What is the practical use of calculus in various fields?

[Butterfingers]

Hello all,

I am a newbie here, and I have a couple of things to ask with relevance to what I'm doing here... but first I'll want to introduce myself, I'm an Electronics and Communications Engineering freshman (turning sophomore this school year 2006-2007) studying in the Philippines.

I'm curious towards what calculus (differential, integral, multivariable) has to do with what I'll be doing for a living someday.

And what else is calculus applied for... thanks for your time. ^_^

 

[arildno]

I'm curious towards what calculus (differential, integral, multivariable) has to do with what I'll be doing for a living someday.

Basically, everything.

 

[berkeman]

Well, for starters, pretty much all of electromagnetics is based on Maxwell's equations, which are expressed in either integral or differential form. To work with E&M, you use calculus a lot to derive solutions for real world situations like antennas, transmission lines, transformers, etc.

And when you work with semiconductors, the equations that govern how currents flow and how voltages form involve differential equations.

And when you work with designing and simulating and solving circuits for their behavior (and optimizing their behavior), you are working with differential and integral equations. And when you use tricks like switching back and forth between the time domain and frequency domain for signals that you are working with, you use integral calculus to do it.

And...

 

[Pythagorean]

differentation is better conecptualized when changed into a difference. Basically, as a physicist, I would be exploring the numerical relationships between things, but sometimes things don't have a static relationship.

Instead you can only write an equation for how one thing changes as another thing changes...

Berkeman's examples where excellent.

Try changing a differential into a difference (or asking a teacher how) and plugging real numbers into it. Differences are not accurate, because they use real numbers and approximations, where as a differential uses an 'infinitesimals' which is a lot like infinite, only going towards zero instead of away from it. To put it another way, you're using 'infintely small numbers' in differentation.

Difference tries to use really small numbers, but not infinitely small.

Honestly, I didn't learn differentation from my differential equations class. It wasn't until Computational Physics, where we had to convert differentation to a difference (because computers don't know a thing about infinite, they don't think continously like we do) that I was able to conceptualize it.

Once you see how differentiation works, and you've seen a few differential physics equations, you'll get it. I don't think it's something that you can learn in one thread.