Is integration tiresome for you too?

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    Integration
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Discussion Overview

The discussion revolves around the challenges and frustrations associated with integration, particularly in the context of finding Fourier series. Participants express varying opinions on the process, its complexity, and the tools available for performing integrations, including both traditional methods and modern computational approaches.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants find integration to be tedious and mindless, particularly when it involves lengthy calculations like Fourier series.
  • Others suggest alternative methods, such as using Bessel functions, to make the process more engaging.
  • A few participants reflect on their initial dislike for integration, noting that their perspective changed over time as they recognized its utility.
  • There are claims that traditional methods, such as physically measuring areas under curves, can be effective for numerical integration without advanced techniques.
  • Some participants emphasize the importance of the results obtained from integrals rather than the process itself, advocating for the use of computational tools.
  • One participant mentions the historical context of integration, referencing the Riemann hypothesis and its significance in mathematics.
  • Several humorous exchanges occur regarding the terminology and the concept of integration, with some participants making light-hearted jokes about the topic.

Areas of Agreement / Disagreement

Participants express a range of opinions on integration, with some finding it tedious while others appreciate its importance. There is no clear consensus on the best approach to integration or the value of traditional versus modern methods.

Contextual Notes

Some participants highlight the limitations of relying solely on computational tools, suggesting that understanding the underlying mathematics is still valuable. Additionally, there are references to the historical and cultural implications of the term "integration," which may distract from the primary mathematical discussion.

ainster31
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Integration is so mindlessly tiring!

Finding the Fourier series of a function is so long and boring. I don't even get to use my brain to think. Just mindlessly integrating for several pages.

So mind-numbingly boring...
 
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Do it with Bessel functions for a change!
:smile:
 
hmm...now that I think about it, I didn't like integration much at all when I first learned it. I wanted to go back to that awesome differentiation.

That preference didn't last long though. Integration became just another cool tool in my toolbox.
 
there's a reason people compiled integral tables
 
I hate doing it. It's a waste of time if it isn't easy and can't be done in 5 minutes. That's why we have computers and tables. What's more important is the information that an integral spits out.
 
@gravenewworld, it's good you're not trying to be a mathematician or a theoretical physicist or a theoretical engineer. Most work isn't done in 5 minutes... :-D
 
Nah I'm not a theorist, I work in the real world. It's amazing how effective printing out a curve on a piece of paper, cutting it out, and weighing the paper on a scale again is for numerically calculating an integral. No fancy tricks, computer programs, of advanced numerical methods needed :o.

There are curves that have god awful equations. Sure there may be some fancy techniques to describe it as a series or soemthing else, but I don't want to spend a week trying to figure it out. I want to know the AUC and clearance rate of my drug now. Old school tricks can still work very well. I even know some people that have solved 3-D problems by cutting out contour plots and weighing paper.
 
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MathematicalPhysicist said:
@gravenewworld, it's good you're not trying to be a mathematician or a theoretical physicist or a theoretical engineer. Most work isn't done in 5 minutes... :-D
It is hardly the daily work of any professional within these groups to do integrals by hand, computing one Fourier coefficient after the other.
 
arildno said:
It is hardly the daily work of any professional within these groups to do integrals by hand, computing one Fourier coefficient after the other.

Obviously if someone already calculated for you the integral and you believe his calculations to be valid then there is no wrong in using his results.

But if the reference is not trustworthy, buildings may tumble.
 
  • #10
gravenewworld said:
Nah I'm not a theorist, I work in the real world. It's amazing how effective printing out a curve on a piece of paper, cutting it out, and weighing the paper on a scale again is for numerically calculating an integral. No fancy tricks, computer programs, of advanced numerical methods needed :o.

There are curves that have god awful equations. Sure there may be some fancy techniques to describe it as a series or soemthing else, but I don't want to spend a week trying to figure it out. I want to know the AUC and clearance rate of my drug now. Old school tricks can still work very well. I even know some people that have solved 3-D problems by cutting out contour plots and weighing paper.

This is just precious. It sounds like something my dad would do (a smart person, but very technology-averse).

FTR, numerical integration is pretty quick (quicker than cutting out bits of paper), once you get over the initial learning curve. Plus you can integrate over lots of dimensions and in all sorts of fancy coordinate systems. Software like Matlab has lots of pre-loaded scripts for computing integrals, doing Fourier transforms and the like.

Also FTR, I have done plenty of integrals by hand - usually to check simple cases and make sure the script is working-as-intended, before letting the computer attack general problems.

Claude.
 
  • #11
ainster31 said:
Integration is so mindlessly tiring!

Finding the Fourier series of a function is so long and boring. I don't even get to use my brain to think. Just mindlessly integrating for several pages.

So mind-numbingly boring...

Hi,

I'm working on a beautiful contour integral:

https://www.physicsforums.com/showthread.php?t=718609

The beautiful part of it is where the integration path is going: it's traversing, weaving is a better word, through a wonderfully beautiful object called a multi-valued function and if you saw a picture of it, I think you'd agree. But there's much more to it than that through the concept of "analytic continuation", that is, how we can analytically extend the definition of a function beyond the bounds of it's definition. Riemann used analytic continuation to extend the definition of the Euler product and in so doing, invented the zeta function and by association, created currently, the juiciest price in mathematics today: The Riemann hypothesis.
 
  • #12
What's an integral?
 
  • #13
I think it is the part on the inside.
 
  • #14
meBigGuy said:
I think it is the part on the inside.

Yup - don't confuse them with extegrals.
 
  • #15
AlephZero said:
Yup - don't confuse them with extegrals.

:biggrin:
 
  • #16
Back in the 70s when George Wallace was governor of Alabama (US), he opposed integration in the schools.
 
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  • #17
SW VandeCarr said:
Back in the 70s when George Wallace was governor of Alabama (US), he opposed integration in the schools.

That's what differentiated him (from humanity?)
 
  • #18
meBigGuy said:
That's what differentiated him (from humanity?)

Actually he was pro differentiation. He once said "Differentiation now, and differentiation forever!" or something like that. Anyway, he did not like integration. If you talked about integration around him, you'd be in a heap of trouble.
 
  • #19
Sigh. Threads like this one always end up going off on tangents.
 
  • #20
... responsibly suppressing tangent jokes ...

I pretty much use the web to do my integrals, but I sure liked the construction paper idea. Luckily I never had a curve that would cause me to resort to such a tactic, but now it's in my toolbox.
 
  • #21
use the rules like x^n ->x^n+1/n+1. if there is no antiderivative use wolfram oline or better yet download the app
 

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