The Wolfram Alpha resource, called a knowledge engine, is somewhat unconventional, and I found the coverage of areas of science uneven, but this is a real gem for any students or professionals in mathematics and science. It is nice in that you simply can type what you want in a way that is similar to everyday life - e.g. typing "integrate cos x dx from x=0 to pi" will then produce the symbolic form for the integral, the answer (0 in this case) and a graph with the integral area shaded.
Even if you use only the mathematical features, it is well worth the investment. For example, if you want to perform symbolic algebraic derivatives or integrals, it is simply a matter of entering the input function. There are also tools for numerically computing functions and definite integrals. It comes with samples, and most of the time you can go to one of these, and then change the function to meet your needs. A particularly nice feature is there is a link to show the intermediate steps in a solution that can be turned on or off. Functions are plotted automatically as part of the solution, and alternative forms are often displayed. The matrix operations are nice - provide the entries for a matrix, and it will show you the determinant, trace, eigenvectors and eigenvalues, for example.
The Statistics and Data Analysis has a number of very useful features, including the possibility of doing regression analysis with linear, cubic and exponential fits. It also does various distributions including norma and Poisson. Those with a more elementary interest in the topic of probability and statistics may want to play with entering different numbers of coin tosses, and check out the probability of various answers (e.g. there is apparently a 14% chance of exactly equal numbers of heads and tails if you do 32 coin flips).
I explored the engineering functions a little bit. One topic that I am interested in is the design of digital filters, and it allows you to design Chebyshev type 2 filters, for example. It comes up with a canned example, but if you click on change input values it allows you to specify the gain, cut-ff attenuation, stopband attenuation, and frequency range, and it will both compute the filter and show a pole-zero plot as well as the response function. Very nice!
Units and measures will be helpful to most users. The open format allows you to type in something like "25 acres in hectares" and it gives the result, as well as additional conversions. It also will display comparisons (e.g. in this case it told me that 25 acres is about 1.8 times the area of the base of the Great Pyramid in Gaza).
To see how much more there is beyond the categories given, I tried a topic from general relativity, typing in gravitational time dilation. What it came up with was the closest match of time dilation, which was simply the special relativity time dilation. Therefore those not familiar with an area have to be careful that it is giving you what you want. I think the tool is best used as a way to rapidly perform computations, or to independently check a computation. It is useful, for the topics covered, in an instructional mode using the show steps feature.
Now at $1.99 (initially it was many times this cost) it is hard to argue that any scientist or engineer should not purchase this app! I think many others, including those with an armchair interest in science, will find it a fascinating way to explore topics from a wide range of topics. In that connection the sections Interesting Modern Results and Famous Paradoxes are good starting places. For example, Famous Paradoxes in physics include the twin paradox in special relativity, the Boltzmann paradox and the EPR paradox in quantum mechanics.
It will also be useful beyond science of course. I typed the name of my small town (Sackville) and it gave the current population, a map, distances to nearby towns and cities, as well as the current weather, coordinates, etc. The Word Properties section allows you to do everything from finding words that rhyme with another word, to finding synonyms of words (and a lot more). It even allows you to type Scrabble xylophone, for example, and it confirms that it is a word, and will give you the scrabble score for the word.
I give it a rating of 9.0 (out of 10). It is excellent value for the money, is amazing particularly for mathematical computations, and is a broad and useful resource. It is the somewhat uneven coverage that keeps me from giving it a perfect 10.
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