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Writing Maths and Physics Equations using MathJax





Bernoulli's principle

\({v^2 \over2} + gz + {P \over \rho} = constant \)

Where v is the fluid velocity, g is acceleration due to gravity, z is elevation, P is the pressure and
\(\rho\)
is the fluid density.
Binomial Theorum

\((1+x)^n = ({n \over 0}) x^0 + ({n \over 1}) x^1 + ({n \over 2}) x^2 ... + ({n \over n-1}) x^{n-1} + ({n \over n}) x^n \)


Or
\((1 + x)^n = {\sum_{i=0}^n} ({n \over i}) x^i\)
Kinematic Equations

\(d = v_i t+{1 \over2} a t^2 \)

\({v_f}^2 = {v_i}^2 +2ad \)

\({v_f} = {v_i} +2at \)

\(d = {{v_i} + {v_f} \over2}t \)


Where d is displacement, vi is initial velocity, vf is final velocity, t is time and a is acceleration.

Least Squares Regression


\(m = {{N \sum xy - \sum x \sum y} \over {N (\sum x^2)-(\sum x)^2}} \)


\(b = {{\sum y - m \sum x}\over{N}} \)


Where N is the number of data points and m and b are the slope and intercept respectively of a line y = mx + b.

Luminosity of a Star


Luminosity of a Black Body Object (Approximation for a Star)
\(L = \sigma A T^4 \)

Where L is the luminosity (kW), A is the surface area (m2)
\(\sigma\)
is the Stefan-Boltzmann Constant (5.670367x10-8 W m-2 K-4) and T is the surface temperature.

Mohr's Stress Circle Equations


\(\sigma_n = {1 \over2}(\sigma_x + \sigma_y)+{1 \over2}(\sigma_x - \sigma_y)cos2\theta + \tau_{xy} sin2\theta \)


\(\tau_n = -{1 \over2}(\sigma_x - \sigma_y)sin2\theta + \tau_{xy} cos2\theta \)


\(R = \sqrt{[{1 \over2}(\sigma_x-\sigma_y)]^2 + \tau^2_{xy}} \)


Quadratic Equations


When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)
.

Special Relativity


\({t' \over t} = {1 \over {\sqrt{{1 - ({v\over c})^2}}}} \)
\({L' \over L} = {1 \over {\sqrt{{1 - ({v\over c})^2}}}} \)
\({m' \over m} = {1 \over {\sqrt{{1 - ({v\over c})^2}}}} \)
\(E = {\sqrt{m^2 c^4 + p^2 c^2}} \)

c is the speed of light in a vacuum (299 792 458 m/s) and v is the velocity of a body.

t is time as measured from a stationary perspective, likewise L is the length measured from the same perspective and m is the mass.

t', L' and m' are the time, length and mass respectively as measured from the perspective of instruments traveling at velocity v.

E = Energy, P = momentum.

Physics and Maths Formulae



These are some simple or relatively simple formulae used in maths and physics. To display the formulae I use a javaScript library called MathJax. MathJax is easy to learn and free to use so if you're a technical author please check it out.

The point of this page isn't to teach anyone maths or physics, I just wanted to show that formulae can be incorporated in a webpage without relying on creating and incorporating images.