece of either of them.

If one identifies C with R < sup > 2 </ sup >, then the holomorphic functions coincide with those functions of two real variables with continuous first derivatives which solve the Cauchy-Riemann equations, a set of two partial differential equations.

For the real case this corresponds to the dot product of the results of directionally differential scaling of the two vectors, with positive scale factors and orthogonal directions of scaling.

In Berlin, he published the two works which he would be most renowned for: the Introductio in analysin infinitorum, a text on functions published in 1748, and the Institutiones calculi differentialis, published in 1755 on differential calculus.

Microphotonics employs at least two different materials with a large differential index of refraction to squeeze the light down to a small size.

The column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube.

From the point of view of functional analysis, calculus is the study of two linear operators: the differential operator, and the indefinite integral operator.

Other types of differential amplifier include the fully differential amplifier ( similar to the op-amp, but with two outputs ), the instrumentation amplifier ( usually built from three op-amps ), the isolation amplifier ( similar to the instrumentation amplifier, but with tolerance to common-mode voltages that would destroy an ordinary op-amp ), and negative feedback amplifier ( usually built from one or more op-amps and a resistive feedback network ).

The amplifier's differential inputs consist of a V < sub >+</ sub > input and a V < sub >−</ sub > input, and ideally the op-amp amplifies only the difference in voltage between the two, which is called the differential input voltage.

In 1884 he recast Maxwell's mathematical analysis from its original cumbersome form ( they had already been recast as quaternions ) to its modern vector terminology, thereby reducing twelve of the original twenty equations in twenty unknowns down to the four differential equations in two unknowns we now know as Maxwell's equations.

* Interest rate parity, in finance, the notion that the differential in interest rates between two countries is equal to the differential between the forward exchange rate and the spot exchange rate