| align=contour integral of |  |  |  |  |  |
| align=நுண்கணிதம் |  |  |  |  |  |
| rowspan=9 bgcolor=#d0f0d0 align=<div>∇</div> | gradient | ∇*f* (x<sub>1</sub>, …, x<sub>*n*</sub>) is the vector of partial derivatives (*∂f* / *∂x*<sub>1</sub>, …, *∂f* / *∂x*<sub>*n*</sub>). | If *f* (*x*,*y*,*z*) := 3*xy* + *z*², then ∇*f*&nbsp;=&nbsp;(3*y*, 3*x*, 2*z*) |  |  |
| align=டெல் இயக்கி, nabla, gradient of |  |  |  |  |  |
| align=vector calculus |  |  |  |  |  |
| விரிதல் (திசையன் நுண்கணிதம்) | <math> \nabla \cdot \vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} </math> | If <math> \vec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} </math>, then <math> \nabla \cdot \vec v = 3y + 2yz </math>. |  |  |  |
| align=del dot, divergence of |  |  |  |  |  |
| align=vector calculus |  |  |  |  |  |
| curl | <math> \nabla \times \vec v = \( {\partial v_z \over \partial y} - {\partial v_y \over \partial z} \) \mathbf{i} + \( {\partial v_x \over \partial z} - {\partial v_z \over \partial x} \) \mathbf{j} + \( {\partial v_y \over \partial x} - {\partial v_x \over \partial y} \) \mathbf{k} </math> | If <math> \vec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} </math>, then <math> \nabla\times\vec v = -y^2\mathbf{i} - 3x\mathbf{k} </math>. |  |  |  |
| align=curl of |  |  |  |  |  |
| align=vector calculus |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>∂</div> | partial differential | With *f* (x<sub>1</sub>, …, x<sub>*n*</sub>), ∂f/∂x<sub>i</sub> is the derivative of *f* with respect to x<sub>i</sub>, with all other variables kept constant. | If *f*(x,y) := x<sup>2</sup>y, then ∂*f*/∂x = 2xy |  |  |
| align=partial, d |  |  |  |  |  |
| align=நுண்கணிதம் |  |  |  |  |  |
| boundary | ∂*M* means the boundary of *M* | ∂{x : x ≤ 2} = {x : x = 2} |  |  |  |
| align=boundary of |  |  |  |  |  |
| align=இடவியல் |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>&perp;</div> | செங்குத்து | *x*&nbsp;&perp;&nbsp;*y* means *x* is perpendicular to *y*; or more generally *x* is orthogonal to *y*. | If *l*&nbsp;&perp;&nbsp;*m* and *m*&nbsp;&perp;&nbsp;*n* then *l*&nbsp;&nbsp;*n*. |  |  |
| align=is perpendicular to |  |  |  |  |  |
| align=வடிவவியல் |  |  |  |  |  |
| bottom element | *x* = &perp; means *x* is the smallest element. | &forall;*x*&nbsp;: *x*&nbsp;∧&nbsp;&perp;&nbsp;= &perp; |  |  |  |
| align=the bottom element |  |  |  |  |  |
| align=lattice theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div></div> | சமாந்தரம் | *x*&nbsp;&nbsp;*y* means *x* is parallel to *y*. | If *l*&nbsp;&nbsp;*m* and *m*&nbsp;&perp;&nbsp;*n* then *l*&nbsp;&perp;&nbsp;*n*. |  |  |
| align=is parallel to |  |  |  |  |  |
| align=வடிவவியல் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align= <div></div> | entailment | *A*&nbsp;&nbsp;*B* means the sentence *A* entails the sentence *B*, that is in every model in which *A* is true, *B* is also true. | *A*&nbsp;&nbsp;*A*&nbsp;∨&nbsp;¬*A* |  |  |
| align=entails |  |  |  |  |  |
| align= model theory |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align= <div></div> | inference | *x*&nbsp;&nbsp;*y* means *y* is derived from *x*. | *A*&nbsp;→&nbsp;*B*&nbsp; ¬*B*&nbsp;→&nbsp;¬*A* |  |  |
| align=infers or is derived from |  |  |  |  |  |
| align=propositional logic, predicate logic |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align= <div></div> | இயல்நிலை உட்குலம் | *N*&nbsp;&nbsp;*G* means that *N* is a normal subgroup of group *G*. | *Z*(*G*)&nbsp;&nbsp;*G* |  |  |
| align=is a normal subgroup of |  |  |  |  |  |
