When would I use Differential Equations and Calculus in real-world situations?

Question

give examples.

Answer 1

Natural processes are described with remarkable accuracy by differential equations - so, whenever you want to model something in the observable universe, you use differential equations.

Answer 2

In science they're everywhere -- most obviously in physics and economics, but in biology and other sciences as well.

What's more, the underpinnings of statistics are all calculus, and statistics is everywhere in science, and increasingly in business as well (think data mining).

Structural and mechanical engineering are full of differential equations. So is any kind of engineering, such as chemical engineering, that has to do with heat or thermodynamics. So is any kind that has to do with aerodynamics or hydrodynamics.

Quantitative finance -- e.g., bonds and derivatives, which are most of Wall Street -- depend heavily on differential equations. At least two of my fellow math grad students at Harvard went into that area.

That should be enough to get you started. :)

Answer 3

AP calculus AB is relating to the equivalent of a school Calc a million direction. AP calculus BC is relating to the equivalent of a school Calc 2 direction. on the grounds which you're asking approximately BC, might desire to i assume which you have taken AB? if so, the homework load and attempt concern is approximately what you're unsleeping of. in case you haven't any longer have been given from now on taken AB first or a minimum of a calculus direction of a few variety, you will possibly want to. as right now as I somewhat have taught AP Calc, my scholars might desire to need to assume some million hour of math homework on an customary foundation (with approximately 20 minutes in college time to start). The ideas are of direction extra beneficial no longer ordinary, yet as quickly as you have understood the mathematics you have taken so a methods, it is going to be a organic and organic progression. i did no longer assign any outdoors initiatives. assessments have been complicated whether the point became to teach scholars for the AP examination.

Answer 4

A good example is energy usage
the rate of doing work or power times time is energy
y axis is power vs time x axis. The integral is total energy used. Conversely if Energy is known vs time
its differential is power at any particular time.
This is a very useful concept in electrical and mechanical design in this energy hungry world

Answer 5

I am a Chemical Engineer, and most of my coursework required calc/diffEQs.
Once out into industry, I didn't use them much, but I did now & then. Once I had to derive the formula for the volume of an almost horizontal cylinder [at a tilt] as a function of height, to figure out how much spilled [to tell the EPA] when someone tried to overfill it. Really ugly math - easy for a sphere, ugly for cyl.
It will depend a LOT on what you do once you get your degree. Some of my classmates used it a lot.

I draw an analogy: In the earlier part of the 20th century, Chemistry grad students were required to learn German, since the important papers were in German. Once they knew their chemistry, though, they could forget their German [not really if they intended to stay up to date]. Engineering isn't taught in English, it is taught in Math.

Nonprofessionally, I don't use calc much at all, though I do use things I learned that were taught in calc

Answer 6

Transfer phenomena is a good example.

Heat transfer, Mass transfer and Momentum transfer are three phenomea that necessitate the us eof differential equations.

Calculating current or tension in an electric component in transient analysis is another good example.

Answer 7

My Calc. 3 teacher said you probably won't use most of the stuff unless you become a math professor or an electrical engineer. I'm sure it applies to other fields of engineering too.