Let’s talk more on Calculus. Recently I have just taken the AP Calculus AB test in May. It didn’t really give me a big headache studying (unlike someone else), since if you understand the basics and the fundamental stuff behind it you are good to go. Here’s some main topics discussed in the course:

Notice: This article is not a Calculus tutorial.

Some concepts in Calculus actually existed way back before Issac Newton was hit by an apple. Ancient Greek mathematicians had been using infinitesimals to calculate areas and volumes in about 200 BC. Until 17th century, modern calculus started to appear. Several European mathematicians worked on the idea of derivative, published books including *Methodus ad disquirendam maximam et minima*. Issac Newton later wrote *De analysi per aequationes numero terminorum infinitas* based on their ideas. Then, calculus started booming.

Did I tell you that calculus was actually two different subjects before? I thought I did… but anyway, deferential calculus and integral calculus were totally different things. Until the 1600′s, the *Fundamental Theorem of Calculus was finally created and proven by *James Gregory, a classy Scottish mathematician; it linked the two parts together, and boom, modern calculus was born.

Later on, infinite series was created to find the sum of a infinite amount of numbers. (It is not included in AP Calculus AB.)

Limits sound weird when you first heard it. Basically it is just filling holes in a function (curve) and finding its y-coordinate. Imagine a line *f*(*x*) = *x* with a hole at 0. At x = 0, y would be not exist. However, applying the concepts of limits and now it would be 0 regardless of there is a hole or not.

Now this is the fun part: you can find a line that exactly touches *f*(*x*) once!… okay I guess it is not that exciting at all. Derivative is just a function that will give you the slopes of *tangent* lines, and it comes out that you can also find the *instantaneous rate* of the original function. (how amazing is that!)

Ever thought about how you can find the area of an irregular shape? (say yes) Well before calculus you can’t. Tries to combine all those formulas of finding areas of squares and circles, and headaches will come to haunt you. Introducing the integral! Integrals can be used to find the area under a curve, such as *x*^{2}. It turns out that that area between the curve *x*^{2} and the x-axis from 0 to 2 is exactly 8/3 unit^{2}. How incredible is that!

Related rates is a cleverly-created tool in mathematics used to determine different rates based on known rates. In other words, you can find out how fast your money is disappearing by knowing how much snacks you bought in a day.

Thank me because now you know how fun and useful calculus is. You’re welcome.

]]>This image right here is made with Blender. Took me about 15 minutes to draw, and 15 minutes to render. (Very slow with CPU rendering ) In the upcoming year, most importantly I hope that I can get into a good university , and I will continue on updating my website and developing my little extensions for Chrome. And again, Happy New Year!

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]]>To win the Mega Millions lottery, you will have to pick 5 correct numbers from 1 through 56 and 1 number from 1 to 46. We can calculate the probability of winning using the following formula:

Which is

or AKA – *Mission Impossible*.

In the newly designed layout of my blog, as you can see, there is a “beautiful” sidebar on the left, along with some useful links like “Archives” and “Categories”. Also, notice there are RSS links! (Very cool, WordPress) In the left hand side, there are the main posts, newest on top, and older on the bottom. When you click on any links that links back to my site, you will see a loading GIF, indicating it is loading the page with Ajax. This makes the page loads faster since it doesn’t need to load redundant stuffs like header and footer.

When you look at the bottom of each post, you can see that you can leave comments there! It supports comment threading, which means you can reply to comments! By the way, most of the stuff above talked are not made by myself, instead they are included in WordPress 3.3.1.

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