Importance of calculus for Engineers

Calculus to an engineer is wind to a sailboat

I want to motivate engineering students to consider calculus as the most important mathematical tool. I will do this by explaining how essential it is for engineers with an analogy.

An analogy

Let us begin the analogy by comparing nuts and bolts with numbers, tools with mathematical operations.

I would say the household tools such as the screwdrivers, wrenches, and pliers are comparable to the mathematical operations such as addition, multiplication, and division. I say this because we all use these in our everyday life. Also, we expect any randomly selected adult to know this.

And then comes a specialized tool such as a tire jack. We can compare it to mathematical operations such as trigonometric operations. Why do I say this? Well, it is because most of us have one of those in our cars, but we rarely use these tools.

Now let us see where the engineers and calculus fit in this analogy. I would say that the power tools are equivalent to the calculus, and the engineer would be a car mechanic. I have two reasons to make this comparison.

The first and most important reason is that a mechanic cannot complete several tasks in the absence of power tools.

The second reason is a mechanic may save a considerable amount of time by skipping employing power-tools for the tedious jobs.

So, What do I want to explain with this analogy?

1. Without calculus, engineering students cannot fully grasp several topics which they are going to study in the following semesters.
2. Also, sometimes knowing calculus helps us avoid tedious calculations.

What do I mean by calculus?

Single variable differentiation and integration are the first two topics you should be comfortable with as an engineer before going to the multivariable calculus.

How is it different from the rest of mathematics?

If you see a person standing at a distance from a point light source, you expect a shadow. The mathematics without the calculus would let you predict the shadow length.

If I ask you: How fast the shadow moves if the person is moving at a certain speed? You must be looking at the calculus knowingly or unknowingly.

I give this example because regularly, we use the term static for mathematics not involving calculus and the term dynamic with the mathematics to do with calculus.

With the help of calculus, Newton was able to uncover the mystery of why planets move in an elliptical orbit. However, It would be unfair to say that he could accomplish this without the help of his law of gravity.

I am not a mechanical engineer. Why should I learn calculus?

To stimulate student’s imagination, most of the examples used in calculus class are the physically moving objects, which may give the impression that calculus is for mechanical engineers. However, this is not at all true. All branches of engineering required calculus.

Conclusion

Calculus is a required, useful, and inseparable mathematical tool for an Engineer. If you want to be an engineer, you might know the calculus already, or today is the best day to start your calculus learning.