Is Relying on Integral Tables Over Manual Calculation Common in Physics Careers?

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Discussion Overview

The discussion revolves around the reliance on integral tables and computational tools versus manual calculation of integrals in physics careers. Participants explore the implications of using these resources, including the balance between efficiency and understanding, as well as the potential risks of over-reliance on technology.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants express a preference for using integral tables or software like Mathematica to save time, especially for complex integrals.
  • Others argue that understanding the process of integration is crucial, and that relying solely on tools can lead to a lack of comprehension.
  • A few participants mention the importance of being able to recognize correct answers, suggesting that without a solid understanding, one might not notice errors produced by computational tools.
  • There is a suggestion that for new or unfamiliar integrals, manual calculation is still beneficial to grasp the concepts involved.
  • Some participants highlight the risk of becoming overly dependent on technology, which might hinder the development of fundamental skills in integration and problem-solving.
  • Alternative software options, such as Maxima, are discussed as free resources for performing integrals.
  • Participants note that while tools can be helpful, they should not replace the foundational knowledge required to understand the underlying mathematics.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus; instead, multiple competing views remain regarding the use of integral tables and computational tools versus manual calculations. Some advocate for the efficiency of tools, while others emphasize the importance of manual integration for understanding.

Contextual Notes

Participants express varying opinions on the balance between efficiency and understanding, with some acknowledging the potential pitfalls of relying too heavily on technology without a solid grasp of the material.

Who May Find This Useful

This discussion may be of interest to physics students, educators, and professionals who are considering the role of computational tools in their work and the importance of maintaining fundamental skills in mathematics.

dipole
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As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig functions.

What are your thoughts on integrals?
 
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As long as you understand how you would go about solving the particular integrals, and you're not taking a class where you're graded on your ability to solve them by hand, why waste your time? Just look them up in a table or plug them into a program.

The only danger with doing this is when people with little experience with integrals don't know what the right answer should look like, so if the computer gives them a wrong answer they won't be able to recognize it. As long as you understand the process and have a general idea of how the answer should look, I don't see the harm in using programs/tables.
 
I have better things to do than waste time on integrals I've already done before.
 
dipole said:
As time goes by in my physics career I find myself less and less motivated to do integrals by hand and more relying on integral tables to quickly look up the answer. I just find doing integration out by hand tedious, especially ones that require multiple integrations by parts or involve trig functions.

What are your thoughts on integrals?

It is still best to do it if that is the first time you see such integrals.
 
Tables? I just shove them in Mathematica.
 
K^2 said:
Tables? I just shove them in Mathematica.

Is there a free version of Mathematica?

Not a 30-day trial either.
 
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

Wolfram Alpha can do integrals I'm pretty sure. It's just not as easy to type out complex ones. You can probably get mathematica pretty cheap if you attend a university.
 
Sometimes I've needed a general expression rather than a number, so I've had to solve integrals for that.
 
Wolfram Alpha and a few others can do indefinite as well as definite integrals with arbitrary constants. The only trouble is typing the equation out correctly with complex equations...

As for bothering to integrate, I don't if I already know how to integrate the expression, however long it might turn out.

Its always fun to try out new, never-seen-before integrals! :smile:
 
  • #10
Try a calculator that does integrals like HP50g or TI89ti. The 50g has an Equation Writer so you see the expression written out in Pretty Type.
 
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  • #11
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

MMA isn't free but Maxima is.
 
  • #12
Neandethal00 said:
Is there a free version of Mathematica?

Not a 30-day trial either.

Try Maxima, it is a FOSS project and works very well

http://maxima.sourceforge.net/
 
  • #13
  • #14
Neandethal00 said:
Is there a free version of Mathematica?
A lot of universities have free licenses for their students. That's how I got my license. Otherwise, you have to pay or use an alternative program.

You can, indeed, do a lot of things with Wolfram Alpha, but if your integral times out, you are out of luck. For integrals, you can use Mathematica syntax to make sure Alpha doesn't screw up.
 
  • #15
Trouble is that there is a risk of relying on the computer too much, to do your thinking for you. It must be good for people to go through the agony of basic integration and learning how to solve differential equations and not to reach for Mathematica before you even have an idea what it is doing for you.
There's a similar problem with this new generation of students and the reliance on circuit simulation programs rather than using analysis methods even for the simplest problems. (And using calculators to multiply by 100!)
I wouldn't be without computers to help me but I couldn't bring myself to rely entirely on what they tell me. After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.
 
  • #16
sophiecentaur said:
Trouble is that there is a risk of relying on the computer too much, to do your thinking for you. It must be good for people to go through the agony of basic integration and learning how to solve differential equations and not to reach for Mathematica before you even have an idea what it is doing for you.
There's a similar problem with this new generation of students and the reliance on circuit simulation programs rather than using analysis methods even for the simplest problems. (And using calculators to multiply by 100!)
I wouldn't be without computers to help me but I couldn't bring myself to rely entirely on what they tell me. After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.

Yes I agree with this, which is why I prefer not to use Wolfram. At least with a table I may need to manipulate the integral slightly to get it into a desired form, which hopefully will make me more careful. With computers you can be exceptionally lazy.
 
  • #17
sophiecentaur said:
After all, GIGA applies whenever computers are involved. You need to be able to recognise garbage when it comes out.

Wouldn't that be GIGO?
 
  • #18
Yep. I guess that sort of makes my point. Haha.

I guess the "A" could stand for the Essex pronunciation "AAHT"
 
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