Divergence and convergence. What is divergence in the Forex market? Divergence - this is a common topic divergence

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Meaning of the word divergence

divergence in the crossword dictionary

Dictionary of medical terms

divergence (divergentia; di- + lat. vergo to be directed, to tend) in biology

divergence of characters in the process of evolution, leading to the emergence of morphological and functional differences between groups of organisms that arose from common ancestors.

Explanatory dictionary of the Russian language. D.N. Ushakov

divergence

divergence, w. (French divergence) (scientific). Divergence in signs.

New explanatory dictionary of the Russian language, T. F. Efremova.

divergence

and. Divergence, branching, demarcation.

Encyclopedic Dictionary, 1998

divergence

DIVERGENCE (from the medieval Latin divergo - I deviate) in biology is the divergence of characteristics and properties in initially close groups of organisms in the course of evolution. The result of living in different conditions and unequally directed natural selection. The concept of divergence was introduced by Charles Darwin to explain the diversity of varieties of cultivated plants, breeds of domestic animals and biological species. Wed. Convergence.

divergence

in linguistics -

the transformation of variants of a linguistic unit (usually variants of a phoneme) into independent units due to the elimination of the conditions that determined the variation.

Differences in the implementation of one linguistic unit, e.g. Phonemes.

The delimitation of dialects or variants of one language and their transformation into independent languages. Contrasted with convergence.

divergence

in mathematics - a scalar field characterizing the density of sources of a given vector field a(P); div notation a. Thus, the divergence of the velocity field in the steady motion of an incompressible fluid characterizes the intensity of the source at a given point.

Divergence

Divergence- a differential operator that maps a vector field onto a scalar one, “how much the incoming and outgoing field from a small neighborhood of a given point diverges,” more precisely, how much the incoming and outgoing flows diverge.

If we take into account that an algebraic sign can be assigned to a flow, then there is no need to take into account the incoming and outgoing flows separately; everything will be automatically taken into account when summing taking into account the sign. Therefore, we can give a shorter definition of divergence:

divergence is a linear differential operator on a vector field that characterizes the flow of a given field through the surface of a sufficiently small neighborhood of each internal point of the domain of definition of the field.

The divergence operator applied to the field $\ \mathbf F$ is denoted as

$\ \operatorname(div) \mathbf F$

$\ \nabla \cdot \mathbf F$.

Divergence (biology)

Divergence(in biology) - divergence of characters and properties in initially close groups of organisms during evolution, the result of living in different conditions and unequally directed natural selection

Divergence (linguistics)

Divergence(in linguistics) - a process of linguistic change that causes the separation of variants of one linguistic unit and the transformation of these variants into independent units, or the emergence of new variants in an already existing linguistic unit. When applied to linguistic entities, the term divergence denotes the historical divergence of two or more related languages, dialects, or variants of the literary norms of one language. The process of divergence is contrasted with the closely related process of linguistic convergence.

Examples of the use of the word divergence in literature.

In the process of subsequent evolution, there was mainly divergence types of the animal world and the replacement of the original low-organized primitive forms with more highly organized ones through even greater differentiation of the structure and functions of the tissues and organs of organisms.

They are reflected in solving a number of problems: divergence troglodytids and hominids, necrophagy, shortening of history, a special mechanism of inter-individual communication between prehumans, the place and role of language-words in the restructuring of the entire system of psychophysiological reactions and a number of others.

This wouldn't happen if divergence from the very beginning was accompanied by the demarcation of areas.

This kind of divergence will pose very serious problems to people in the near future.

He followed the sound, reached a narrow corridor and then made out the first words: Divergence de is equal to four pi po.

This conceptual turn was decisive: it opens up a field of study where each fact, established, isolated, and then opposed to a certain totality, could take a place in the entire series of events, convergence or divergence which would be, in principle, measurable.

Let us only note that the main reason divergence their systemic organization was the need to follow the laws of the Development of Matter.

Biological problem divergence paleoanthropes and neoanthropes, which proceeds quickly, is the most acute and relevant in the entire complex of questions about the beginning of human history facing modern science.

But we will turn our main attention to psychopathology as another source that can lead the researcher into the depths of that divergence, with which the human race began.

We cannot use what is said in this section to reconstruct the exact scheme divergence troglodytids and hominids, which began in the world of late paleoanthropes and ended only somewhere during the transition from fossil neoanthropes to modern ones.

