Calculus & analysis symbols
Calculus:
The branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two main types are differential calculus and integral calculus.
Symbol | Symbol Name | Meaning / definition | Example |
---|---|---|---|
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 – Leibniz’s notation | (3x^{3})’ = 9x^{2} |
y ” | second derivative | derivative of derivative | (3x^{3})” = 18x |
y^{(n)} | nth derivative | n times derivation | (3x^{3})^{(3)} = 18 |
derivative | derivative – Lagrange’s notation | d(3x^{3})/dx = 9x^{2} | |
second derivative | derivative of derivative | d^{2}(3x^{3})/dx^{2} = 18x | |
nth derivative | n times derivation | ||
time derivative | derivative by time – Newton notation | ||
time second derivative | derivative of derivative | ||
partial derivative | ∂(x^{2}+y^{2})/∂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+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 | |||
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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