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Some Simple Displayed Formulas:

The character $\hat{\ }$ is for superscripts and $\underline{\ }$ is for subscripts. Single character subscripts don't need to be enclosed in $\{\}$.

e^{ i \theta_1} = \cos{\theta_1} + i \sin{\theta_1}

                e^{ i \theta_1} = \cos{\theta_1} + i \sin{\theta_1}

\frac{\partial^2 u}{\partial x^2}= \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2}

                \frac{\partial^2 u}{\partial x^2}= 
                \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2}

Sometimes it is important not to leave a blank line before the $\backslash]$ ending a math mode display.

Formulas can also be displayed inline by enclosing in $ signs; e.g. $f(x) =\frac{d}{dx} \int_a^x f(t) \ dt$.

                $f(x) =\frac{d}{dx} \int_a^x f(t) \ dt$