Based on a simple pendulum's mass (m), length (l), initial angle and velocity (y0), its motion is calculated. If the constant c is greater than zero, the motion will be damped.
Graph of Pendulum Motion
A graph of the motion of the pendulum modelled above.
Create HTML Interfaces
An HTML form object is used to wrap a simple calculation with a user interface. It takes height and weight and uses them to calculate a body mass index. Note the use of mixed units in the inputs.
Graph of Least Squares Fit
A graph showing the results of using the optimizer to fit a group of randomized points with a parabola.
E = MC^2
I am apparently a huge bundle of energy when totally annihilated. This is Einstein's famous e = mc^2 formula with 85 kg as weight. The unit lightc is a velocity unit equivalent to the speed of light in a vacuum. Math Minion figures out it the result is an energy and I have chosen to display it in more dramatic units than the standard kJ.
A Future Value Report
Simple text or CSV reports can be generated for export. Here a single expression is reported. The expression produces a table of future values given an initial amount and an annual interest rate, which is assumed to be compounded monthly.
initial * (1 + interest/12)^(1:20*12)
is interesting for the use of the 1:20 range operator in the power. This produces an array of integers from 1 to 20 and shows how arrays can be used in algebraic expressions.
There is an expanded keyboard when editing formulas and it includes buttons for browsing conversion units, functions and objects and their contents. A tap will insert whatever you choose into the formula.
This model uses the equation solver to calculate 100 bubble points for an ethanol/water system.
The results of the bubble point calculation as a plot.
A McCabe Thiele distillation column diagram is constructed on the ethanol water equilibrium diagram.
Please see the Examples page as well.
Math Minion started out as a powerful scientific calculator and modelling system with a deep understanding of conversion units, but over time it has evolved into much more. When string handling was introduced to its powerful array handling, it became an adept string processor. The addition of data tables allowed it to handle many small database and spreadsheet problems and the introduction of HTML interface objects now makes it something of an app minion. The journey continues.
It combines a mind map style representation of the relationships between expressions, with a formula system that operates transparently on scalars, arrays and matrices. A hierarchical model system helps encapsulate calculations in logical and easily duplicated units and a flexible unit conversion system tracks the fundamental property types through calculations. This allows it to know, for instance, that some fathoms divided by a few days is in fact a velocity that should not be added to a kilogram.
Some interesting features include:
- equations that work equally well with scalars, arrays and matrices
- a function library that in addition to the usual suspects includes:
- matrix multiplication, inversion, transpose and redimensioning
- comparison (eq, ne, lt, ge, if etc)
- string functions (split, join, regular expressions, etc.)
- interpolation, indexof, select
- complex number and statistical functions
- time, sorting, random, web reading and many more.
- a flexible unit conversion system that helps automate dimensional analysis
- data tables for storing and manipulating tabular data whether numeric or string
- models and model arrays for information and calculation encapsulation
- a solver for one or more nonlinear equations
- an optimizer
- an ordinary differential equation solver
- an iterator tool.
- a x-y graph tool.
- an HTML interface object for creating calculation user interfaces.
- share sessions between iOS and Mac devices using iCloud
- store and retrieve sessions from Dropbox
Math Minion is a universal app that runs on the iPhone and iPod Touch as well as the iPad.
A completely compatible version for Mac OS/X Lion is also available for free in the Mac App Store.
All versions support iCloud document handling, so you can easily switch from device to device while working on the same sessions.
The manual from the application is also available (iOS, Mac).