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Math Expressions in LaTeX (Practice)

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goals: - learn the basic syntax of latex - insert mathematical symbols - format certain mathematical expressions such as fractions, matrices, and integrals

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$a \pm b$ \ open bracket a \pm b\ close bracket

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$a \le b$ \ open bracket a \le b\ close bracket use ge for greater than or equal to

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$a \approx b$ \ open bracket a \approx \b close bracket use \neq for not equal to

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$\alpha$ \alpha for alpha symbol, substitute with the appropriate code as necessary \beta

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$\int\limits_{a}^{b}$ \int\limits_{lowerlimit}^{upperlimit} for integrals

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$\sum_{a}^{b}$ \sum_{lower limit}^{upper limit} for sigma notation/summation

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$\lim_{a \rightarrow b}$ \limit_{a \rightarrow b} limit notation

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$\leftarrow$ \leftarrow or \rightarrow useful for showing steps or for chemical equations

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$\Rightarrow$ \Rightarrow with capital R implication arrow

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$\sqrt[exponent]{radicand}$ \sqrt[exponent]{radicand}

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$f\prime \prime$ \prime for derivatives or for distinguishing elements with the same name

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as a side note square brackets are typically used for optional arguments and curly braces are used for required arguments, as with the radical example

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$\log_{base}$ \log_{base} use ln instead of log for natural log

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$\sin (x)$ \sin(x) can replace with cos, tan, sinh, cosh, tanh, etc.

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$\sin^{-1} (x)$ \sin^{-1} for inverse trig functions

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$\frac{ a }{ b }$ \frac{numerator}{denominator}

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$\left[\begin{matrix}entry 1 & entry 2 \\ entry 3 & entry 4\end{matrix}\right]$ \left[\begin{matrix}entry 1 & entry 2 \\ entry 3 & entry 4\end{matrix}\right] use \\ to separate rows and & to separate entries within row

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