Differential Equation And Areas Of Plane

Imagine a growing or shrinking area of a plane, the change that will be occurring will happen at a predetermined rate. This rate of change is governed by natural factors and limitations. But it can be measured. And by measuring this change, we can predict its value and prepare for the consequent change. This is where differential equations come in. They allow you to measure the rate of change in any variable happening in relation to another variable. The relation between the rates of change and the physical quantities is known as the differential equation.

What are differential equations?

Imagine an area of a plane and any two points on it. These two points will have predetermined values on them. Now, imagine that these two points are moving, and you have the task of predicting the position or value on one of these variables in relation to the other.

Sounds like a difficult task, doesn’t it? Not if you know differential equations. A differential equation is used to calculate the relation between two different functions. These two functions are nothing but the representation of these two points that lie somewhere within the area of plane in question.

With knowledge, you will be not only able to correctly predict the rate at which they are changing in relation to each other but also be able to pinpoint where they are going to be at any point in time in the future.

What is the area of the plane?

The area of a 2D figure is what we know as the area of a plane. The mention of the number of dimensions that we work in is necessary. In math, we work with a number of figures; they can be in either 2D or 3D.

The areas of these figures are calculated differently and thus, the distinction between them. In the present case, we will only talk about 2D figures since we are discussing the area of a ‘plane.’

A plane is any flat, 2D figure (that can extend up to infinity). When we talk about a plane, we always talk about a fixed shape on the plane. And when we talk about the area of a plane, we are talking of the area of this particular shape.

Relation between the two

The relation between the two is quite beautiful when represented graphically. It is about tracking the movement of a point in an enclosed area. We are going to require an understanding of both of the above-mentioned concepts if we are going to depict them.

The area of the 2D figure shall be our entire graph. And the point that we are to track will be the determining line on the graph. The rate of change of position of this point can be determined by solving for its value. 

And once we know the rate at which it is going to change, the point being a vector quantity, we can point the direction that it is going to go in.

Formula

You can denote a point on a plane figure using the following formula:

P=(x, y)

In the above-mentioned formula,

P = the plane in question

x = point on the plane on the x-axis

y = point on the plane on the y-axis

Now, let us talk about a differential equation. It can be represented in the following manner:

dydx

In the above-mentioned formula,

x = independent variable

y = dependent variable 

Applications

All these equations, formulas, and discussions about the area of planes naturally raise the question of when are you going to use all this?

These are complex calculations with not much use in life, right? WRONG!

You are going to find plenty of use for differential equations and a plane figure. Whenever we talk about the change in any commodity, the spread of any phenomenon, we are talking about the rate of change. In medical science, differential equations are used to predict the rate of spread of diseases.

Even in the financial sector, they are used to predict the change in return on investment over a period of time. So you see, the concepts we talked about in this article have far-reaching implications in our daily life.

The world turns on indicators of economics today. And forecasting the direction that these indicators are likely to determine the decisions to employ or withhold our resources. And that is the beauty of math. It can be trusted to lead you to the right conclusion even when you don’t know all the factors influencing the change.

Conclusion

All this naturally raises the question, are you going to need these technical skills in your daily life? Well, yes. To gain a better understanding of the world around you and how it changes, you need to know how to measure that change. 

The next time you are waiting for your hot cup of tea to cool down a little, know that there is mathematics happening right there. The difference in temperature brings about cooling. And you can measure this rate of change by using differential equations.