Mathematical tools
There are plenty of tools on the internet that can help you while you study. Many programs can work out a maths problem in an instant, and some even show the working, so you can learn the material better.
Wolfram Alpha
Wolfram Alpha is currently (2011) probably the best online tool for mathematical calculations. You can find it at wolframalpha.com. The whole interface is in English, but usually all you need to do is type the expression you want to calculate into the input field and Wolfram Alpha will somehow cope. It helps to know a few keywords – for example, if you want to differentiate, just write “derive” in front of the expression.
Wolfram Alpha has quite detailed help with a heap of examples, including purely mathematical examples.
A few examples. Suppose you have a pair of simultaneous equations:
Enter “x+y=0, x+2y=2” into Wolfram and look at the result on the website. You will find both the graphical solution and the final result there. If you wanted to work out the derivative of this function:
enter “derive ((2x+3)/(x-2)^2)*log x” into the field and again look at the result on the website. If you click “Show steps”, it will also show you the steps Wolfram took to arrive at that derivative.
But Wolfram Alpha is not just a maths tool – you can ask it other questions too. For example, whether Skynet exists, or what the capital of France is.
Limit Calculator
An online tool that calculates limits of functions, both one-sided and two-sided. You can find it at numberempire.com. The interface is very simple: in the top field you type the function whose limit you want to find, in the bottom two fields you type the variable you are taking the limit in (the default setting with x will probably be enough for you) and the value the variable should approach. In the drop-down list you can choose a two-sided limit (“two-sided”) or a one-sided one.
GeoGebra
GeoGebra is a program for simple geometric constructions. It is written in Java, which some people may mind. But most people probably don’t know what Java is, so it doesn’t matter :-). You can download the program from the home page at geogebra.org.
First of all, it can draw lines, rays and line segments defined by two points. You first click two points and the program joins them with a line. A huge advantage is that if you later move one of the key points, all the lines turn with it. In general, if you move any point that is part of a shape, the shape changes too, where possible. You can also draw a line segment by entering its length, for example, without specifying both points. GeoGebra can handle vectors as well.
It also copes with polygons, various angles, parallel and perpendicular lines. Drawing circles in several different ways is no problem. GeoGebra will also measure distances or areas of the objects you have drawn. You can also create a checkbox, which lets you show and hide parts of the drawing that you choose.
I drew the pictures in the article about angles with this program, so you can see what such a result looks like.