| align=குலக் கோட்பாடு |  |  |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>/</div> | ஈவு குலம் | *G*&nbsp;/&nbsp;*H* means the quotient of group *G* modulo its subgroup *H*. | {0, *a*, 2*a*, *b*, *b*+*a*, *b*+2*a*}&nbsp;/&nbsp;{0, *b*}&nbsp;= , {*a*, *b*+*a*}, |  |  |
| align= mod |  |  |  |  |  |
| align= குலக் கோட்பாடு |  |  |  |  |  |
| quotient set | *A*/~ means the set of all ~ சமானப் பகுதிes in *A*. | If we define ~ by x&nbsp;~&nbsp;y ⇔ x&nbsp;−&nbsp;y&nbsp;∈ , then
/~&nbsp;= |  |  |  |
| rowspan=6 bgcolor=#d0f0d0 align=<div>≈</div> | approximately equal | *x*&nbsp;≈&nbsp;*y* means *x* is approximately equal to *y*. | π&nbsp;≈&nbsp;3.14159 |  |  |
| align=is approximately equal to |  |  |  |  |  |
| align=everywhere |  |  |  |  |  |
| isomorphism | *G*&nbsp;≈&nbsp;*H* means that group *G* is isomorphic to group *H*. | *Q*&nbsp;/&nbsp;{1,&nbsp;−1}&nbsp;≈ *V*,
where *Q* is the quaternion group and *V* is the கிளைன் நான்குறுப்புக்குலம். |  |  |  |
| is isomorphic to |  |  |  |  |  |
| align= குலக் கோட்பாடு |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>~</div> | same order of magnitude | *m*&nbsp;~&nbsp;*n* means the quantities *m* and *n* have the same order of magnitude, or general size.  
(*Note that* ~ *is used for an approximation that is poor, otherwise use * ≈&nbsp;.) | 2&nbsp;~&nbsp;5  
8&nbsp;×&nbsp;9&nbsp;~ 100  
but π<sup>2</sup> ≈ 10 |  |  |
| align=roughly similar  
poorly approximates |  |  |  |  |  |
| align=அண்ணளவாக்கக் கோட்பாடு |  |  |  |  |  |
| )  
< , >  
·  
:</div> | inner product | 〈*x*,*y*〉 means the inner product of *x* and *y* as defined in an inner product space.  
For spatial vectors, the புள்ளிப் பெருக்கல் notation, *x*·*y* is common.  
For matricies, the colon notation may be used. | The standard inner product between two vectors *x*&nbsp;=&nbsp;(2,&nbsp;3) and *y*&nbsp;=&nbsp;(−1,&nbsp;5) is:
〈x,&nbsp;y〉&nbsp;=&nbsp;2&nbsp;×&nbsp;−1&nbsp;+&nbsp;3&nbsp;×&nbsp;5&nbsp;= 13  
<math>A:B = \sum_{i,j} A_{ij}B_{ij}</math> |  |  |
| align=inner product of |  |  |  |  |  |
| align=நேரியல் இயற்கணிதம் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div></div> | tensor product | *V*&nbsp;&nbsp;*U* means the tensor product of *V* and *U*. | {1, 2, 3, 4}&nbsp;&nbsp;{1, 1, 2}&nbsp;=
, {1, 2, 3, 4}, |  |  |
| align= tensor product of |  |  |  |  |  |
| align= நேரியல் இயற்கணிதம் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div>*</div> | convolution | *f*&nbsp;*&nbsp;*g* means the convolution of *f* and *g*. | <math>(f * g )(t) = \int f(\tau) g(t - \tau)\, d\tau</math> |  |  |
| align= convolution, convoluted with |  |  |  |  |  |
| align= functional analysis |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div><math>\bar{x}</math>
</div> | கூட்டுச்சராசரி | <math>\bar{x}</math> (often read as "x bar") is the கூட்டுச்சராசரி (average value of <math>x_i</math>). | <math>x = \{1,2,3,4,5\}; \bar{x} = 3</math>. |  |  |
| align=overbar, … bar |  |  |  |  |  |
| align=புள்ளியியல் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div><math> \overline{z} </math> | complex conjugate | <math> \overline{z} </math> is the complex conjugate of *z*. | <math> \overline{3+4i} = 3-4i </math> |  |  |
| align=conjugate |  |  |  |  |  |
| align=சிக்கலெண் |  |  |  |  |  |
| rowspan=3 bgcolor=#d0f0d0 align=<div><math>\triangleq</math></div> | delta equal to | <math>\triangleq</math> means equal by definition. When <math>\triangleq</math> is used, equality is not true generally, but rather equality is true under certain assumptions that are taken in context. Some writers prefer ≡. | x_{\pi_i})</math>. |  |  |
| align=equal by definition |  |  |  |  |  |
| align=everywhere | } |  |  |  |  |