Ancient greek letters are a daily part of an Physicists's life and it comes out of their mouth like it's part of their normal grammar. Physicists use Greek letters as an alternative for numbers or to describe an object's characteristic. So, let's go through all of the 24 Greek letters and what they mean in the world of physics.
Greek Alphabet
| Letter Name & Pronounce | Upper Case Letter | Most Common Uses | Lower Case Letter | Most Common Uses |
|---|---|---|---|---|
| Alpha | Α | α | alpha particle | |
| Beta | Β | β | beta particle | |
| Gamma | Γ | γ |
gamma radiation (photon), relativistic factor |
|
| Delta | Δ |
change of, small quantity of |
δ | Delta functions |
| Epsilon | Ε | ε | a small quantity | |
| Zeta | Ζ | ζ | ||
| Eta | Η | η | ||
| Theta | Θ | θ | angle | |
| Iota | Ι | identity matrix | ι | |
| Kappa | Κ | κ | Einstein's constant of gravitation | |
| Lambda | Λ | λ |
wavelength, eigenvalue |
|
| Mu | Μ | μ |
'micro' in terms of measurement, muon, coefficient of friction |
|
| Nu | Ν | ν |
neutrino, frequency (f) |
|
| Xi | Ξ | ξ | ||
| Omicron | Ο | ο | ||
| Pi | Π | π | circle's circumference / diameter | |
| Rho | Ρ | ρ |
density, resistivity |
|
| Sigma | Σ | sum of | σ | conductivity |
| Tau | Τ | τ | torque | |
| Upsilon | Υ | υ | ||
| Phi | Φ | flux | φ | phase angle |
| Chi | Χ | χ | structural analysis | |
| Psi | Ψ | ψ | wave functions | |
| Omega | Ω |
# of microstates, Ohm, precession angular frequency |
ω |
angular frequency, angular speed |
Math symbols are used to perform different mathematical operations and represent various mathematical concepts. Symbols save time and space when writing.
There are a lot of math symbols applied in any given mathematical concept ranging from simple addition and subtraction to complicated operations like integration. Here are the most common mathematical symbols:
Basic Math Symbols
| Symbol | Meaning | Example |
|---|---|---|
| $a+b$ | add | $3+7 = 10$ |
| $a−b$ | subtract | $5−2 = 3$ |
| $a \pm b$ | both plus and minus sign | $3 \pm 5 = 8$ or $-2$ |
| $\begin{matrix} a \times b \\ \\ a \cdot b \\ \\ a * b \end{matrix}$ | multiply | $\begin{cases} & 4 \times 3 = 12 \\ \\ & a \cdot b = 4 \\ \\ & ab = 4 \end{cases}$ |
| $\begin{matrix} a \div b \\ \\ a/b \end{matrix}$ | divide / fraction | $\begin{cases} & 20 \div 5 = 4 \\ \\ & 20 / 5 = 4 \\ \\ & \dfrac{20}{5} = 4 \end{cases}$ |
| $( )$ | grouping symbols (calculate expression inside first) | $2\times (3+5)= 16$ |
| [ ] | grouping symbols (calculate expression inside first) | $[ (1+2) \times (1+5) ] = 18$ |
| $\{ \}$ | set symbols | $\{1,2,3\}$ |
| $\pi$ | pi | $A = \pi r^2$ |
| $\infty$ | infinity | $\infty$ is endless |
| $=$ | equals | $1+1 = 2$ |
| $\approx$ | approximately equal to | $\pi \approx 3.14$ |
| $\neq $ | not equal to | $\pi \neq 2$ |
| $< \;\;\; \leq $ | less than, less than or equal to | $2 < 3$ |
| $> \;\;\; \geq$ | greater than, greater than or equal to | $5 > 1$ |
| $\ll \;\;\; \gg$ | much less than, much greater than | $1 \ll 1000000$ $1000000 \gg 1$ |
| $a^b$ | exponent | $2^3 = 8$ |
| $\sqrt{ a}$ | square root ("radical") | $\sqrt{4} = \pm 2$ |
| $\sqrt[3]{ a}$ | cube root | $\sqrt[3]{ 8} = 2$ |
| $\sqrt[n]{ a}$ | nth root | for $n=3$, $\sqrt[n]{ 8} = 2$ |
| $^o$ | degrees | $360 ^o $ (a full rotation!) |
| $\therefore$ | therefore | $a=b \;\; \therefore \;\; b=a$ |
| $\Rightarrow $ | implies (if ... then) | $a$ and $b$ are odd $\Rightarrow $ $a+b$ is even |
| $\Leftrightarrow $ | "if and only if" or iff or "is equivalent to" | $x=y+1 \Leftrightarrow y=x−1$ |
| $a!$ | Factorial | $4! = 4 \times 3 \times 2 \times 1 = 24$ |
| % | percent | 10 % $\times 30 = \dfrac {10}{100} \times 30 = 3$ |
| $\propto$ | proportional to | $y \propto x$ when $y = kx, k$ constant$ |
| $\left | a \right |$ | absolute value | $\left | -5 \right | = 5$ |
| $\Delta $ | change / difference | $\Delta t = t_f – t_i$ |
Calculus & Analysis Symbols
| Symbol | Meaning | Example |
|---|---|---|
| $$\sum$$ | summation – sum of all values in range of series | $$\sum x_i=x_1+x_2+......+x_n$$ |
| $\prod $ | product – product of all values in range of series | $\prod x_i=x_1.x_2.….x_n$ |
| $\lim_{x \rightarrow 0}$ | limit value of a function | |
| $\begin{matrix} {y}' \\ \\ \frac{\mathrm{d} }{\mathrm{d} x} y \\ \\ D_x y \end{matrix}$ | derivative | $\begin{cases} {(3x^3)}'= 9x^2 \\ \\ \frac{\mathrm{d} }{\mathrm{d} x} 3x^3 = 9x^2 \\ \\ D_x (3x^3) = 9x^2 \end{cases}$ |
| $\begin{matrix} {y}'' \\ \\ \frac{\mathrm{d^2} }{\mathrm{d} x^2} y \\ \\ D_x^2 y \end{matrix}$ | second derivative – derivative of derivative | $\begin{cases} {(3x^3)}'' = 18x \\ \\ \frac{\mathrm{d^2} }{\mathrm{d} x^2} 3x^3 = 18x \\ \\ D_x^2 (3x^3) = 18x \end{cases}$ |
| $\frac{\partial }{\partial x} f(x,y)$ | partial derivative | $\frac{\partial }{\partial x} (x^2+y^2) = 2x$ |
| $\int $ | integral - opposite to derivation | $\int f(x)dx$ |
| $\iint $ | double integral - integration of function of 2 variables | $\iint f(x,y)dxdy$ |
| $\oint $ | line integral | |
| $i $ | imaginary unit | $z = 3 + 2i$ |
| $z^* $ | complex conjugate | $z^* = 3 + 2i$ |
| $\bigtriangledown $ | gradient / divergence operator | $\bigtriangledown f (x,y,z)$ |
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