mathcomesalive

Introduction

This program lets you construct and edit algebraic expressions and equations, and apply basic algebraic operations such as “collect like terms”, “take out common factors”, “combine common factors”, insert or delete brackets, “add ??? to both sides”, etc. In every case you have to select those parts of the expression to which the process is to be applied.

The algebraic construction is based on “expression”, “term”, and “factor”, where expressions are made up of terms, terms are made up of factors, and factors are either single variables or expressions themselves, with (…) naturally.

All the basic standard functions can be used, and anything can be raised to the power of anything.

The variables can all be given values, and the value of an expression can then be calculated. There is a graphing facility which will show single plots, several different plots, or repeated plots of the same expression as the value of a parameter changes. Full zoom and shifting is included.

Finally, there is an expression generator where one can choose “number of terms”, “Variable names”, “highest power”, etc, etc, etc, and an expression is generated with the help of random numbers.

“Algebra is OK”

Here are more examples of expressions, and an equation

The expressions are displayed correctly as in the example on the right, and the editing process always displays an algebraically correct expression. For example, when inserting a “+” the expression always inserts a dummy variable “O” as well, to hold the actual stuff to be added.

The expression generator -

Any expression can be displayed as a graph. One of the variables is chosen as the ‘x’ variable, the others are given numerical values and are the ‘constants’.

Graph plotting

In this case one of the ‘constants’ is picked a the parameter, and the graph is plotted for successive values of this parameter for the chosen step length.

Commands

The commands for algebra are grouped into ‘ Brackets’, ‘Rearrange’, ‘Change order’ and ‘Solve’, each with a drop down menu.

There is also a set of questions under ‘Structure’ such as ‘Is it a term?’.

Right click will bring up a relevant help window for almost everything.

The ‘Rearrange’ drop down menu.

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