My task is not to anticipate these future paleopsychological studies, but only to pose, along with the previous ones, this part of the problem divergence troglodytid and hominid.

After all, differences deepen only in the process divergence varieties, but at first they are insignificant.

To begin the analysis, it is only clear that, being a biological process, it at the same time had something that distinguished it from any other divergence in living nature.

But it is in this segment that almost the entire mystery is contained. divergence who gave birth to people.

From these facts, the conclusion is clear: neoanthropes settled to the farthest edges of the habitable world especially early in the era divergence with paleoanthropes.

divergence is a linear differential operator on a vector field that characterizes the flow of a given field through the surface of a sufficiently small (under the conditions of a specific problem) neighborhood of each internal point of the domain of definition of the field.

Divergence operator applied to a field F (\displaystyle \\mathbf (F) ), denoted as

div ⁡ F (\displaystyle \\operatorname (div) \mathbf (F) ) ∇ ⋅ F (\displaystyle \\nabla \cdot \mathbf (F) ).

Encyclopedic YouTube

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✪ What is divergence in Forex?

✪ Operator Nabla in 10 minutes. Gradient, Divergence, Rotor, Laplacian

✪ MACD. Convergence and Divergence

✪ Maxwell's equations. Lecture 2: field flow, divergence.

✪ Divergence and convergence in Forex. Where to open trades?

Subtitles

Definition

The definition of divergence looks like this:

div F = lim V → 0 Φ F V (\displaystyle \operatorname (div) \,\mathbf (F) =\lim _(V\rightarrow 0)((\mathit (\Phi ))_(\ \mathbf (F ) ) \over V)) div F = ∇ ⋅ F (\displaystyle \operatorname (div) \,\mathbf (F) =\nabla \cdot \mathbf (F) \ \ \ )

Multidimensional, as well as two-dimensional and one-dimensional, divergence is defined in Cartesian coordinates in spaces of the corresponding dimension in a completely similar way (in the upper formula only the number of terms changes, while the lower one remains the same, implying the nabla operator of the appropriate dimension).

Physical interpretation

From the point of view of physics (both in the strict sense and in the sense of the intuitive physical image of a mathematical operation), the divergence of a vector field is an indicator of the extent to which a given point in space (more precisely, a fairly small neighborhood of the point) is the source or sink of this field:

div F > 0 (\displaystyle \operatorname (div) \,\mathbf (F) >0)- the field point is the source; div F< 0 {\displaystyle \operatorname {div} \,\mathbf {F} <0} - the field point is a drain; div F = 0 (\displaystyle \operatorname (div) \,\mathbf (F) =0)- there are no sinks and sources, or they compensate each other.

A simple, although perhaps somewhat schematic, example can be a lake (for simplicity - a constant unit depth with an everywhere horizontal velocity of water flow, independent of depth, thus giving a two-dimensional vector field in two-dimensional space). If you want to have a more realistic picture, then you can consider the horizontal projection of velocity integrated over the vertical spatial coordinate, which will give the same picture of a two-dimensional vector field in two-dimensional space, and the picture will not be qualitatively different for our purposes from the simplified first one, but quantitatively it will be generalization (very realistic). In such a model (both in the first and second variants), springs gushing from the bottom of the lake will give a positive divergence of the flow velocity field, and underwater drains (caves where water flows) will give a negative divergence.

The divergence of the current density vector gives a minus rate of charge accumulation in electrodynamics (since the charge is conserved, that is, it does not disappear or appear, but can only move across the boundaries of some volume in order to accumulate in it or leave it; and if they arise or positive and negative charges disappear somewhere - then only in equal quantities). (See continuity equation).

Geometric interpretation

If we take the set of directions of steepest descent on the earth's surface as a vector field (in two-dimensional space), then the divergence will show the location of the peaks and troughs, and at the peaks the divergence will be positive (the directions of descent diverge from the peaks), and at the troughs it will be negative (towards the troughs the direction of descent converge).

Divergence in physics

Divergence is one of the most widely used operations in physics. It is one of the fairly few basic concepts of theoretical physics and is one of the basic elements of physical language.

In the standard formulation of classical field theory, divergence occupies a central place (in alternative formulations it may not be at the very center of the presentation, but is still an important technical tool and an important idea).

