SciLearn: August 2008

Friday, August 22, 2008

differential table

This is a table that lists everything in differentials, so it can be used for differentiation and integration at the same time.

I'm not sure if everyone can find this useful, since some might prefer non-differential forms because they are easier to understand and use - so I don't think this table would be suitable for calculus beginners.

Okay, here's what the symbols in my table means:

k is a constant;
f, g are functions of a variable t.

And here's the table (click the image if the equations get cropped):
$\begin{array}{ll}d \left( f \cdot g \right) = df \cdot g + f \cdot dg &d \left( \frac{f}{g} \right) = \frac{df \cdot g - f \cdot d g}{g^2} \\d \left( f^k \right) = k f^{k - 1} df &d \left( f^g \right) = g f^{g - 1} \, df + f^g \ln f dg \\d \left( k^f \right) = k^f \ln k \, df &d \log_k f = d \left( \frac{\ln f}{\ln k} \right) = \frac{df}{f \ln k} \\d \left( e^t \right) = e^t dt &d \ln t = \frac{dt}{t} \\d \sin t = \cos f \, dt &d \cos t = - \sin t \, dt \\d \tan t = \sec^2 t \, dt &d \cot t = - \csc^2 t \, dt \\d \sec t = \sec t \tan t \, dt &d \csc t = - \csc t \cot t \, dt \\d \arcsin t = - d \arccos t = \frac{d t}{\sqrt{1 - t^2}} \\d \arctan t = - d \operatorname{arccot} t = \frac{d t}{1 + t^2} \\d \operatorname{arcsec} f = - d \operatorname{arccsc} t = \frac{dt}{|t| \sqrt{-1 + t^2}} \\d \sinh t = \cosh t \, dt &d \cosh t = \sinh t \, dt \\d \tanh t = \operatorname{sech}^2 t \, dt &d \coth t = - \operatorname{csch}^2 t \, dt \\d \operatorname{sech} t = - \operatorname{sech} t \tanh t \, dt &d \operatorname{csch} t = - \operatorname{csch} \coth t \, dt \\d \operatorname{arsinh} t = \frac{dt}{\sqrt{1 + t^2}} &d \operatorname{arcosh} t = \frac{dt}{\sqrt{-1 + t^2}} \\d \operatorname{artanh} t = d \operatorname{arcoth} t = \frac{dt}{1 - t^2} \\d \operatorname{arsech} t = - \frac{dt}{t \sqrt{1 - t^2}} &d \operatorname{arcsch} t = - \frac{dt}{|t| \sqrt{1 + t^2}}\end{array}$

You can tell me if this is useful or not.

Saturday, August 16, 2008

trademark?

Oops. While I don't think anyone uses 'SciLearn' as a blog name in its entirety, I just hope that no-one complains that I'm using it. Would you call that a trademark issue?

Changing the name of a blog won't be easy, even for a no-name blog that no-one knows. (This also means that the URL has to be changed, and that means: broken links.)

I just hope that I might come up with a catchier name than 'SciLearn' someday.

Monday, August 11, 2008

unspecified specs

Recently I was looking all around the web for a good laptop to buy, so perhaps I should share some of the new knowledge I learned about laptop specifications.

There are tons of stuff that you should look out for in laptops, and it's hard to look at them all. So here are some basic specs to look out for. ("^" means the higher the better; "~" means the lower the better)

processor (a.k.a. CPU)

This is what determines basic performance of your computer, as in computational speed.

Factors to consider:
L2 cache (in MB)^
clock rate (in GHz)^

For normal uses, a laptop doesn't need an extreme high-end processor, unless you want to dedicate it to number-crunching and complex mathematical calculations. A moderate to fairly high speed CPU is good enough in most cases.

Typical brands: Intel, AMD.

graphics card

This determines how your computer will fare with heavy graphic-intensive applications, including 3D applications & games.

It's hard to determine the performance of graphics card by plainly looking at the specs. In general, the second digit is the one that determines speed, while the first digit is the generation of the graphics card. For detailed info, check this thread. Also, take note of the amount of dedicated graphics memory available (in MB)^. You can also use benchmarks as a guide, but remember that benchmarks only provide a rough comparison between graphics cards.

Typical brands: NVIDIA, ATI (AMD), Intel.

system memory

Factors to consider:
latency~
bandwidth^
size (MB)^

The minimum RAM nowadays is typically 512MB, so you should aim at something higher than that to achieve the best performance. Any addition of RAM, up to 2GB, will give a noticeable performance boost. Most laptops allow you to upgrade the RAM fairly easily. (Another detailed article)

hard drive

Factors to consider:
rotational speed (in rpm)^
size (in GB)^

The size of the hard driver mainly matters if you want to store a lot of stuff. However, the real bottleneck here is the rotational speed of the hard drive. Typical speeds include 5400rpm and 7200rpm. The reason is simple: swap memory uses the hard drive, which needs to be fast enough in order to serve its purpose. Otherwise, you may encounter considerable lag in performance.

These are the main and often most important things to consider when getting a laptop. Of course, there are plenty of other things that should be taken into consideration: