Calculus symbols

Calculus & analysis math symbols table

Symbol Symbol Name Meaning / definition Example
\lim_{x\to x0}f(x) limit limit value of a function  
ε epsilon represents a very small number, near zero ε 0
e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞
y ' derivative derivative - Lagrange's notation (3x3)' = 9x2
y '' second derivative derivative of derivative (3x3)'' = 18x
y(n) nth derivative n times derivation (3x3)(3) = 18
\frac{dy}{dx} derivative derivative - Leibniz's notation d(3x3)/dx = 9x2
\frac{d^2y}{dx^2} second derivative derivative of derivative d2(3x3)/dx2 = 18x
\frac{d^ny}{dx^n} nth derivative n times derivation  
\dot{y} time derivative derivative by time - Newton's notation  
time second derivative derivative of derivative  
Dx y derivative derivative - Euler's notation  
Dx2y second derivative derivative of derivative  
\frac{\partial f(x,y)}{\partial x} partial derivative   ∂(x2+y2)/∂x = 2x
integral opposite to derivation  
double integral integration of function of 2 variables  
triple integral integration 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}  
i imaginary unit i ≡ √-1 z = 3 + 2i
z* complex conjugate z = a+biz*=a-bi z* = 3 + 2i
z complex conjugate z = a+biz = a-bi z = 3 + 2i
Re(z) real part of a complex number z = a+bi → Re(z)=a Re(3 - 2i) = 3
Im(z) imaginary part of a complex number z = a+bi → Im(z)=b Im(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 number The angle of the radius in the complex plane arg(3 + 2i) = 33.7°
nabla / del gradient / divergence operator f (x,y,z)
unit vector    
x * y convolution y(t) = x(t) * h(t)  
Laplace transform F(s) = {f (t)}  
Fourier transform X(ω) = {f (t)}  
δ delta function    
lemniscate infinity symbol  


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