4

I had this question? Why do we need integration?

The embedded link doesn't really answer what satisfies my curiosity.

However based on that embedded question, is it worrh just focusing on differentiation and move on to multi-variable differentiation instead of spending more time on integration?

Do we have integrals in multi variable calculus? Is there any practical use of integration?

What is the most important prerequisite for Stochastic calculus?

Can you enlighten me with regards to above set of questions please?

Community
  • 1
aspiring
  • 177
  • 2
    http://math.stackexchange.com/questions/570138/whats-the-deal-with-integration – jimjim Dec 01 '13 at 08:26
  • 3
    I would make the question even simpler. Is there any prectical use of addition ? All physics is based on integrals. How to compute the average of a function on a given interval ? How to compute the trajectory of a mobile from speed and initial location ? What is the chemical potential ? – Claude Leibovici Dec 01 '13 at 08:43
  • 1
    If you want to know the area under a curve such as $\frac{1}{1+x^2}$ would you rather grab a ruler and calculator to measure and add up the area or find the integral (antiderivative of the function) and evaluate it? Plus, the integral symbol is one of the most beautiful symbols in math IMO! – zerosofthezeta Dec 01 '13 at 08:54
  • "One of the most beautiful symbols" agree. In fact until I saw that link in my question, I thought integration was important (although I didn't know why). Now that @claude and zeta pointed out, I will read further to have a better understanding. It is just that I also saw finding anti derivative of certain functions take lots of undetermined coefficients...guess and check... – aspiring Dec 01 '13 at 09:24
  • I just had a course done to cover basics of differentiating. There were lots of prctical scenarios discussed. However in terms of intergrals I am yet to dive in. I should have reserached more reckon... – aspiring Dec 01 '13 at 09:28
  • There was another answer and it is missing. – aspiring Dec 02 '13 at 02:04

2 Answers2

5

Why do we need integration?

In physics, integration crops up pretty much everywhere. Work is the integral of force over a distance, for example. Electric flux is an integral of the electric field over a surface. In other sciences, you might want to compute the area under a curve. (Don't re-invent calculus like this though). In pure math, integrals are used for concepts such as winding numbers and are irreplaceable for results such as the general Stokes' theorem.

However based on that embedded question, is it worrh just focusing on differentiation and move on to multi-variable differentiation instead of spending more time on integration?

No.

Do we have integrals in multi variable calculus? Is there any practical use of integration?

Absolutely. See multiple integral, line integral, surface integral, contour integral (admittedly, a particular type of line integral, but it holds special importance).

What is the most important prerequisite for Stochastic calculus?

Calculus and probability theory (not statistics!)

By the way, is this question motivated by how difficult it is to do integrals vs. the relative easiness of finding derivatives?

Henry Swanson
  • 12,972
  • Thanks. This question was indeed motivated by two things. 1. The guess n check method of finding anti-derivative. 2. While doing I wanted to know why integration is used in reality. So the first article I hit was the above mentioned question and that made me think integration is a useless part. But not anymore :-) I want to vote up everyone here. Let me earn a bit more rep to do so. – aspiring Dec 02 '13 at 02:02
  • Can you share some links or articles about integral usage within stochastic calculus? – aspiring Dec 02 '13 at 02:05
  • 1
    I actually haven't done any stochastic calculus, so I'm afraid I can't be of any help there. As for the guess-and-check method, you'll learn better ways too. (It's still going to be harder than derivatives though) – Henry Swanson Dec 02 '13 at 02:39
3

... is it worth just focusing on differentiation and move on to multi-variable differentiation instead of spending more time on integration?

No, you should learn how to integrate before moving onto multivariate calculus.

Do we have integrals in multi variable calculus?

Yes, http://en.wikipedia.org/wiki/Multiple_integral

Is there any practical use of integration?

Yes. Engineering, physics (for example electric field), almost everything scientific uses integration.

What is the most important prerequisite for Stochastic calculus?

Calculus

Stoof
  • 715
  • I want to vote up everyone here. Let me earn a bit more rep to do so. – aspiring Dec 02 '13 at 02:03
  • Thanks! Let me know if you have any more questions. – Stoof Dec 02 '13 at 05:43
  • I was reading on the topics of slope fields. It is quite hard for me to absorb. And I saw that utilizing intergrals we could easily figure out the slope fields of differentials. I guess it's something along the lines that you guys have pointed out. So I am reading up and working through the anti-derivs now. Hopefully once I cover intergrals perhaps I will have a better understanding on slope fields as well. – aspiring Dec 03 '13 at 10:21