This condition is based on the fact that a vector field F is conservative if and only if F=∇f for some potential function. We can calculate that the curl of a gradient is zero, curl∇f=0, for any twice continuously differentiable f:R3→R. Therefore, if F is conservative, then its curl must be zero, as curlF=curl∇f=0.

If a three-dimensional vector field F(p,q,r) is conservative, then py = qx, pz = rx, and qz = ry. Since F is conservative, F = ∇f for some function f and p = fx, q = fy, and r = fz.

In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field.

The scalar mp(x, y) is usually called the potential energy of the object at the given location and is measured in units of work, such as centimeter-dynes.) In general, if a vector field P(x, y) i + Q(x, y) j is the gradient of a function f(x, y), then −f(x, y) is called a potential function for the field.

If F is the gradient of a function, then curlF = 0. So far we have a condition that says when a vector field is not a gradient. The converse of Theorem 1 is the following: Given vector field F = Pi + Qj on D with C1 coefficients, if Py = Qx, then F is the gradient of some function.

1 Answer. The answer is affirmative. A conservative field is a vector field which is the gradient of some function. So, if v is a constant vector field, that is v(x1,…,xn)=(a1,…,an), you can takeF(x1,…,xn)=a1x1+⋯+anxn.

The gradient of a function is a vector field. It is obtained by applying the vector operator V to the scalar function f(x, y). Such a vector field is called a gradient (or conservative) vector field.

To calculate the gradient of a straight line we choose two points on the line itself. The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates). If the answer is a positive value then the line is uphill in direction. If the answer is a negative value then the line is downhill in direction.

What is another word for gradient?

In this page you can discover 31 synonyms, antonyms, idiomatic expressions, and related words for gradient, like: angle, slope, list, pitch, grade, inclination, rake, slant, tilt, tip and rise.

Also called density gradient .

A color gradient is also known as a color ramp or a color progression. In assigning colors to a set of values, a gradient is a continuous colormap, a type of color scheme.

What is the opposite of gradient?

What is diffusion?

1. Diffusion is the movement of a substance from an area of high concentration to an area of low concentration.
2. Diffusion happens in liquids and gases because their particles move randomly from place to place.

Concentration Synonyms – WordHippo Thesaurus….What is another word for concentration?

1 : the action or process of collecting in a mass the agglomeration of matter into stars and galaxies. 2 : a heap or cluster of usually disparate (see disparate sense 1) elements …

Antonyms: dilution, dispersion, distribution. Synonyms: tightness, immersion, assiduity, compactness, absorption, denseness, assiduousness, density, engrossment. concentration(noun)

What is the opposite of concentrate?

1. Train your brain. Playing certain types of games can help you get better at concentrating.
2. Get your game on. Brain games may not be the only type of game that can help improve concentration.
3. Improve sleep.
4. Make time for exercise.
5. Spend time in nature.
6. Give meditation a try.
7. Take a break.
8. Listen to music.

In this page you can discover 55 synonyms, antonyms, idiomatic expressions, and related words for inevitable, like: certain, unavoidable, destined, fatal, evitable, inescapable, inexorable, foreordained, assured, fated and prescribed.

sane

An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. Any word or phrase that exactly reproduces the letters in another order is an anagram.

: full of scorn : contemptuous.

: to corrupt, debase, or make impure by the addition of a foreign or inferior substance or element especially : to prepare for sale by replacing more valuable with less valuable or inert ingredients He was in the same plight as the manufacturer who has to adulterate and misrepresent his product.

adjective Referring to a drug or device which: contains decomposed or putrid material; has been produced, prepared, packed or held under unsanitary conditions, and/or not in accordance with good manufacturing practice; contains an unsafe colour additive; has a strength and/or quality or purity which differs from that …

To adulterate, in the context of the focus verse, is to mix the right thing with the wrong thing in a way that might be injurious to those who take it in or achieve less than it should, if anything at all.

Other contaminants like urea, starch, glucose, formalin along with detergent are used as adulterants. These adulterants are used to increase the thickness and viscosity of the milk as well as to preserve it for a longer period.