Calculus & analysis symbols
| Symbol | Symbol Name | Meaning/Definition | Example |
|---|---|---|---|
| $$ \lim_{x\to x_0} f(x) $$ | 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 | \( (3x^3)' = 9x^2 \) |
| \( y '' \) | second derivative | derivative of derivative | \( (3x^3)'' = 18x \) |
| \( y^{(n)} \) | nth derivative | n times derivation | \( (3x^3)^{(3)} = 18 \) |
| \( \frac {dy}{dx} \) | derivative | derivative - Leibniz's notation | \( d(3x^3)/dx = 9x^2 \) |
| \( \frac {d^2y}{dx^2} \) | second derivative | derivative of derivative | \( d^2(3x^3)/dx^2 = 18x \) |
| \( \frac {d^ny}{dx^n} \) | nth derivative | n times derivation | \( \) |
| \( \dot y \) | time derivative | derivative by time - Newton's notation | \( \) |
| \( \ddot y \) | time second derivative | derivative of derivative | \( \) |
| \( D_x y \) | derivative | derivative - Euler's notation | \( \) |
| \( D_x^2y \) | second derivative | derivative of derivative | \( \) |
| \( \frac {\partial f(x,y)}{\partial x} \) | partial derivative | \( ∂(x2+y2)/∂x = 2x \) | |
| \( ∫ \) | 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 | \( \) | |
| ∯ | 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 | \( z = 3 - 2i \) |
| \( Re(z) \) | 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 | \( ∇f (x,y,z) \) |
| \( \overrightarrow {x} \) | vector | \( \) | |
| \( \hat x \) | unit vector | \( \) | |
| \( x * y \) | convolution | y(t) = x(t) * h(t) | \( \) |
| \( δ \) | delta function | \( \) | |
| \( ∞ \) | lemniscate | infinity symbol | \( \) |
