What Are the Basic Functions and Applications of Calculus in Real Life?

[Mattius_]

can someone tell me

A) the basic function of calculus
B) the basic mode of operation in calculus when solving a problem
C) if calculus is intergrated with Euclidian geometry

i am not incredibly math friendly but my questions didnt really warrant any intense mathematical explanation...

 

[HallsofIvy]

A very strangely phrased request! If you are not friendly (to math or whatever), could tell us why your question really warrants ANY explanation?


I take it when you say "the basic function of calculus" you mean "application" rather than a mathematical function (I puzzled over that for a moment!). Basically, calculus allows us to define and work with "instantaneous change". Here's an example I've used before: Imagine being in a spaceship well above the ecliptic: take a photo that shows includes both the sun and the earth. Of course, from a single, static photgraph, you CAN'T find the speed of the Earth around the sun, much less the acceleration: to calculate the speed you need two photos: measure the distance the Earth has moved and divide by the time between the photos to find the average speed between the two. To find acceleration you would need a third photo so you could find two different speeds and find the change in speed.

Yet, you COULD measure the distance from the sun to the Earth from a single photo, then use Newton's gravitational formula to find the force. But F= ma. We are able get the left side of this from a single photo but not the right!

Calculus allows us to define "instantaneous change" (speed AT a specific instant) and make sense of this.

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I have no idea what you mean by "basic mode".

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Yes, calculus is based on Euclidean geometry. The "integration" is through Cartesian geometry.

 

[Imperial]

The functions of calculus in practice include finding rate of change at an instantaneous moment and finding the area under curves. There are many different practical applications to theoretical physics, for example the derivation of equations, and complex numbers (real and imaginary numbers, which provide answers to equations where real numbers do not suffice).

Calculus itself is based pretty much on "limits" and limiting values. This basically means that a variable tends towards a particular value, without ever actually hitting that value. This allows for an almost 100% precise approximation to many questions, which otherwise cannot be answered.

There is no "basic mode of operation" in calculus; there are simply so many branches that every problem requires a different approach.

As for your third question, there are parts of calculus which link with Euclidian geometry, but the majority links in more with Cartesian geometry (integration especially).

 

[Sting]

One application of using Calculus for real life situations is finding work. If you take a non-Calculus based Physics course, they'll tell you that work = force(displacement). This great in the ideal world but it doesn't work in real life situations because the force will be variable. Here's where Calculus comes into place.

What you want to do is find the interval where you are doing the work and then you want to take a small portion of that interval, and find the work perfomed over that portion. Then you want to add up each portion's worth of work and then you obtain the work performed with a variable force. The addition is replaced with a definite integral. Your limits of integration will be your interval and you integrate the force over that interval.

 

[HallsofIvy]

Sting wrote:

One application of using Calculus for real life situations is finding work.

You mean if I learn calculus it will easier for me to find work?

In general if one has a formula which, as long as things remain constant, involves a division, for variables, it becomes a derivative:
example: speed = distance/time becomes derivative of distance with respect to time.

If one has a formula which, as long as things remain constant, involves a product, for variables, it becomes and integral.
example: area of a rectangle (height above x-axis is a constant) is
hw. If the height varies, we integrate height with respect to the base variable.

other example: work as Sting said.