Speaking of calculus, most of math and science students learn it at high school, I guess, but how many people, who were major in non-math & non-science, remember it correctly?

Well, maybe you know, if you differentiate the square of x, it becomes 2x. If you integrate cosine of x, it becomes sine of x.  It’s not so hard, right?

This is an easy process, but how many people can actually answer to “What is it for?” When do you use it? Otherwise, it will be meaningless.

OK. Let’s make it easy. The derivative is the division (the rate of change) and the integration is the addition. Look. It becomes easy now.

Yes. Calculus is easy. No pain at all.

However, there is a little conceptual differences. The derivative is the ratio at the moment. The integration is the addition of a series of very fine pieces.

Now, what are the daily applications of calculus?

Here is a daily one you are always doing. When you turn left in your driving a car, you sense exactly how fast the oncoming car is moving. In fact, this is a derivative you are doing in your mind.

In other words, you instantaneously divide out how far the oncoming car travels per unit time.

How about integration? Let’s draw a shape you like on paper. It may be an irregular shape that is neither a circle nor a square. What would you do when determining its area? There is no official formula for it.

OK. Let’s try how many 5-mm square squares (25 square mm) are filled in that shape. If you are able to fit 100 pieces, it will be 2,500 square millimeters as the area.

Actually, this is integral. In formal way, you will use “infinitely” tiny pieces to calculate the area and volume as integral.

That’s the bottom line of calculus.