In electrodynamics, divergence appears as a main construct in two of Maxwell's four equations. The basic equation of the theory of Newtonian gravity in field form also contains divergence (gravitational field strength) as the main structure. In tensor theories of gravity (including General Relativity, and with it in mind first of all), the basic field equation (in General Relativity, but as a rule - one way or another - in alternative modern theories too) also includes divergence in some generalization. The same can be said about the classical (that is, non-quantum) theory of almost any of the fundamental fields, both experimentally known and hypothetical.

In addition, as can be seen from the above examples, divergence is also applicable in a purely geometrical sense, and also - especially often - to various material flows (divergence in the speed of flow of a liquid or gas, divergence in the density of electric current, etc.).

Properties

The following properties can be obtained from the usual rules of differentiation.

Linearity: for any vector fields F And G and for all real numbers a And b

div ⁡ (a F + b G) = a div ⁡ (F) + b div ⁡ (G) (\displaystyle \operatorname (div) (a\mathbf (F) +b\mathbf (G))=a\; \operatorname (div) (\mathbf (F))+b\;\operatorname (div) (\mathbf (G)))

If φ is a scalar field, and F- vector, then:

div ⁡ (φ F) = grad ⁡ (φ) ⋅ F + φ div ⁡ (F) , (\displaystyle \operatorname (div) (\varphi \mathbf (F))=\operatorname (grad) (\varphi)\ cdot \mathbf (F) +\varphi \;\operatorname (div) (\mathbf (F)),) or ∇ ⋅ (φ F) = (∇ φ) ⋅ F + φ (∇ ⋅ F) . (\displaystyle \nabla \cdot (\varphi \mathbf (F))=(\nabla \varphi)\cdot \mathbf (F) +\varphi \;(\nabla \cdot \mathbf (F)).)

Property relating vector fields F And G, specified in three-dimensional space, with a rotor:

div ⁡ (F × G) = rot ⁡ (F) ⋅ G − F ⋅ rot ⁡ (G) , (\displaystyle \operatorname (div) (\mathbf (F) \times \mathbf (G))=\operatorname ( rot) (\mathbf (F))\cdot \mathbf (G) \;-\;\mathbf (F) \cdot \operatorname (rot) (\mathbf (G)),) or ∇ ⋅ (F × G) = (∇ × F) ⋅ G − F ⋅ (∇ × G) . (\displaystyle \nabla \cdot (\mathbf (F) \times \mathbf (G))=(\nabla \times \mathbf (F))\cdot \mathbf (G) -\mathbf (F) \cdot (\ nabla \times \mathbf (G)).)

The divergence from the gradient is the Laplacian:

div ⁡ (grad ⁡ (φ)) = Δ φ (\displaystyle \operatorname (div) (\operatorname (grad) (\varphi))=\Delta \varphi )

Divergence from rotor:

div ⁡ (rot ⁡ (F)) = 0 (\displaystyle \operatorname (div) (\operatorname (rot) (\mathbf (F)))=0)

Divergence in orthogonal curvilinear coordinates

Div ⁡ (A) = div ⁡ (q 1 A 1 + q 2 A 2 + q 3 A 3) = (\displaystyle \operatorname (div) (\mathbf (A))=\operatorname (div) (\mathbf ( q_(1)) A_(1)+\mathbf (q_(2)) A_(2)+\mathbf (q_(3)) A_(3))=)

1 H 1 H 2 H 3 [ ∂ ∂ q 1 (A 1 H 2 H 3) + ∂ ∂ q 2 (A 2 H 3 H 1) + ∂ ∂ q 3 (A 3 H 1 H 2) ] (\displaystyle =(\frac (1)(H_(1)H_(2)H_(3)))\left[(\frac (\partial )(\partial q_(1)))(A_(1)H_(2) H_(3))+(\frac (\partial )(\partial q_(2)))(A_(2)H_(3)H_(1))+(\frac (\partial )(\partial q_(3 )))(A_(3)H_(1)H_(2))\right]), Where H i (\displaystyle H_(i))- Lame coefficients.

Cylindrical coordinates

Lamé coefficients:

Hr = 1; Hθ = r; H z = 1. (\displaystyle (\begin(matrix)H_(r)=1;\\H_(\theta )=r;\\H_(z)=1.\end(matrix))) div ⁡ A (r , θ , z) = 1 r ∂ ∂ r (A r r) + 1 r ∂ ∂ θ (A θ) + ∂ ∂ z (A z) (\displaystyle \operatorname (div) \mathbf (A ) (r,\theta ,z)=(\frac (1)(r))(\frac (\partial )(\partial r))(A_(r)r)+(\frac (1)(r) )(\frac (\partial )(\partial \theta ))(A_(\theta ))+(\frac (\partial )(\partial z))(A_(z)))

Spherical coordinates

Lamé coefficients:

Hr = 1; Hθ = r; H ϕ = r sin ⁡ θ . (\displaystyle (\begin(matrix)H_(r)=1;\\H_(\theta )=r;\\H_(\phi )=r\sin (\theta ).\end(matrix))) div ⁡ A (r , θ , ϕ) = 1 r 2 ∂ ∂ r [ A r r 2 ] + 1 r sin ⁡ θ ∂ ∂ θ [ A θ sin ⁡ θ ] + 1 r sin ⁡ θ ∂ ∂ ϕ [ A ϕ ] (\displaystyle \operatorname (div) \mathbf (A) (r,\theta ,\phi)=(\frac (1)(r^(2)))(\frac (\partial )(\partial r) )\left+(\frac (1)(r\sin (\theta )))(\frac (\partial )(\partial \theta ))\left+(\frac (1)(r\sin (\theta )) )(\frac (\partial )(\partial \phi ))(\big [)A_(\phi )(\big ]))

Parabolic coordinates

Lamé coefficients:

H ξ = ξ + η 2 ξ ; H η = ξ + η 2 η ; H ϕ = η ξ (\displaystyle (\begin(matrix)H_(\xi )=(\frac (\sqrt (\xi +\eta ))(2(\sqrt (\xi ))));\\H_ (\eta )=(\frac (\sqrt (\xi +\eta ))(2(\sqrt (\eta ))));\\H_(\phi )=(\sqrt (\eta \xi )) \end(matrix))). div ⁡ A (ξ , η , ϕ) = 4 ξ + η ∂ ∂ ξ [ A ξ ξ 2 + ξ η 2 ] + 4 ξ + η ∂ ∂ η [ A η η 2 + ξ η 2 ] + 1 ξ η ∂ ∂ ϕ [ A ϕ ] (\displaystyle \operatorname (div) \mathbf (A) (\xi ,\eta ,\phi)=(\frac (4)(\xi +\eta ))(\frac (\ partial )(\partial \xi ))\left+(\frac (4)(\xi +\eta ))(\frac (\partial )(\partial \eta ))\left+(\frac (1)(\sqrt (\xi \eta )))(\frac (\partial )(\partial \phi ))(\Big [)A_(\phi )(\Big ]))

Elliptical coordinates

Lamé coefficients:

H ξ = σ ξ 2 − η 2 ξ 2 − 1 H η = σ ξ 2 − η 2 1 − η 2 H ϕ = σ (ξ 2 − 1) (1 − η 2) (\displaystyle (\begin(matrix )H_(\xi )=\sigma (\sqrt (\frac (\xi ^(2)-\eta ^(2))(\xi ^(2)-1)))\\H_(\eta )= \sigma (\sqrt (\frac (\xi ^(2)-\eta ^(2))(1-\eta ^(2))))\\H_(\phi )=\sigma (\sqrt (( \xi ^(2)-1)(1-\eta ^(2))))\end(matrix))). div ⁡ A (ξ , η , ϕ) = 1 σ (ξ 2 − η 2) ∂ ∂ ξ [ A ξ (ξ 2 − η 2) (ξ 2 − 1) ] + (\displaystyle \operatorname (div)\ mathbf (A) (\xi ,\eta ,\phi)=(\frac (1)(\sigma (\xi ^(2)-\eta ^(2))))(\frac (\partial )(\ partial \xi ))\left+) 1 σ (ξ 2 − η 2) ∂ ∂ η [ A η (ξ 2 − η 2) (1 − η 2) ] + 1 σ (ξ 2 − 1) (1 − η 2) ∂ ∂ ϕ [ A ϕ ] (\displaystyle (\frac (1)(\sigma (\xi ^(2)-\eta ^(2))))(\frac (\partial )(\partial \eta ))\left+(\frac ( 1)(\sigma (\sqrt ((\xi ^(2)-1)(1-\eta ^(2)))))(\frac (\partial )(\partial \phi ))(\Big [)A_(\phi )(\Big ]))

Divergence in arbitrary curvilinear coordinates and its generalization

The formula for the divergence of a vector field in arbitrary coordinates (in any finite dimension) can be easily obtained from the general definition through the limit of the flux-to-volume ratio, using the tensor notation of the mixed product and the tensor volume formula.

