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

  • Context: Undergrad 
  • Thread starter Thread starter dipole
  • Start date Start date
  • Tags Tags
    Integrate
Click For Summary
SUMMARY

In the discussion, participants express a growing reliance on integral tables and computational tools like Mathematica and Wolfram Alpha for solving integrals, particularly in professional physics careers. The consensus is that while using these tools can save time, it is crucial to understand the underlying processes to avoid misinterpretation of results. Users caution against over-reliance on technology, emphasizing the importance of foundational knowledge in integration and differential equations. Alternatives like Maxima, a free and open-source software, are recommended for those seeking cost-effective solutions.

PREREQUISITES
  • Understanding of integral calculus and its applications
  • Familiarity with computational tools such as Mathematica and Wolfram Alpha
  • Basic knowledge of free software alternatives like Maxima
  • Experience with mathematical notation and syntax for inputting equations
NEXT STEPS
  • Explore the features and capabilities of Maxima for integral calculations
  • Learn how to effectively use Mathematica for complex integrals
  • Investigate the limitations and best practices for using Wolfram Alpha
  • Study the fundamental principles of integration and differential equations to enhance problem-solving skills
USEFUL FOR

Physics students, educators, and professionals in scientific fields who are looking to optimize their approach to solving integrals and enhance their computational skills.

dipole
Messages
553
Reaction score
149
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?
 
Physics news on Phys.org
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.
 
Last edited:
  • #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"
 
Last edited:

Similar threads

Undergrad In which sense(s) do square integrable functions go to zero at infinity?
  • · Replies 2 ·
Replies
2
Views
3K
Other Considering a career shift and seeking general guidance
  • · Replies 9 ·
Replies
9
Views
2K
What is Baseband RF communication?
  • · Replies 5 ·
Replies
5
Views
2K
Physics Looking to pivot to physics at 31, could use some guidance
  • · Replies 10 ·
Replies
10
Views
4K
Physics Careers in Physics for Equation-Writing Problem-Solvers
  • · Replies 18 ·
Replies
18
Views
4K
Is it possible to switch from physics to maths after undergrad?
  • · Replies 2 ·
Replies
2
Views
2K
Physics Employability with a degree in theoretical physics vs physics
  • · Replies 10 ·
Replies
10
Views
4K
Job Skills [Career] - What kind of life does a career in physics entail?
  • · Replies 2 ·
Replies
2
Views
3K
Other Leveraging engineering B.E. after pivoting to Physics - impossible?
  • · Replies 19 ·
Replies
19
Views
3K
Studying What to do in a gap year to prepare for a Physics + Math degree
  • · Replies 15 ·
Replies
15
Views
3K