கணிதக் குறியீடுகள்

கணித தகவல்களை வெளிப்படுத்த கணிதக் குறியீடுகள் பயன்படுகின்றன. எழுத்துக்கள் எப்படி மொழியூடாக தகவல்களை வெளிப்படுத்த அவசியமோ அதேபோல் குறியீடுகள் கணிதத்தினூடாக தகவல்களை வெளிப்படுத்த அவசியம். ஒரு மொழியை அறிய, பயன்படுத்த எப்படி அதன் எழுத்துக்களை அறிவது அவசியமோ அதேபோல் கணிதத்தை அறிய, பயன்படுத்த கணிதக் குறியீடுகளை அறிவது அவசியம். எண்கள், செயற்பாட்டுக் குறியீடுகள், கருத்துருக் குறியீடுகள், சமன்பாடுகள் என பலநிலையிலான குறியீடுகள் கணிதத்தில் உண்டு.
அடிப்படை கணிதக் குறியீடுகள் அட்டவணை

= \infty
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|align=center|எண்ணிலி
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|align=right|எண்s

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| rowspan=3 bgcolor=#d0f0d0 align=center|||…||
||norm
| rowspan=3| || x || is the norm of the element x of a normed vector space.
| rowspan=3| || x + y || ≤ || x || + || y ||
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|align=center|norm of length of
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|align=right| நேரியல் இயற்கணிதம்

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| rowspan=3 bgcolor=#d0f0d0 align=center|∑
||summation
| rowspan=3|
\sum_{k=1}^{n}{a_k} means a1 + a2 + … + an.
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\sum_{k=1}^{4}{k^2} = 12 + 22 + 32 + 42
::= 1 + 4 + 9 + 16 = 30
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|align=center|sum over … from … to … of
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|align=right|எண்கணிதம்

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| rowspan=6 bgcolor=#d0f0d0 align=center|∏
||product
| rowspan=3|
\prod_{k=1}^na_k means a1a2···an.
| rowspan=3|
\prod_{k=1}^4(k+2) = (1+2)(2+2)(3+2)(4+2)
::= 3 × 4 × 5 × 6 = 360
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|align=center|product over … from … to … of
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|align=right|எண்கணிதம்

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||கார்ட்டீசியன் பெருக்கற்பலன்
| rowspan=3|
\prod_{i=0}^{n}{Y_i} means the set of all (n+1)-tuples
::(y0, …, yn).
| rowspan=3|
\prod_{n=1}^{3}{\mathbb{R}} = \mathbb{R}\times\mathbb{R}\times\mathbb{R} = \mathbb{R}^3
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|align=center|the Cartesian product of; the direct product of
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|align=right|set theory

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| rowspan=3 bgcolor=#d0f0d0 align=center|
||coproduct
| rowspan=3|
| rowspan=3|
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|align=center|coproduct over … from … to … of
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|align=right|category theory

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| rowspan=3 bgcolor=#d0f0d0 align=center|′ •
||வகையிடல்
| rowspan=3|f ′(x) is the derivative of the function f at the point x, i.e., the சாய்வு of the தொடுகோடு to f at x.
The dot notation indicates a time derivative. That is \dot{x}(t)=\frac{\partial}{\partial t}x(t).
| rowspan=3|If f(x) := x2, then f ′(x) = 2x
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|align=center|… prime derivative of
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|align=right|நுண்கணிதம்

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| rowspan=6 bgcolor=#d0f0d0 align=center|∫
||indefinite integral or antiderivative
| rowspan=3|∫ f(x) dx means a function whose derivative is f.
| rowspan=3| ∫x2 dx = x3/3 + C
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|align=center|indefinite integral of the antiderivative of
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|align=right|நுண்கணிதம்

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||தொகையீடு
| rowspan=3|∫ab f(x) dx means the signed பரப்பளவு between the x-axis and the graph of the function f between x = a and x = b.
| rowspan=3|∫0b x2 dx = b3/3;
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|align=center|integral from … to … of … with respect to
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|align=right|நுண்கணிதம்

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| rowspan=3 bgcolor=#d0f0d0 align=center|∮
||contour integral or closed line integral
| rowspan=3|Similar to the integral, but used to denote a single integration over a closed curve or loop. It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface. Instances where the latter requires simultaneous double integration, the symbol would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol .
The contour integral can also frequently be found with a subscript capital letter C, ∮C, denoting that a closed loop integral is, in fact, around a contour C, or sometimes dually appropriately, a circle C. In representations of Gauss's Law, a subscript capital S, ∮S, is used to denote that the integration is over a closed surface.
| rowspan=3|
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|align=center|contour integral of
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|align=right|நுண்கணிதம்

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| rowspan=9 bgcolor=#d0f0d0 align=center|∇
| gradient
| rowspan=3|∇f (x1, …, xn) is the vector of partial derivatives (∂f / ∂x1, …, ∂f / ∂xn).
| rowspan=3|If f (x,y,z) := 3xy + z², then ∇f = (3y, 3x, 2z)
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|align=center|டெல் இயக்கி, nabla, gradient of
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|align=right|vector calculus

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| விரிதல் (திசையன் நுண்கணிதம்)
| rowspan=3| \nabla \cdot \vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z}
| rowspan=3|If \vec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} , then \nabla \cdot \vec v = 3y + 2yz .

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|align=center|del dot, divergence of
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|align=right|vector calculus

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| curl
|rowspan=3| \nabla \times \vec v = \left( {\partial v_z \over \partial y} - {\partial v_y \over \partial z} \right) \mathbf{i} + \left( {\partial v_x \over \partial z} - {\partial v_z \over \partial x} \right) \mathbf{j} + \left( {\partial v_y \over \partial x} - {\partial v_x \over \partial y} \right) \mathbf{k}
|rowspan=3|If \vec v := 3xy\mathbf{i}+y^2 z\mathbf{j}+5\mathbf{k} , then \nabla\times\vec v = -y^2\mathbf{i} - 3x\mathbf{k} .

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|align=center|curl of
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|align=right|vector calculus

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| rowspan=6 bgcolor=#d0f0d0 align=center|∂
||partial differential
| rowspan=3| With f (x1, …, xn), ∂f/∂xi is the derivative of f with respect to xi, with all other variables kept constant.
| rowspan=3| If f(x,y) := x2y, then ∂f/∂x = 2xy
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|align=center|partial, d
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|align=right|நுண்கணிதம்

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|boundary
| rowspan=3| ∂M means the boundary of M
| rowspan=3| ∂{x : ||x|| ≤ 2} = {x : ||x|| = 2}
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|align=center|boundary of
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|align=right|இடவியல்

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| rowspan=6 bgcolor=#d0f0d0 align=center|⊥
||செங்குத்து
| rowspan=3|x ⊥ y means x is perpendicular to y; or more generally x is orthogonal to y.
| rowspan=3|If l ⊥ m and m ⊥ n then l || n.
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|align=center|is perpendicular to
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|align=right|வடிவவியல்

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||bottom element
| rowspan=3|x = ⊥ means x is the smallest element.
| rowspan=3|∀x : x ∧ ⊥ = ⊥
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|align=center|the bottom element
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|align=right|lattice theory

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| rowspan=3 bgcolor=#d0f0d0 align=center|||
||சமாந்தரம்
| rowspan=3|x || y means x is parallel to y.
| rowspan=3|If l || m and m ⊥ n then l ⊥ n.
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|align=center|is parallel to
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|align=right|வடிவவியல்

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| rowspan=3 bgcolor=#d0f0d0 align=center|
||entailment
| rowspan=3| A B means the sentence A entails the sentence B, that is in every model in which A is true, B is also true.
| rowspan=3| A A ∨ ¬A
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|align=center|entails
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|align=right| model theory

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| rowspan=3 bgcolor=#d0f0d0 align=center|
||inference
| rowspan=3|x y means y is derived from x.
| rowspan=3| A → B ¬B → ¬A
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|align=center|infers or is derived from
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|align=right|propositional logic, predicate logic

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| rowspan=3 bgcolor=#d0f0d0 align=center|
||இயல்நிலை உட்குலம்
| rowspan=3| N G means that N is a normal subgroup of group G.
| rowspan=3| Z(G) G
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|align=center|is a normal subgroup of
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|align=right|குலக் கோட்பாடு


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| rowspan=6 bgcolor=#d0f0d0 align=center|/
||ஈவு குலம்
| rowspan=3| G / H means the quotient of group G modulo its subgroup H.
| rowspan=3| {0, a, 2a, b, b+a, b+2a} / {0, b} = , {a, b+a},
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|align=center| mod
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|align=right| குலக் கோட்பாடு

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|quotient set
| rowspan=3| A/~ means the set of all ~ சமானப் பகுதிes in A.
| rowspan=3| If we define ~ by x ~ y ⇔ x − y ∈ , then /~ = {{x + n : n ∈ } : x ∈ (0,1])
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|align=center| mod
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|align=right| கணக் கோட்பாடு

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| rowspan=6 bgcolor=#d0f0d0 align=center|≈
|approximately equal
| rowspan=3|x ≈ y means x is approximately equal to y.
| rowspan=3|π ≈ 3.14159
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|align=center|is approximately equal to
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|align=right|everywhere
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||isomorphism
| rowspan=3| G ≈ H means that group G is isomorphic to group H.
| rowspan=3| Q / {1, −1} ≈ V, where Q is the quaternion group and V is the கிளைன் நான்குறுப்புக்குலம்.
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|align=center | is isomorphic to
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|align=right| குலக் கோட்பாடு
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| rowspan=3 bgcolor=#d0f0d0 align=center|~
||same order of magnitude
| rowspan=3| m ~ 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 ≈ .)
| rowspan=3|2 ~ 5 8 × 9 ~ 100 but π2 ≈ 10
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|align=right|roughly similar poorly approximates
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|align=right|அண்ணளவாக்கக் கோட்பாடு

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| rowspan=3 bgcolor=#d0f0d0 align=center|〈,〉( | )·:
||inner product
| rowspan=3|〈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.
| rowspan=3|The standard inner product between two vectors x = (2, 3) and y = (−1, 5) is:〈x, y〉 = 2 × −1 + 3 × 5 = 13
A:B = \sum_{i,j} A_{ij}B_{ij}
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|align=center|inner product of
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|align=right|நேரியல் இயற்கணிதம்

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| rowspan=3 bgcolor=#d0f0d0 align=center|
||tensor product
| rowspan=3| V U means the tensor product of V and U.
| rowspan=3| {1, 2, 3, 4} {1, 1, 2} = , {1, 2, 3, 4},
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|align=center| tensor product of
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|align=right| நேரியல் இயற்கணிதம்

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| rowspan=3 bgcolor=#d0f0d0 align=center|*
||convolution
| rowspan=3| f * g means the convolution of f and g.
| rowspan=3| (f * g )(t) = \int f(\tau) g(t - \tau)\, d\tau
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|align=center| convolution, convoluted with
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|align=right| functional analysis

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| rowspan=3 bgcolor=#d0f0d0 align=center|\bar{x}
||கூட்டுச்சராசரி
| rowspan=3|\bar{x} (often read as "x bar") is the கூட்டுச்சராசரி (average value of x_i).
| rowspan=3|x = \{1,2,3,4,5\}; \bar{x} = 3.
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|align=center|overbar, … bar
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|align=right|புள்ளியியல்

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|rowspan=3 bgcolor=#d0f0d0 align=center| \overline{z}
||complex conjugate
| rowspan=3| \overline{z} is the complex conjugate of z.
| rowspan=3| \overline{3+4i} = 3-4i
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|align=center|conjugate
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|align=right|சிக்கலெண்

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| rowspan=3 bgcolor=#d0f0d0 align=center|\triangleq
||delta equal to
| rowspan=3|\triangleq means equal by definition. When \triangleq is used, equality is not true generally, but rather equality is true under certain assumptions that are taken in context. Some writers prefer ≡.
| rowspan=3|p(x_1,x_2,...,x_n) \triangleq \prod_{i=1}^n p(x_i | x_{\pi_i}).
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|align=center|equal by definition
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|align=right|everywhere
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See also


* Mathematical alphanumeric symbols
* Table of logic symbols
* கணிதக் குறியீடுகள்
* ISO 31-11
* Roman letters used in mathematics
* Greek letters used in mathematics
* Notation in probability
* இயற்பியல் மாறிலிs
* Variables commonly used in physics

External links

* Jeff Miller: Earliest Uses of Various Mathematical Symbols
* TCAEP – Institute of Physics
* GIF and PNG Images for Math Symbols
* Mathematical Symbols in Unicode

பகுப்பு:கணிதக் குறியீடுகள்
பகுப்பு:தரமுயர்த்தப்பட வேண்டிய கட்டுரைகள்