What is the Purpose and Application of Calculus?

[.ultimate]

What are the applications/uses/purpose of Calculus?
Why Do we NEED to find derivative of x wrt to y?

Are there any uses of calculus or is it restricted to Classical Physics - Inertial Frame of References?

 

[theperthvan]

because everything is calculus (except things that aren't).
But really, it solves everything.

 

[.ultimate]

What consititues this everything? Can yo give me an instance of the use of Calculus?

 

[matt grime]

Differential equations govern phyiscal phenomena in our models of the world. C.F. all applied mathematics: fluid dynamics, quantum mechanics, mechanics in general, etc etc etc.

 

[usahockey]

Not to hijack this topic, but which introductory Calculus text would include the best applications for solving physics or engineering problems? I have heard that Courant's shows a lot of uses for physics, but maybe this work is too in-depth for starting in calculus.

Just wondering, because it's a lot easier for me to work through books where you are solving real-world problems and seeing what the math is useful for, rather than just crunching equations that you don't truly understand.

 

[.ultimate]

Not to hijack this topic, but which introductory Calculus text would include the best applications for solving physics or engineering problems? I have heard that Courant's shows a lot of uses for physics, but maybe this work is too in-depth for starting in calculus.

Just wondering, because it's a lot easier for me to work through books where you are solving real-world problems and seeing what the math is useful for, rather than just crunching equations that you don't truly understand.

Yes, I agree with you. Can anyone recommend any good Introduction to Calculus emphasizing on its applications.

 

[cshum00]

You will usually get application problems in the middle of the Calculus courses. At the beggining of the course is definitely going to be about formulas, where they come from, how are they derived, how to use them, how to transform them, etc. Because without them, you won't know how to solve the application problems later.

It is true that it is easier to see mathematics related to the real world. But sometimes, the abstract process cannot be directly be translated to real world solusions. There are mathematical calculations where the process doesn't make sense at all to the real world except the results.

However, it is funny that solving word problems in calculus is often one of the hardest too because we have to correctly translate the word problem to mathematical formulas.

 

[reilly]

Let's see: finance and economics use calculus for working out interest payments and so forth, for determining optimal bond portfolios, for examining so-called marginal costs; figuring out the most economic way to cut circles from a bolt of cloth. Then, lot's of calculus in the design of airplanes, ships, rockets, computers, radio and TV transmitters, radios, TVs, best uses of a particular shipment of crude oil, airline scheduling procedures, where to point the rocket to get to the moon. And that's just a drop in the bucket -- and why are buckets designed the way they are?look for Calculus for the Practical Man, old, but excellent intro.
Regards,
Reilly Atkinson

 

[CPL.Luke]

I remeber my calc 3 course that used thomas had a fair number of physics problems in it.so you could try that book and see what the first few chapters are like, I make no guarentees however because I only used the last third of the book, and only bought the last third.

however you can get the full version which has calc 1-3