There is a generalization of the divergence operation to act not only on vectors, but also on tensors of higher rank.

In general, divergence is determined by the covariant derivative:

div = (∇ ⋅) = R → α ∇ α ⋅ (\displaystyle \operatorname (div) =(\nabla \cdot)=(\vec (R))^(\alpha )\nabla _(\alpha )\cdot ), Where R → α (\displaystyle (\vec (R))^(\alpha ))- coordinate vectors.

This allows you to find expressions for divergence in arbitrary coordinates for a vector:

∇ ⋅ v → = R → α ∇ α ⋅ v i R → i = ∇ i v i (\displaystyle \nabla \cdot (\vec (v))=(\vec (R))^(\alpha )\nabla _(\ alpha )\cdot v^(i)(\vec (R))_(i)=\nabla _(i)v^(i)). ∇ ⋅ T = R → α ∇ α ⋅ T i j R → i R → j = R → j ∇ i T i j (\displaystyle \nabla \cdot T=(\vec (R))^(\alpha )\nabla _ (\alpha )\cdot T^(ij)(\vec (R))_(i)(\vec (R))_(j)=(\vec (R))_(j)\nabla _(i )T^(ij)).

In general, divergence lowers the rank of the tensor by 1.

Properties of tensor divergence

∇ ⋅ v → v → = v → ∇ ⋅ v → + (v → ⋅ ∇) v → (\displaystyle \nabla \cdot (\vec (v))(\vec (v))=(\vec (v) )\nabla \cdot (\vec (v))+\left((\vec (v))\cdot \nabla \right)(\vec (v)))

The most important question that haunts all traders in the world concerns how to determine the moment when the price is ready to change its direction. But, as it turns out, technical analysis has long offered one of the very effective solutions that, with the highest degree of probability, allows you to do this. What kind of miracle remedy is this? We are talking about divergence in Forex. It is this that makes it possible to enter the market using the most favorable moment. Given such an important characteristic, every trader should carefully study what divergence is and how you can apply it time after time, increasing your income.

How to make a profit

Divergence is a signal that shows the market is ready to reverse, so it is extremely important to find, identify and use it to your advantage. In order to better understand what divergence is in Forex, you need to go back to the origins of technical analysis and remember how price movements occur.

At this stage, you need to understand that, as a rule, quotes fluctuate within a certain range, reach points of support and resistance, can rebound and reverse, set new levels, and so on. If you trace any price chart, it becomes obvious that the price always reverses at certain intervals. These reversal points are extremely important for making a profit, regardless of the trading strategy used for trading or the chosen time frame.

What indicators are used to search for divergences?

Typically, any indicator from the Oscillators class helps to find divergence:

stochastic;
MACD;
CCI and so on.

Why oscillators? Because in practice, they are the ones who best show the resulting difference in values, which indicates the market’s readiness to change the trend - trend. Given the alternating movement of prices up and down, Forex divergence can be either bullish or bearish.

How to determine divergence

It is extremely difficult to overestimate the importance of searching for turning points, because they provide the best signals for entry and, more importantly, for exit, since the statistics of traders’ failures show that not all traders can close a deal on time; they often overextend the position or exit too early, losing resulting in some or even all of the profit. How do you determine divergence on a price chart? There is nothing complicated about this; it is enough to find the discrepancy between the quote level diagram and the picture of the indicator used.

Types of divergences

All divergences can be divided into three main types, within which there is a division into two types.

1. The strongest is Forex divergence, which is classified as the first type. By the way, this is also the most pronounced of the divergences, which is quite easy to determine. The main thing is to remember the basic rule: there should be two extreme points on the price chart, which are reflected in the opposite direction in the indicator picture.

Convergence

However, when using divergences, it is necessary to remember certain exception situations, when, after the formation of the necessary conditions for a trend change, the initial trend continues to develop without a reversal. In such cases we are talking about convergence or, as it is also called, hidden divergence.

