ND0 RPN Graphing Calculator

Caution: This calculator works with RPN entry (like an HP 28, 48, 49, 50g), as well as with algebraic entry. Switch to 'alg' mode to get a "=" key.

This calculator does not work like an ordinary calculator, and is not merely an improved version of the Apple calculator. It's designed for calculator enthusiasts, students, professionals. You'd be an unusual kid (in a good sense), if you used it in school.
There're 300 pages of documentation on the app's website. You will have to do at least the "Quick Tour" to make good use of it.

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ND0 is a highly programmable calculator with graphing abilities. It's the free three stack positions version of ND1, which has an unlimited stack.

More than 500 commands operate on numbers, complex numbers, expressions, vectors, matrices, strings, and other types of objects, such as "Chemical Formula" and "Color".
Over 2,000 functions result from all type/command combinations. (The "+" key alone has ~20.)

The calculator supports RPN and algebraic entry.

ND0 doesn't (yet) have a CAS, although it supports a level of symbolic manipulation (incl. symbolic vectors and matrices) and has functions like prime factorization and BigNum arithmetic, which are sometimes listed as CAS functionality.
For integration, differentiation, Taylor, and solving, the app goes out to WolframAlpha™ and displays results in an app-integrated browser.

ND0 is programmable in JavaScript and RPL+, directly on the device or from a computer. It and ND1 are the only non-HP calculators that can run many 50g programs.

Data exchange with a computer, and access of the Internet is easy. Also, shared folders are available for download in-app, for things like "Project Euler" problems, or the symbolic manipulation of polynomials.

Please see the app's website for full specs, a "Quick Tour", tutorials, reference documentation, and forums, where a range of topics are discussed and support can be found.