Ditch that graphing calculator for TYDLIG, THE SUPER CALCULATOR OF THE FUTURE!! By Andreas Karlsson ($1.99)

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Tydlig is a beautifully designed calculator with built in mathematical functions such as sine and logarithmic functions.

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Symbolic calculator

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CALCA the Symbolic Calculator (by Kruegar Systems, inc) gives you instant answers to math equations as you type. All equations are solved inline and can use normal English. ($2.99)

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This is an example document.

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Formulas

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Write formulas freehand using MyScript MathPad! (Free)

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My handwriting...

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The formula! You can swipe across mistakes to delete them. Swipe across the 2 to remove it.

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Draw in a "D" after the x to add it in.

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Calculus stuff.

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Conversions

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The best conversion tool on the planet! Amount by Marco Torretta! ($.99)

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Type in a number, then tap a category, and you get a list of all relative conversion factors. Whichever unit you choose will use the number you typed as an amount.

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Math Document Publication

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LaTex is a markup language that formats documentation. Use TexWriter by Chaoji Li to generate professional-grade mathematical publications. ($9.99)

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This is how LaTex looks.

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And this is the generated document.

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Close-up

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Math Programming

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Need to make your own custom math software? If you know a little programming, you can use Pythonista by Ole Zorn to code one in the Python programming language. ($6.99)

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Some code for a math plotting program.

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The result.

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Workflow

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I've mentioned a Editorial often. It's a must for all writing needs. Editorial is a markdown editor, which used a workflow system to automate your writing needs. Also by Ole Zorn. ($6.99)

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Now you are supa! Nice!

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Thank you Gary Velez for this recommendation. Wolfram Alpha is a must! ($2.99)