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Calculus Symbols Guide

This document defines and provides examples of common symbols used in calculus and analysis. It includes symbols for limits, derivatives, integrals, imaginary numbers, operators like nabla, and transforms such as Laplace and Fourier. Symbols are defined for concepts like derivatives, integrals, intervals, vectors, and more advanced topics such as convolutions and the delta function. Examples are provided to illustrate the meaning and usage of each symbol.

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1K views1 page

Calculus Symbols Guide

This document defines and provides examples of common symbols used in calculus and analysis. It includes symbols for limits, derivatives, integrals, imaginary numbers, operators like nabla, and transforms such as Laplace and Fourier. Symbols are defined for concepts like derivatives, integrals, intervals, vectors, and more advanced topics such as convolutions and the delta function. Examples are provided to illustrate the meaning and usage of each symbol.

Uploaded by

pcr123
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Symbol Symbol Name Meaning / definition Example

limit limit value of a function n/a


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 ,


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
derivative derivative - Leibniz's notation d(3x3)/dx = 9x2

second derivative derivative of derivative d2(3x3)/dx2 = 18x

nth derivative n times derivation n/a

time derivative derivative by time - Newton's notation n/a


time second derivative derivative of derivative n/a
Dx y derivative derivative - Euler's notation n/a
Dx2y second derivative derivative of derivative n/a
partial derivative n/a ∂(x2+y2)/∂x = 2x

∫ integral opposite to derivation ∫ f(x)dx


∫∫ double integral integration of function of 2 variables ∫∫ f(x,y)dxdy
∫∫∫ triple integral integration of function of 3 variables ∫∫∫ f(x,y,z)dxdydz
∮ closed contour / line integral n/a n/a
∯ closed surface integral n/a n/a
∰ closed volume integral n/a n/a
[a,b] closed interval [a,b] = {x | a ≤ x ≤ b} n/a
(a,b) open interval (a,b) = {x | a < x < b} n/a
i imaginary unit I ≡ √-1 z = 3 + 2i
z* complex conjugate Z = a+bi → z*=a-bi z* = 3 - 2i
z complex conjugate Z = a+bi → z = a-bi z = 3 - 2i
∇ nabla / del gradient / divergence operator ∇f (x,y,z)
vector n/a n/a
unit vector n/a n/a
x*y convolution y(t) = x(t) * h(t) n/a
Laplace transform F(s) = {f (t)} n/a
Fourier transform X(ω) = {f (t)} n/a
δ delta function n/a n/a
∞ lemniscate infinity symbol n/a

Calculus & Analysis


Symbols

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