In such cases, it is worth revisiting the cyclical nature of the market and understanding the trading opportunities created by convergence formation. In practice, it can have many benefits, which will be reflected in the form of profits that end up in the pockets of traders. In such cases, when Forex divergence is observed and the trader opens an order based on a signal, he should in no case forget that price movement in the opposite direction may not indicate a change in trends, but a correction. Naturally, it would be appropriate to close the trade with a slight minus or plus on the trailing stop (depending on the volume of the rollback) and join the trend in a very promising place in terms of making a profit.

How to Define Convergence

There are also rules for finding and defining convergence or hidden divergence, so the trader does not need to guess; he is, with a high degree of probability, always ready to make a profitable trade. So, in particular, if two descending bottoms have formed on the chart, and the indicator shows the corresponding two tops, where the second is higher than the first, we can state the fact of a hidden bullish divergence that has developed in the market, which indicates that it is still relevant to sell the currency, expecting good returns .

Identification rules

Quite often, a difficulty arises in defining divergence, which lies in the meaning of this phenomenon as given by financial market theorists. This problem lies in the need to comply with the rule of two consecutive tops or bottoms. But as practice shows, in order for a trader to start using a divergence signal to his advantage, it is not at all necessary to observe ideal conditions.

Therefore, if there was an unclear movement between two tops that established new levels of resistance and support with the formation of a weak top, then the appearance of such market “noise” can be ignored and without any fear, use the advantages that the bearish divergence signal provides in this case.

How to use divergence in trading

The advantage of using divergence in trading is that the signals it generates work well on any time frame. Therefore, you can use such simple and effective forecasts both for scalping and for long-term trading, choosing options that are more preferable for yourself. The main quality of divergences is revealed here - their versatility, which, combined with the accuracy of the results, makes familiarization with them and their use in trading mandatory for everyone who wants to have a positive result from trading on Forex.

To correctly “understand” how Forex divergence trading occurs, a trader must understand what it signals. Here it is extremely important to remember the following: “Divergence always indicates that the market will reverse, but does not indicate to what point this reversal will last.” Simply put, a trader cannot be 100% sure whether a trend change has occurred or whether a divergence signal only indicates the onset of a correction.

When to close a deal

Since it is very easy to enter the market on a divergence signal, the main problem with how to effectively make money using it is finding the optimal exit point. There are many strategies here, but probably the simplest and most effective of them is the approach using different time frames.

That is, if, for example, on M30, after a divergence signal, a reversal began and the price sets new peaks one after another, allowing one to catch the strong movement that has begun, then a signal about the completion of such a direction can be looked for on the hourly timeframe. As soon as it shows that the trend is ready to change again, you need to urgently exit the market. In this case, in no case should we forget about the use of trailing stops, which should help minimize losses or even make a small profit in case of weak price pullbacks.

Bottom line

Thus, having learned what Forex divergence is, how to identify it and, most importantly, how to apply it for practical purposes to make good profits, a trader can only use it by building a simple and effective trading strategy. As practice shows, the use of divergence always gives an accurate signal to place an order and with a high degree of probability we can say that this excellent tool will still be relevant in many years, allowing currency speculators to increase their capital.

Divergence

Physical interpretation

From the point of view of physics (both in the strict sense and in the sense of the intuitive physical image of a mathematical operation), the divergence of a vector field is an indicator of the extent to which a given point in space (or a very small neighborhood of a point) is the source or sink of this field:

- the field point is the source; - the field point is a drain; - there are no sinks and sources, or they compensate each other.

Geometric interpretation

Divergence in physics

Divergence is one of the most widely used operations in physics. It is one of the fairly few basic concepts of theoretical physics and is one of the basic elements of physical language.

In electrodynamics, divergence appears as a major construct in two of Maxwell's four equations. The basic equation of the theory of Newtonian gravity in field form also contains divergence (gravitational field strength) as the main structure. In tensor theories of gravity (including General Relativity, and with it in mind first of all), the basic field equation (in General Relativity, but as a rule - one way or another - in alternative modern theories too) also includes divergence in some generalization. The same can be said about the classical (i.e., non-quantum) theory of almost any of the fundamental fields, both experimentally known and hypothetical.

Properties

The following properties can be obtained from the usual rules of differentiation.

Linearity: for any vector fields F And G and for all real numbers a And b

If φ is a scalar field, and F- vector, then:

Property relating vector fields F And G, specified in three-dimensional space, with a rotor:

The divergence from the gradient is the Laplacian:

Divergence from rotor: