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Calculus Symbols

Calculus and analysis math symbols and definitions.

Calculus & analysis math symbols table

SymbolSymbol NameMeaning / definitionExample
\lim_{x\to x0}f(x)limitlimit value of a function 
εepsilonrepresents a very small number, near zeroε 0
ee constant / Euler's numbere = 2.718281828...e = lim (1+1/x)x, x→∞
y 'derivativederivative - Lagrange's notation(3x3)' = 9x2
y ''second derivativederivative of derivative(3x3)'' = 18x
y(n)nth derivativen times derivation(3x3)(3) = 18
\frac{dy}{dx}derivativederivative - Leibniz's notationd(3x3)/dx= 9x2
\frac{d^2y}{dx^2}second derivativederivative of derivatived2(3x3)/dx2= 18x
\frac{d^ny}{dx^n}nth derivativen times derivation 
\dot{y}time derivativederivative by time - Newton's notation 
time second derivativederivative of derivative 
Dx yderivativederivative - Euler's notation 
Dx2ysecond derivativederivative of derivative 
\frac{\partial f(x,y)}{\partial x}partial derivative ∂(x2+y2)/∂x= 2x
integralopposite to derivation 
double integralintegration of function of 2 variables 
triple integralintegration of function of 3 variables 
closed contour / line integral  
closed surface integral  
closed volume integral  
[a,b]closed interval[a,b] = {x | a x b} 
(a,b)open interval(a,b) = {x | a < x< b} 
iimaginary uniti ≡ √-1z = 3 + 2i
z*complex conjugatez = a+biz*=a-biz* = 3 + 2i
zcomplex conjugatez = a+biz = a-biz = 3 + 2i
Re(z)real part of a complex numberz = a+bi → Re(z)=aRe(3 - 2i) = 3
Im(z)imaginary part of a complex numberz = a+bi → Im(z)=bIm(3 - 2i) = -2
| z |absolute value/magnitude of a complex number|z| = |a+bi| = √(a2+b2)|3 - 2i| = √13
arg(z)argument of a complex numberThe angle of the radius in the complex planearg(3 + 2i) = 33.7°
nabla / delgradient / divergence operatorf (x,y,z)
vector  
unit vector  
x * yconvolutiony(t) = x(t) * h(t) 
Laplace transformF(s) = {f (t)} 
Fourier transformX(ω) = {f (t)} 
δdelta function  
lemniscateinfinity symbol