Where there is life, there is calculus

For the vast majority of students, studying maths means locking them up in the room and making their way into those endless textbooks. I, as an exception, appreciate that mathematics is to be applied in real life. This semester, we learn calculus which is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. I find that where there is life, there is the knowledge of calculus.

When I am riding a bike, it reminds me of calculus. One of the most practical problems in differential calculus is the connections between position, velocity, and acceleration. I have to stop when I meet a red light, if the speed of the bike increases from rest up to 6m/s in 30 seconds, how long can I travel during 30 seconds?

To solve this problem, first and foremost, we need to recall the formulas in calculus. Velocity is the first derivative of the position function and the acceleration is both the first derivative of the velocity function and the second derivative of position function. The equations are shown below.

With the help of the equations, we can get the acceleration.

^0.2

From the previous results we can now express the velocity as shown.

^0.2t

We now find the displacement

^{0.2 0.2 0.2 60}

Furthermore, there is another way to solve this question. We can compute an expression for the velocity and the position at a given time.

This implies that

Do you familiar with that? Yes, this is the formula given in physics.

That is the basic formula in physics. It confirms the truth that calculus is used in almost every aspect of life from position problems to field of physics. We use the derivatives in the problem above to determine the position of a object. As I shown at first, calculus contains derivatives and integrals. We can use integrals to calculate the area of an irregular object. Draw a curvy line from the left side all the way to the right side, so that the figure is now closed in space. Even if the curvy line is complicated or convoluted, we can get its area immediately.

Math is everywhere, from time, to pay, to work, driving, purchases and business. Math is the basic science of all of the science. As a result, we can find it in the field of other subjects. All in all, Math is an unavoidable and constant in everyone's life daily.

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This work is licensed by Qi Yang under a Creative Commons Attribution License (CC-BY 3.0), and is an Open Educational Resource.

Last edited by Ed Woodward on Dec 19, 2011 12:55 pm -0600.