Engine of calculus

1. Aug 3, 2007

Substance D

"engine of calculus"

hey

hope this is the correct section, but im just starting to learn differential equations and in our book there is a quote about how differentials are the "engines of calculus". Could someone explain that a bit better to me?

Thanks!

2. Aug 3, 2007

HallsofIvy

Staff Emeritus
Darned if I know what is meant! Certainly, basic calculus concerns itself with two basic concepts- the integral and the derivative. Most modern calculus books start with the derivative and then introduce the integral in terms of the "anti- derivative". Perhaps that is what is meant.

3. Aug 3, 2007

Substance D

but isnt there a sleight difference between derivatives and differentials?

4. Aug 3, 2007

symbolipoint

The word, "engine", might not be the best vocabulary choice; but differentials are an essential detail constituting Calculus. A differential is an infinitessimally small increment.

5. Aug 3, 2007

Substance D

ah, ok I see what you mean. when I hear "engine" I picture the driving force behind something, which is why it didnt make sense to me or I thought I was missing something fundamental to calculus.

6. Aug 3, 2007

z-component

The differential determines which variable is affected by the differentiation and/or integration, so we can say that they are the "engines" for differentiation and integration, I suppose. I've come across this when students in introductory calculus forget to write their differentials, and don't realize how important they are to the problem.

7. Aug 4, 2007

Substance D

by "differentials" it would be like dy = 2x dx (if y = x^2), then dx would be the differential? so whats the difference between that and differential equations, sorry if this sounds like a really confused question. thanks for all the replies

8. Aug 4, 2007

HallsofIvy

Staff Emeritus
If y= x2, then dy/dx= 2x is the "derivative of y with respect to x". In dy= 2xdx, both dx and dy are "differentials". A "differential equation" is an equation that involves either derivatives or differentials of the unknown function.

9. Aug 4, 2007

Substance D

and so when the text asks you to solve the differential equation, you are working with the differentials and going back to get the original function that has those differentials, correct?

10. Aug 4, 2007

Gib Z

Yup :) [ 10 character limit ]

11. Aug 4, 2007

Substance D

perfect!

thanks for all the replies!